<description/> <author>Robert Mutel</author> <company/> <keywords/> <revisedBy>Robert Mutel</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>a5d72f4a-cbd2-4b9c-88ad-65d14e28a393</documentID> <versionID>c12f3dea-e61e-42b6-b3eb-dde3ff8d0692</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr 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</results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="true" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="450" page-height="600"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}{\f1\fswiss\fprq15\fcharset0 Arial;}} \viewkind4\uc1\pard\f0\fs18\{n\}\f1 of \{nn\}\f0\par } </left> <center>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qc\f0\fs18\par \f1\par } </center> <right>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18 Saved: \f1\{fd\}\par } </right> </header> <footer use-full-page-width="true"> <center>{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss 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exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1581" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="132" left="12" top="14.25" width="351.75" height="36" align-x="12" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Verification of JAVA Celestial Navigation paper calculation: 3 star solution</inlineAttr> </f> RLM 29 Jan 2004 </text> </region> <region region-id="757" left="456" top="32.25" width="151.5" height="12" align-x="456" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f">JD given y,m,d,ut (Meeus p. 61-62)</c> </text> </region> <region region-id="758" left="468" top="63" width="202.5" height="110.25" align-x="531" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">JD</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">ut</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:localDefine> 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xml:space="preserve">c</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ut</ml:id> <ml:real>24</ml:real> </ml:apply> </ml:apply> <ml:real>13</ml:real> </ml:apply> <ml:real>1524.5</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">jd</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="134" left="12" top="68.25" width="246.75" height="12" align-x="24.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define ancilliary variables, function definitions, constants</inlineAttr> </f> </text> </region> <region region-id="3" left="24" top="92.25" width="96" height="13.5" align-x="56.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="7" left="138" top="92.25" width="94.5" height="13.5" align-x="171" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="11" left="276" top="92.25" width="51.75" height="12" align-x="276" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 11 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<ml:boundVars> <ml:id xml:space="preserve">ζ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ζ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="762" left="186" top="116.25" width="53.25" height="13.5" align-x="198" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">κ</ml:id> <ml:real>1.002738</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="238" left="12" top="158.25" width="154.5" height="12" align-x="12" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> 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</ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="360" left="168" top="194.25" width="109.5" height="12" align-x="174" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to geocentric latitude </text> </region> <region region-id="760" left="444" top="194.25" width="151.5" height="12" align-x="444" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <sp/> <c val="#00f">GMST (radians)<sp count="2"/>at 0h UT (AA B6)</c> </text> </region> <region region-id="759" left="456" top="219" width="239.25" height="204" align-x="517.5" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GST0</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">j</ml:id> <ml:apply> <ml:id xml:space="preserve">JD</ml:id> <ml:sequence> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>2451545.0</ml:real> </ml:apply> <ml:real>36525</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult 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<ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:localDefine> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="358" left="30" top="236.25" width="93.75" height="13.5" align-x="73.5" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="359" left="174" top="236.25" width="69" height="12" align-x="180" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to longitude </text> </region> <region region-id="574" left="6" top="272.25" width="211.5" height="12" align-x="18.75" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define some handy functions at right (GST0, JD)</inlineAttr> </f> </text> </region> <region region-id="764" left="18" top="301.5" width="194.25" height="28.5" align-x="102.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">hh</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">hh</ml:id> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>60</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ss</ml:id> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>12</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="831" left="18" top="349.5" width="284.25" height="28.5" align-x="102.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">dd</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">dd</ml:id> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> <ml:real>60</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">ss</ml:id> </ml:apply> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>180</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1045" left="12" top="386.25" width="193.5" height="12" align-x="13.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Epoch of observation: 19 Feb 2004 at 20 UT</inlineAttr> </f> </text> </region> <region region-id="1046" left="18" top="410.25" width="234" height="13.5" align-x="48" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">GST0</ml:id> <ml:sequence> <ml:real>2004</ml:real> <ml:real>2</ml:real> <ml:real>19</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>20</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1052" left="282" top="410.25" width="77.25" height="13.5" align-x="311.25" align-y="420" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>89.116718450249451</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="1047" left="18" top="440.25" width="96.75" height="13.5" align-x="57.75" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">SHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1048" left="168" top="440.25" width="46.5" height="12" align-x="186" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 1 </text> </region> <region region-id="1049" left="18" top="464.25" width="159.75" height="13.5" align-x="58.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1079" left="198" top="464.25" width="110.25" height="13.5" align-x="223.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1054" left="18" top="488.25" width="60" height="12" align-x="25.5" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Star positions</inlineAttr> </f> </text> </region> <region region-id="1070" left="96" top="489" width="32.25" height="12.75" align-x="104.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1581" left="156" top="488.25" width="177.75" height="24" align-x="156" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Zenith angles derived from test case: </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false">F</inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 35.000N, </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <f family="Symbol" charset="2" size="10"> l </f> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 75.000E</inlineAttr> </f> </text> </region> <region region-id="1066" left="12" top="530.25" width="87.75" height="82.5" align-x="40.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>6</ml:real> <ml:real>45</ml:real> <ml:real>19.08</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>39</ml:real> <ml:real>30.24</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>4</ml:real> <ml:real>36</ml:real> <ml:real>8.52</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>45</ml:real> <ml:real>33.18</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1076" left="126" top="530.25" width="93" height="82.5" align-x="154.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>-16</ml:real> <ml:real>43</ml:real> <ml:real>12.1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:real>12</ml:real> <ml:real>58.8</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>16</ml:real> <ml:real>31</ml:real> <ml:real>6</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>28</ml:real> <ml:real>01</ml:real> <ml:real>5.4</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1077" left="246" top="530.25" width="46.5" height="82.5" align-x="267" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:mult style="default"/> <ml:real>78.83</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>54.22</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>84.64</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>40.90</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1078" left="342" top="528" width="67.5" height="84.75" align-x="350.25" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:str xml:space="preserve">Sirius</ml:str> <ml:str xml:space="preserve">Procyon</ml:str> <ml:str xml:space="preserve">Aldebaran</ml:str> <ml:str xml:space="preserve">Pollux</ml:str> </ml:sequence> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="584" left="12" top="650.25" width="301.5" height="12" align-x="12" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for three stars from Megastar</inlineAttr> </f> </text> </region> <region region-id="1080" left="18" top="681" width="24.75" height="12.75" align-x="30.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1081" left="72" top="681" width="24.75" height="12.75" align-x="84.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1455" left="120" top="681" width="24.75" height="12.75" align-x="132.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i3</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1456" left="6" top="705" width="73.5" height="18" align-x="33.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str 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item-idref="58"/> </region> <region region-id="1563" left="30" top="1070.25" width="90.75" height="13.5" align-x="72.75" align-y="1080" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>34.993347126550567</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="59"/> </region> <region region-id="1580" left="174" top="1083" width="93" height="18" align-x="201.75" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i3</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="1135" left="12" top="1376.25" width="294" height="12" align-x="12" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">sitions, observed zenith angles for first pair of stars from Table1</inlineAttr> </f> </text> </region> <region region-id="1136" left="18" top="1407" width="24.75" height="12.75" align-x="30.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="1137" left="72" top="1407" width="24.75" height="12.75" align-x="84.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="1138" left="120" top="1407" width="73.5" height="18" align-x="147.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Sirius</ml:str> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="1139" left="216" top="1407" width="93" height="18" align-x="243.75" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="1140" left="6" top="1430.25" width="37.5" height="15.75" align-x="22.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="1141" left="72" top="1430.25" width="37.5" height="15.75" align-x="88.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> 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disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="1146" left="12" top="1460.25" width="78" height="15.75" align-x="42" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="1147" left="114" top="1461" width="81.75" height="12.75" align-x="143.25" align-y="1470" 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xml:space="preserve">GHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="1149" left="324" top="1461" width="82.5" height="12.75" align-x="354" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>347.78721845024944</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="74"/> </region> <region region-id="1150" left="12" top="1490.25" width="48.75" height="15.75" align-x="27" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="1151" left="78" top="1490.25" width="62.25" height="13.5" align-x="92.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.212781549750565</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="76"/> </region> <region region-id="1152" left="168" top="1490.25" width="48.75" height="15.75" align-x="183" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="1153" left="240" top="1490.25" width="66.75" height="13.5" align-x="254.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="1154" left="12" top="1520.25" width="149.25" height="12" align-x="12" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1155" left="36" top="1544.25" width="56.25" height="13.5" align-x="51" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="79"/> </region> <region region-id="1156" left="114" top="1544.25" width="56.25" height="13.5" align-x="129" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1157" left="204" top="1544.25" width="57.75" height="13.5" align-x="219.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1158" left="282" top="1544.25" width="57.75" height="13.5" align-x="297.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="1159" left="36" top="1568.25" width="42.75" height="13.5" align-x="51" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1160" left="108" top="1568.25" width="42.75" height="13.5" align-x="123" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1161" left="186" top="1568.25" width="44.25" height="13.5" align-x="201.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1162" left="258" top="1568.25" width="44.25" height="13.5" align-x="273.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1163" left="12" top="1599" width="75.75" height="12.75" align-x="25.5" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1164" left="120" top="1599" width="74.25" height="12.75" align-x="132" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="1165" left="228" top="1604.25" width="51.75" height="12" align-x="228" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1166" left="12" top="1623" width="75.75" height="12.75" align-x="24" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1167" left="120" top="1623" width="73.5" height="12.75" 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<ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1169" left="120" top="1647" width="73.5" height="12.75" align-x="131.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1170" left="12" top="1676.25" width="71.25" height="27.75" align-x="39" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1171" left="114" top="1676.25" width="72.75" height="27.75" align-x="141" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1172" left="222" top="1682.25" width="65.25" height="12" align-x="222" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1173" left="12" top="1706.25" 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xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="1201" left="90" top="2054.25" width="37.5" height="15.75" align-x="106.5" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="118"/> </region> <region region-id="1202" left="156" top="2054.25" width="33" height="15.75" align-x="170.25" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">δ1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="1203" left="210" top="2054.25" width="33" height="15.75" align-x="224.25" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">δ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="120"/> </region> <region region-id="1204" left="264" top="2054.25" width="33" height="15.75" align-x="278.25" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="121"/> </region> <region region-id="1205" left="324" top="2054.25" width="33" height="15.75" align-x="338.25" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="1206" left="30" top="2084.25" width="78" height="15.75" align-x="60" align-y="2094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="1207" left="132" top="2085" width="81.75" height="12.75" align-x="161.25" align-y="2094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.6705</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="124"/> </region> <region region-id="1208" left="240" top="2084.25" width="79.5" height="15.75" align-x="270.75" align-y="2094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="1209" left="342" top="2085" width="82.5" height="12.75" align-x="372" align-y="2094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>347.78721845024944</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="126"/> </region> <region region-id="1210" left="30" top="2114.25" width="48.75" height="15.75" align-x="45" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="127"/> </region> <region region-id="1211" left="96" top="2114.25" width="62.25" height="13.5" align-x="110.25" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.212781549750565</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="128"/> </region> <region region-id="1212" left="186" top="2114.25" width="48.75" height="15.75" align-x="201" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="129"/> </region> <region region-id="1213" left="258" top="2114.25" width="62.25" height="13.5" align-x="272.25" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>27.271531549750538</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1214" left="30" top="2144.25" width="149.25" height="12" align-x="30" align-y="2154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1215" left="54" top="2168.25" width="56.25" height="13.5" align-x="69" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="131"/> </region> <region region-id="1216" left="132" top="2168.25" width="56.25" height="13.5" align-x="147" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="132"/> </region> <region region-id="1217" left="222" top="2168.25" width="57.75" height="13.5" align-x="237.75" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="133"/> </region> <region region-id="1218" left="300" top="2168.25" width="57.75" height="13.5" align-x="315.75" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="134"/> </region> <region region-id="1219" left="54" top="2192.25" width="42.75" height="13.5" align-x="69" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="135"/> </region> <region region-id="1220" left="126" top="2192.25" width="42.75" height="13.5" align-x="141" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="136"/> </region> <region region-id="1221" left="204" top="2192.25" width="44.25" height="13.5" align-x="219.75" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="1222" left="276" top="2192.25" width="44.25" height="13.5" align-x="291.75" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="138"/> </region> <region region-id="1223" left="30" top="2223" width="75.75" height="12.75" align-x="43.5" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="139"/> </region> <region region-id="1224" left="138" top="2223" width="74.25" height="12.75" align-x="150" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="140"/> </region> <region region-id="1225" left="246" top="2228.25" width="51.75" height="12" align-x="246" align-y="2238" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1226" left="30" top="2247" width="75.75" height="12.75" align-x="42" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="141"/> </region> <region region-id="1227" left="138" top="2247" width="73.5" height="12.75" align-x="150.75" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="142"/> </region> <region region-id="1228" left="30" top="2271" width="73.5" height="12.75" align-x="41.25" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="143"/> </region> <region region-id="1229" left="138" top="2271" width="73.5" height="12.75" align-x="149.25" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="144"/> </region> <region region-id="1230" left="30" top="2300.25" width="71.25" height="27.75" align-x="57" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="145"/> </region> <region region-id="1231" left="132" top="2300.25" width="72.75" height="27.75" align-x="159" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="146"/> </region> <region region-id="1232" left="240" top="2306.25" width="65.25" height="12" align-x="240" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1233" left="30" top="2330.25" width="60.75" height="12" align-x="30" align-y="2340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1234" left="36" top="2355" width="25.5" height="12.75" align-x="49.5" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="147"/> </region> <region region-id="1235" left="84" top="2354.25" width="40.5" height="12" align-x="84" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1236" left="156" top="2355" width="24" height="12.75" align-x="167.25" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="148"/> </region> <region region-id="1237" left="204" top="2349" width="103.5" height="18.75" align-x="296.25" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> 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show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>25.759281549750536</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="180"/> </region> <region region-id="1272" left="174" top="2726.25" width="48.75" height="15.75" align-x="189" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="181"/> </region> <region region-id="1273" left="246" top="2726.25" width="66.75" height="13.5" align-x="260.25" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="182"/> </region> <region region-id="1274" left="18" top="2756.25" width="149.25" height="12" align-x="18" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1275" left="42" top="2780.25" width="56.25" height="13.5" align-x="57" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="183"/> </region> <region region-id="1276" left="120" top="2780.25" width="56.25" height="13.5" align-x="135" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="184"/> </region> <region region-id="1277" left="210" top="2780.25" width="57.75" height="13.5" align-x="225.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="1278" left="288" top="2780.25" width="57.75" height="13.5" align-x="303.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="186"/> </region> <region region-id="1279" left="42" top="2804.25" width="42.75" height="13.5" align-x="57" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="187"/> </region> <region region-id="1280" left="114" top="2804.25" width="42.75" height="13.5" align-x="129" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="188"/> </region> <region region-id="1281" left="192" top="2804.25" width="44.25" height="13.5" align-x="207.75" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="1282" left="264" top="2804.25" width="44.25" height="13.5" align-x="279.75" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="190"/> </region> <region region-id="1283" left="18" top="2835" width="75.75" height="12.75" align-x="31.5" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="191"/> </region> <region region-id="1284" left="126" top="2835" width="74.25" height="12.75" align-x="138" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="192"/> </region> <region region-id="1285" left="234" top="2840.25" width="51.75" height="12" align-x="234" align-y="2850" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1286" left="18" top="2859" width="75.75" height="12.75" align-x="30" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="1287" left="126" top="2859" width="73.5" height="12.75" align-x="138.75" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="1288" left="18" top="2883" width="73.5" height="12.75" align-x="29.25" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="195"/> </region> <region region-id="1289" left="126" top="2883" width="73.5" height="12.75" align-x="137.25" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="196"/> </region> <region region-id="1290" left="18" top="2912.25" width="71.25" height="27.75" align-x="45" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="197"/> </region> <region region-id="1291" left="120" top="2912.25" width="72.75" height="27.75" align-x="147" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="198"/> </region> <region region-id="1292" left="228" top="2918.25" width="65.25" height="12" align-x="228" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1293" left="18" top="2942.25" width="60.75" height="12" align-x="18" align-y="2952" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1294" left="24" top="2967" width="25.5" height="12.75" align-x="37.5" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="199"/> </region> <region region-id="1295" left="72" top="2966.25" width="40.5" height="12" align-x="72" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1296" left="144" top="2967" width="24" height="12.75" align-x="155.25" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="200"/> </region> <region region-id="1297" left="192" top="2961" width="103.5" height="18.75" align-x="284.25" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="201"/> </region> <region region-id="1298" left="12" top="2997" width="54.75" height="12.75" align-x="26.25" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="202"/> </region> <region region-id="1299" left="84" top="2997" width="45" height="12.75" align-x="99.75" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="203"/> </region> <region region-id="1300" left="150" top="2997" width="43.5" height="12.75" align-x="164.25" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="204"/> </region> <region region-id="1301" left="24" top="3020.25" width="75.75" height="12" align-x="39" align-y="3030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1302" left="12" top="3045" width="25.5" height="12.75" align-x="25.5" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="205"/> </region> <region region-id="1303" left="60" top="3044.25" width="40.5" height="12" align-x="60" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1304" left="132" top="3045" width="24" height="12.75" align-x="143.25" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="206"/> </region> <region region-id="1305" left="180" top="3039" width="103.5" height="18.75" align-x="272.25" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="207"/> </region> <region region-id="1306" left="12" top="3069" width="54.75" height="12.75" align-x="26.25" 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equations</inlineAttr> </f> </text> </region> <region region-id="1335" left="48" top="3398.25" width="56.25" height="13.5" align-x="63" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="235"/> </region> <region region-id="1336" left="126" top="3398.25" width="56.25" height="13.5" align-x="141" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> 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z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="238"/> </region> <region region-id="1339" left="48" top="3422.25" width="42.75" height="13.5" align-x="63" align-y="3432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="239"/> </region> <region region-id="1340" left="120" top="3422.25" width="42.75" height="13.5" align-x="135" align-y="3432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="240"/> </region> <region region-id="1341" left="198" top="3422.25" width="44.25" height="13.5" align-x="213.75" align-y="3432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="241"/> </region> <region region-id="1342" left="270" top="3422.25" width="44.25" height="13.5" align-x="285.75" align-y="3432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="242"/> </region> <region region-id="1343" left="24" top="3453" width="75.75" height="12.75" align-x="37.5" align-y="3462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="243"/> </region> <region region-id="1344" left="132" top="3453" width="74.25" height="12.75" align-x="144" align-y="3462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="244"/> </region> <region region-id="1345" left="240" top="3458.25" width="51.75" height="12" align-x="240" align-y="3468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1346" left="24" top="3477" width="75.75" height="12.75" align-x="36" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="245"/> </region> <region region-id="1347" left="132" top="3477" width="73.5" height="12.75" align-x="144.75" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="246"/> </region> <region region-id="1348" left="24" top="3501" width="73.5" height="12.75" align-x="35.25" align-y="3510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="247"/> </region> <region region-id="1349" left="132" top="3501" width="73.5" height="12.75" align-x="143.25" align-y="3510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="248"/> </region> <region region-id="1350" left="24" top="3530.25" width="71.25" height="27.75" align-x="51" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="249"/> </region> <region region-id="1351" left="126" top="3530.25" width="72.75" height="27.75" align-x="153" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="250"/> </region> <region region-id="1352" left="234" top="3536.25" width="65.25" height="12" align-x="234" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1353" left="24" top="3560.25" width="60.75" height="12" align-x="24" align-y="3570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1354" left="30" top="3585" width="25.5" height="12.75" align-x="43.5" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="251"/> </region> <region region-id="1355" left="78" top="3584.25" width="40.5" height="12" align-x="78" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1356" left="150" top="3585" width="24" height="12.75" align-x="161.25" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="252"/> </region> <region region-id="1357" left="198" top="3579" width="103.5" height="18.75" align-x="290.25" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="253"/> </region> <region region-id="1358" left="18" top="3615" width="54.75" height="12.75" align-x="32.25" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="254"/> </region> <region region-id="1359" left="90" top="3615" width="45" height="12.75" align-x="105.75" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="255"/> </region> <region region-id="1360" left="156" top="3615" width="43.5" height="12.75" align-x="170.25" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="256"/> </region> <region region-id="1361" left="30" top="3638.25" width="75.75" height="12" align-x="45" align-y="3648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1362" left="18" top="3663" width="25.5" height="12.75" align-x="31.5" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="257"/> </region> <region region-id="1363" left="66" top="3662.25" width="40.5" height="12" align-x="66" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1364" left="138" top="3663" width="24" height="12.75" align-x="149.25" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="258"/> </region> <region region-id="1365" left="186" top="3657" width="103.5" height="18.75" align-x="278.25" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="259"/> </region> <region region-id="1366" left="18" top="3687" width="54.75" height="12.75" align-x="32.25" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="260"/> </region> <region region-id="1367" left="90" top="3687" width="45" height="12.75" align-x="105.75" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="261"/> </region> <region region-id="1368" left="156" top="3687" width="43.5" height="12.75" align-x="170.25" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="262"/> </region> <region region-id="1369" left="18" top="3722.25" width="109.5" height="13.5" align-x="74.25" align-y="3732" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Λ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">z1</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>-20.56536321475458</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="263"/> </region> <region region-id="1370" left="150" top="3722.25" width="104.25" height="13.5" align-x="206.25" align-y="3732" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Λ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>75.001428275672467</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="264"/> </region> <region region-id="1371" left="294" top="3723" width="84.75" height="18" align-x="321.75" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Procyon</ml:str> </result> </ml:eval> </math> <rendering item-idref="265"/> </region> <region region-id="1372" left="294" top="3741" width="75" height="18" align-x="321.75" align-y="3750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Pollux</ml:str> </result> </ml:eval> </math> <rendering item-idref="266"/> </region> <region region-id="1373" left="18" top="3746.25" width="99.75" height="13.5" align-x="74.25" align-y="3756" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">z1</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>40.089546641206653</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="267"/> </region> <region region-id="1374" left="150" top="3746.25" width="99.75" height="13.5" align-x="206.25" align-y="3756" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>35.010105477637019</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="268"/> </region> <region region-id="1375" left="24" top="3854.25" width="317.25" height="12" align-x="24" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for first pair of stars from Table1</inlineAttr> </f> </text> </region> <region region-id="1376" left="30" top="3885" width="24.75" height="12.75" align-x="42.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="269"/> </region> <region region-id="1377" left="84" top="3885" width="24.75" height="12.75" align-x="96.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="270"/> </region> <region region-id="1378" left="132" top="3885" width="93" height="18" align-x="159.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="271"/> </region> <region region-id="1379" left="228" top="3885" width="75" height="18" align-x="255.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Pollux</ml:str> </result> </ml:eval> </math> <rendering item-idref="272"/> </region> <region region-id="1380" left="18" top="3908.25" width="37.5" height="15.75" align-x="34.5" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="273"/> </region> <region region-id="1381" left="84" top="3908.25" width="37.5" height="15.75" align-x="100.5" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="274"/> </region> <region region-id="1382" left="150" top="3908.25" width="33" height="15.75" align-x="164.25" align-y="3918" show-border="false" show-highlight="false" is-protected="true" 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height="12.75" align-x="366" align-y="3948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>20.081218450249452</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="282"/> </region> <region region-id="1390" left="24" top="3968.25" width="48.75" height="15.75" align-x="39" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="283"/> </region> <region region-id="1391" left="90" top="3968.25" width="66.75" height="13.5" align-x="104.25" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="284"/> </region> <region region-id="1392" left="180" top="3968.25" width="48.75" height="15.75" align-x="195" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="285"/> </region> <region region-id="1393" left="252" top="3968.25" width="62.25" height="13.5" align-x="266.25" align-y="3978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>27.271531549750538</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="286"/> </region> <region region-id="1394" left="24" top="3998.25" width="149.25" height="12" align-x="24" align-y="4008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1395" left="48" top="4022.25" width="56.25" height="13.5" align-x="63" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="287"/> </region> <region region-id="1396" left="126" top="4022.25" width="56.25" height="13.5" align-x="141" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="288"/> </region> <region region-id="1397" left="216" top="4022.25" width="57.75" height="13.5" align-x="231.75" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="289"/> </region> <region region-id="1398" left="294" top="4022.25" width="57.75" height="13.5" align-x="309.75" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="290"/> </region> <region region-id="1399" left="48" top="4046.25" width="42.75" height="13.5" align-x="63" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="291"/> </region> <region region-id="1400" left="120" top="4046.25" width="42.75" height="13.5" align-x="135" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="292"/> </region> <region region-id="1401" left="198" top="4046.25" width="44.25" height="13.5" align-x="213.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="293"/> </region> <region region-id="1402" left="270" top="4046.25" width="44.25" height="13.5" align-x="285.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="294"/> </region> <region region-id="1403" left="24" top="4077" width="75.75" height="12.75" align-x="37.5" align-y="4086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="295"/> </region> <region region-id="1404" left="132" top="4077" width="74.25" height="12.75" align-x="144" align-y="4086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="296"/> </region> <region region-id="1405" left="240" top="4082.25" width="51.75" height="12" align-x="240" align-y="4092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1406" left="24" top="4101" width="75.75" height="12.75" align-x="36" align-y="4110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="297"/> </region> <region region-id="1407" left="132" top="4101" width="73.5" height="12.75" align-x="144.75" align-y="4110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="298"/> </region> <region region-id="1408" left="24" top="4125" width="73.5" height="12.75" align-x="35.25" align-y="4134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="299"/> </region> <region region-id="1409" left="132" top="4125" width="73.5" height="12.75" align-x="143.25" align-y="4134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="300"/> </region> <region region-id="1410" left="24" top="4154.25" width="71.25" height="27.75" align-x="51" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="301"/> </region> <region region-id="1411" left="126" top="4154.25" width="72.75" height="27.75" align-x="153" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="302"/> </region> <region region-id="1412" left="234" top="4160.25" width="65.25" height="12" align-x="234" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1413" left="24" top="4184.25" width="60.75" height="12" align-x="24" align-y="4194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1414" left="30" top="4209" width="25.5" height="12.75" align-x="43.5" align-y="4218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="303"/> </region> <region region-id="1415" left="78" top="4208.25" width="40.5" height="12" align-x="78" align-y="4218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1416" left="150" top="4209" width="24" height="12.75" 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xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="305"/> </region> <region region-id="1418" left="18" top="4239" width="54.75" height="12.75" align-x="32.25" align-y="4248" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="306"/> </region> <region region-id="1419" left="90" top="4239" width="45" height="12.75" align-x="105.75" align-y="4248" show-border="false" 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push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1424" left="138" top="4287" width="24" height="12.75" align-x="149.25" align-y="4296" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="310"/> </region> <region region-id="1425" left="186" top="4281" width="103.5" height="18.75" align-x="278.25" align-y="4296" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="311"/> </region> <region region-id="1426" left="18" top="4311" width="54.75" height="12.75" align-x="32.25" align-y="4320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="312"/> </region> <region 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font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3" imaginary-value="i" zero-threshold="15"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="true" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="450" page-height="600"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}{\f1\fswiss\fprq15\fcharset0 Arial;}} \viewkind4\uc1\pard\f0\fs18\{n\}\f1 of \{nn\}\f0\par } </left> <center>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qc\f0\fs18\par \f1\par } </center> <right>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18 Saved: \f1\{fd\}\par } </right> </header> <footer use-full-page-width="true"> <center>{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss Arial;}} \viewkind4\uc1\pard\qc\f0\fs20\{p\}\{f\}\par } </center> </footer> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="EN" UI="EN"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1581" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="132" left="12" top="14.25" width="351.75" height="36" align-x="12" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Verification of JAVA Celestial Navigation paper calculation: 3 star solution</inlineAttr> </f> RLM 29 Jan 2004 </text> </region> <region region-id="757" left="456" top="32.25" width="151.5" height="12" align-x="456" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#00f">JD given y,m,d,ut (Meeus p. 61-62)</c> </text> </region> <region region-id="758" left="468" top="63" width="202.5" height="110.25" align-x="531" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">JD</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:id xml:space="preserve">ut</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">m</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>12</ml:real> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:localDefine> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>365.25</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">y</ml:id> <ml:real>4716</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>30.6001</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ut</ml:id> <ml:real>24</ml:real> </ml:apply> </ml:apply> <ml:real>13</ml:real> </ml:apply> <ml:real>1524.5</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">jd</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="134" left="12" top="68.25" width="246.75" height="12" align-x="24.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define ancilliary variables, function definitions, constants</inlineAttr> </f> </text> </region> <region region-id="3" left="24" top="92.25" width="96" height="13.5" align-x="56.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="7" left="138" top="92.25" width="94.5" height="13.5" align-x="171" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">b</ml:id> <ml:boundVars> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="11" left="276" top="92.25" width="51.75" height="12" align-x="276" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 11 </text> </region> <region region-id="135" left="24" top="116.25" width="54" height="13.5" align-x="46.5" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">c</ml:id> <ml:boundVars> <ml:id xml:space="preserve">δ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:id xml:space="preserve">δ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="136" left="102" top="116.25" width="57" height="13.5" align-x="125.25" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ζ</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ζ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="762" left="186" top="116.25" width="53.25" height="13.5" align-x="198" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">κ</ml:id> <ml:real>1.002738</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="238" left="12" top="158.25" width="154.5" height="12" align-x="12" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define xyz -> long-lat<sp count="2"/>(not in paper)</inlineAttr> </f> </text> </region> <region region-id="246" left="24" top="182.25" width="127.5" height="39.75" align-x="67.5" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Φ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">z</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">y</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="360" left="168" top="194.25" width="109.5" height="12" align-x="174" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to geocentric latitude </text> </region> <region region-id="760" left="444" top="194.25" width="151.5" height="12" align-x="444" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <sp/> <c val="#00f">GMST (radians)<sp count="2"/>at 0h UT (AA B6)</c> </text> </region> <region region-id="759" left="456" top="219" width="239.25" height="204" align-x="517.5" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GST0</ml:id> <ml:boundVars> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">j</ml:id> <ml:apply> <ml:id xml:space="preserve">JD</ml:id> <ml:sequence> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">d</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>2451545.0</ml:real> </ml:apply> <ml:real>36525</ml:real> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>24110.54841</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>8640184.812886</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0.093104</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>6.2</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:localDefine> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:localDefine> </ml:ifThen> <ml:localDefine> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">gst</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>86400</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="358" left="30" top="236.25" width="93.75" height="13.5" align-x="73.5" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">atan2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="359" left="174" top="236.25" width="69" height="12" align-x="180" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> xyz to longitude </text> </region> <region region-id="574" left="6" top="272.25" width="211.5" height="12" align-x="18.75" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Define some handy functions at right (GST0, JD)</inlineAttr> </f> </text> </region> <region region-id="764" left="18" top="301.5" width="194.25" height="28.5" align-x="102.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">hh</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">hh</ml:id> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mm</ml:id> <ml:real>60</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ss</ml:id> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>12</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="831" left="18" top="349.5" width="284.25" height="28.5" align-x="102.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:boundVars> <ml:id xml:space="preserve">dd</ml:id> <ml:id xml:space="preserve">mm</ml:id> <ml:id xml:space="preserve">ss</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:id xml:space="preserve">dd</ml:id> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">mm</ml:id> </ml:apply> <ml:real>60</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">sign</ml:id> <ml:id xml:space="preserve">dd</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve">ss</ml:id> </ml:apply> <ml:real>3600</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>180</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1045" left="12" top="386.25" width="193.5" height="12" align-x="13.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Epoch of observation: 19 Feb 2004 at 20 UT</inlineAttr> </f> </text> </region> <region region-id="1046" left="18" top="410.25" width="234" height="13.5" align-x="48" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">GST0</ml:id> <ml:sequence> <ml:real>2004</ml:real> <ml:real>2</ml:real> <ml:real>19</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>20</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">κ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1052" left="282" top="410.25" width="77.25" height="13.5" align-x="311.25" align-y="420" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>89.116718450249451</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="1047" left="18" top="440.25" width="96.75" height="13.5" align-x="57.75" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">SHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1048" left="168" top="440.25" width="46.5" height="12" align-x="186" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 1 </text> </region> <region region-id="1049" left="18" top="464.25" width="159.75" height="13.5" align-x="58.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">GHA</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">mod</ml:id> <ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">GHAγ</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1079" left="198" top="464.25" width="110.25" height="13.5" align-x="223.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">λ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1054" left="18" top="488.25" width="60" height="12" align-x="25.5" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Star positions</inlineAttr> </f> </text> </region> <region region-id="1070" left="96" top="489" width="32.25" height="12.75" align-x="104.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1581" left="156" top="488.25" width="177.75" height="24" align-x="156" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Zenith angles derived from test case: </inlineAttr> </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-style="normal" underline="false" line-through="false">F</inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 35.000N, </inlineAttr> </f> <inlineAttr font-style="normal" underline="false" line-through="false"> <f family="Symbol" charset="2" size="10"> l </f> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> = 75.000E</inlineAttr> </f> </text> </region> <region region-id="1066" left="12" top="530.25" width="87.75" height="82.5" align-x="40.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>6</ml:real> <ml:real>45</ml:real> <ml:real>19.08</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>39</ml:real> <ml:real>30.24</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>4</ml:real> <ml:real>36</ml:real> <ml:real>8.52</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hmsrad</ml:id> <ml:sequence> <ml:real>7</ml:real> <ml:real>45</ml:real> <ml:real>33.18</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1076" left="126" top="530.25" width="93" height="82.5" align-x="154.5" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>-16</ml:real> <ml:real>43</ml:real> <ml:real>12.1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>5</ml:real> <ml:real>12</ml:real> <ml:real>58.8</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>16</ml:real> <ml:real>31</ml:real> <ml:real>6</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">dmsrad</ml:id> <ml:sequence> <ml:real>28</ml:real> <ml:real>01</ml:real> <ml:real>5.4</ml:real> </ml:sequence> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1077" left="246" top="530.25" width="46.5" height="82.5" align-x="267" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:mult style="default"/> <ml:real>78.83</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>54.22</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>84.64</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>40.90</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1078" left="342" top="528" width="67.5" height="84.75" align-x="350.25" align-y="546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:sequence> <ml:str xml:space="preserve">Sirius</ml:str> <ml:str xml:space="preserve">Procyon</ml:str> <ml:str xml:space="preserve">Aldebaran</ml:str> <ml:str xml:space="preserve">Pollux</ml:str> </ml:sequence> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="584" left="12" top="650.25" width="301.5" height="12" align-x="12" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for three stars from Megastar</inlineAttr> </f> </text> </region> <region region-id="1080" left="18" top="681" width="24.75" height="12.75" align-x="30.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1081" left="72" top="681" width="24.75" height="12.75" align-x="84.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1455" left="120" top="681" width="24.75" height="12.75" align-x="132.75" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i3</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1456" left="6" top="705" width="73.5" height="18" align-x="33.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Sirius</ml:str> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="1457" left="102" top="705" width="84.75" height="18" align-x="129.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Procyon</ml:str> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="1458" left="210" top="705" width="93" height="18" align-x="237.75" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i3</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="1504" left="6" top="728.25" width="37.5" height="15.75" align-x="22.5" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1500" left="72" top="728.25" width="37.5" height="15.75" align-x="88.5" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="1496" left="138" top="728.25" width="37.5" height="15.75" align-x="154.5" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α3</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i3</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="1503" left="6" top="746.25" width="33" height="15.75" align-x="20.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">δ1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1499" left="72" top="746.25" width="33" height="15.75" align-x="86.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">δ2</ml:id> <ml:apply> <ml:indexer/> <ml:id 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z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">δ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">δ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="1144" left="246" top="1430.25" width="33" height="15.75" align-x="260.25" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="1145" left="306" top="1430.25" width="33" height="15.75" align-x="320.25" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ζ2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ζ</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="1146" left="12" top="1460.25" width="78" height="15.75" align-x="42" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">SHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="1147" left="114" top="1461" width="81.75" height="12.75" align-x="143.25" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.6705</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="72"/> </region> <region region-id="1148" left="222" top="1460.25" width="79.5" height="15.75" align-x="252.75" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:apply> <ml:id xml:space="preserve">GHA</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="1149" left="324" top="1461" width="82.5" height="12.75" align-x="354" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">GHA1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>347.78721845024944</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="74"/> </region> <region region-id="1150" left="12" top="1490.25" width="48.75" height="15.75" align-x="27" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="1151" left="78" top="1490.25" width="62.25" height="13.5" align-x="92.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.212781549750565</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="76"/> </region> <region region-id="1152" left="168" top="1490.25" width="48.75" height="15.75" align-x="183" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="1153" left="240" top="1490.25" width="66.75" height="13.5" align-x="254.25" align-y="1500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="78"/> </region> <region region-id="1154" left="12" top="1520.25" width="149.25" height="12" align-x="12" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1155" left="36" top="1544.25" width="56.25" height="13.5" align-x="51" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="79"/> </region> <region region-id="1156" left="114" top="1544.25" width="56.25" height="13.5" align-x="129" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="1157" left="204" top="1544.25" width="57.75" height="13.5" align-x="219.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="1158" left="282" top="1544.25" width="57.75" height="13.5" align-x="297.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="1159" left="36" top="1568.25" width="42.75" height="13.5" align-x="51" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="83"/> </region> <region region-id="1160" left="108" top="1568.25" width="42.75" height="13.5" align-x="123" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="1161" left="186" top="1568.25" width="44.25" height="13.5" align-x="201.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="1162" left="258" top="1568.25" width="44.25" height="13.5" align-x="273.75" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="1163" left="12" top="1599" width="75.75" height="12.75" align-x="25.5" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="1164" left="120" top="1599" width="74.25" height="12.75" align-x="132" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="1165" left="228" top="1604.25" width="51.75" height="12" align-x="228" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1166" left="12" top="1623" width="75.75" height="12.75" align-x="24" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="1167" left="120" top="1623" width="73.5" height="12.75" align-x="132.75" align-y="1632" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="90"/> </region> <region region-id="1168" left="12" top="1647" width="73.5" height="12.75" align-x="23.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1169" left="120" top="1647" width="73.5" height="12.75" align-x="131.25" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1170" left="12" top="1676.25" width="71.25" height="27.75" align-x="39" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="1171" left="114" top="1676.25" width="72.75" height="27.75" align-x="141" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1172" left="222" top="1682.25" width="65.25" height="12" align-x="222" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1173" left="12" top="1706.25" width="60.75" height="12" align-x="12" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1174" left="18" top="1731" width="25.5" height="12.75" align-x="31.5" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1175" left="66" top="1730.25" width="40.5" height="12" align-x="66" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1176" left="138" top="1731" width="24" height="12.75" align-x="149.25" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="96"/> </region> <region region-id="1177" left="186" top="1725" width="103.5" height="18.75" align-x="278.25" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="127"/> </region> <region region-id="1211" left="96" top="2114.25" width="62.25" height="13.5" align-x="110.25" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.212781549750565</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="128"/> </region> <region region-id="1212" left="186" top="2114.25" width="48.75" height="15.75" align-x="201" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:apply> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="129"/> </region> <region region-id="1213" left="258" top="2114.25" width="62.25" height="13.5" align-x="272.25" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>27.271531549750538</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1214" left="30" top="2144.25" width="149.25" height="12" align-x="30" align-y="2154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1215" left="54" top="2168.25" width="56.25" height="13.5" align-x="69" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="131"/> </region> <region region-id="1216" left="132" top="2168.25" width="56.25" height="13.5" align-x="147" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="132"/> </region> <region region-id="1217" left="222" top="2168.25" width="57.75" height="13.5" align-x="237.75" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="133"/> </region> <region region-id="1218" left="300" top="2168.25" width="57.75" height="13.5" align-x="315.75" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="134"/> </region> <region region-id="1219" left="54" top="2192.25" width="42.75" height="13.5" align-x="69" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="135"/> </region> <region region-id="1220" left="126" top="2192.25" width="42.75" height="13.5" align-x="141" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="136"/> </region> <region region-id="1221" left="204" top="2192.25" width="44.25" height="13.5" align-x="219.75" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="137"/> </region> <region region-id="1222" left="276" top="2192.25" width="44.25" height="13.5" align-x="291.75" align-y="2202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="138"/> </region> <region region-id="1223" left="30" top="2223" width="75.75" height="12.75" align-x="43.5" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="139"/> </region> <region region-id="1224" left="138" top="2223" width="74.25" height="12.75" align-x="150" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="140"/> </region> <region region-id="1225" left="246" top="2228.25" width="51.75" height="12" align-x="246" align-y="2238" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1226" left="30" top="2247" width="75.75" height="12.75" align-x="42" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="141"/> </region> <region region-id="1227" left="138" top="2247" width="73.5" height="12.75" align-x="150.75" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="142"/> </region> <region region-id="1228" left="30" top="2271" width="73.5" height="12.75" align-x="41.25" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="143"/> </region> <region region-id="1229" left="138" top="2271" width="73.5" height="12.75" align-x="149.25" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="144"/> </region> <region region-id="1230" left="30" top="2300.25" width="71.25" height="27.75" align-x="57" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="145"/> </region> <region region-id="1231" left="132" top="2300.25" width="72.75" height="27.75" align-x="159" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="146"/> </region> <region region-id="1232" left="240" top="2306.25" width="65.25" height="12" align-x="240" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1233" left="30" top="2330.25" width="60.75" height="12" align-x="30" align-y="2340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1234" left="36" top="2355" width="25.5" height="12.75" align-x="49.5" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="147"/> </region> <region region-id="1235" left="84" top="2354.25" width="40.5" height="12" align-x="84" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1236" left="156" top="2355" width="24" height="12.75" align-x="167.25" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="148"/> </region> <region region-id="1237" left="204" top="2349" width="103.5" height="18.75" align-x="296.25" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="149"/> </region> <region region-id="1238" left="24" top="2385" width="54.75" height="12.75" align-x="38.25" align-y="2394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="150"/> </region> <region region-id="1239" left="96" top="2385" width="45" height="12.75" align-x="111.75" align-y="2394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="151"/> </region> <region region-id="1240" left="162" top="2385" width="43.5" height="12.75" align-x="176.25" align-y="2394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="152"/> </region> <region region-id="1241" left="36" top="2408.25" width="75.75" height="12" align-x="51" align-y="2418" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1242" left="24" top="2433" width="25.5" height="12.75" align-x="37.5" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="153"/> </region> <region region-id="1243" left="72" top="2432.25" width="40.5" height="12" align-x="72" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1244" left="144" top="2433" width="24" height="12.75" align-x="155.25" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="154"/> </region> <region region-id="1245" left="192" top="2427" width="103.5" height="18.75" align-x="284.25" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id 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<ml:real>339.91878154975052</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="182"/> </region> <region region-id="1274" left="18" top="2756.25" width="149.25" height="12" align-x="18" align-y="2766" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1275" left="42" top="2780.25" width="56.25" height="13.5" align-x="57" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="183"/> </region> <region region-id="1276" left="120" top="2780.25" width="56.25" height="13.5" align-x="135" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="184"/> </region> <region region-id="1277" left="210" top="2780.25" width="57.75" height="13.5" align-x="225.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b1</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="1278" left="288" top="2780.25" width="57.75" height="13.5" align-x="303.75" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b2</ml:id> <ml:apply> <ml:id xml:space="preserve">b</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ2</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="186"/> </region> <region region-id="1279" left="42" top="2804.25" width="42.75" height="13.5" align-x="57" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c1</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="187"/> </region> <region region-id="1280" left="114" top="2804.25" width="42.75" height="13.5" align-x="129" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="188"/> </region> <region region-id="1281" left="192" top="2804.25" width="44.25" height="13.5" align-x="207.75" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="1282" left="264" top="2804.25" width="44.25" height="13.5" align-x="279.75" align-y="2814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="190"/> </region> <region region-id="1283" left="18" top="2835" width="75.75" height="12.75" align-x="31.5" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="191"/> </region> <region region-id="1284" left="126" top="2835" width="74.25" height="12.75" align-x="138" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="192"/> </region> <region region-id="1285" left="234" top="2840.25" width="51.75" height="12" align-x="234" align-y="2850" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1286" left="18" top="2859" width="75.75" height="12.75" align-x="30" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="1287" left="126" top="2859" width="73.5" height="12.75" align-x="138.75" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="1288" left="18" top="2883" width="73.5" height="12.75" align-x="29.25" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="195"/> </region> <region region-id="1289" left="126" top="2883" width="73.5" height="12.75" align-x="137.25" align-y="2892" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="196"/> </region> <region region-id="1290" left="18" top="2912.25" width="71.25" height="27.75" align-x="45" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="197"/> </region> <region region-id="1291" left="120" top="2912.25" width="72.75" height="27.75" align-x="147" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="198"/> </region> <region region-id="1292" left="228" top="2918.25" width="65.25" height="12" align-x="228" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1293" left="18" top="2942.25" width="60.75" height="12" align-x="18" align-y="2952" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1294" left="24" top="2967" width="25.5" height="12.75" align-x="37.5" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="199"/> </region> <region region-id="1295" left="72" top="2966.25" width="40.5" height="12" align-x="72" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1296" left="144" top="2967" width="24" height="12.75" align-x="155.25" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="200"/> </region> <region region-id="1297" left="192" top="2961" width="103.5" height="18.75" align-x="284.25" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="201"/> </region> <region region-id="1298" left="12" top="2997" width="54.75" height="12.75" align-x="26.25" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="202"/> </region> <region region-id="1299" left="84" top="2997" width="45" height="12.75" align-x="99.75" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="203"/> </region> <region region-id="1300" left="150" top="2997" width="43.5" height="12.75" align-x="164.25" align-y="3006" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="204"/> </region> <region region-id="1301" left="24" top="3020.25" width="75.75" height="12" align-x="39" align-y="3030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1302" left="12" top="3045" width="25.5" height="12.75" align-x="25.5" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="205"/> </region> <region region-id="1303" left="60" top="3044.25" width="40.5" height="12" align-x="60" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1304" left="132" top="3045" width="24" height="12.75" align-x="143.25" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="206"/> </region> <region region-id="1305" left="180" top="3039" width="103.5" height="18.75" align-x="272.25" align-y="3054" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="207"/> </region> <region region-id="1306" left="12" top="3069" width="54.75" height="12.75" align-x="26.25" align-y="3078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="208"/> </region> <region region-id="1307" left="84" top="3069" width="45" height="12.75" align-x="99.75" align-y="3078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="209"/> </region> <region region-id="1308" left="150" top="3069" width="43.5" height="12.75" align-x="164.25" align-y="3078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="210"/> </region> <region region-id="1309" left="12" top="3104.25" width="104.25" height="13.5" 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<ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="244"/> </region> <region region-id="1345" left="240" top="3458.25" width="51.75" height="12" align-x="240" align-y="3468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1346" left="24" top="3477" width="75.75" height="12.75" align-x="36" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="245"/> </region> <region region-id="1347" left="132" top="3477" width="73.5" height="12.75" align-x="144.75" align-y="3486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="246"/> </region> <region region-id="1348" left="24" top="3501" width="73.5" height="12.75" align-x="35.25" align-y="3510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="247"/> </region> <region region-id="1349" left="132" top="3501" width="73.5" height="12.75" align-x="143.25" align-y="3510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="248"/> </region> <region region-id="1350" left="24" top="3530.25" width="71.25" height="27.75" align-x="51" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="249"/> </region> <region region-id="1351" left="126" top="3530.25" width="72.75" height="27.75" align-x="153" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">X</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">B</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="250"/> </region> <region region-id="1352" left="234" top="3536.25" width="65.25" height="12" align-x="234" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 15a,b </text> </region> <region region-id="1353" left="24" top="3560.25" width="60.75" height="12" align-x="24" align-y="3570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">First solution</inlineAttr> </f> </text> </region> <region region-id="1354" left="30" top="3585" width="25.5" height="12.75" align-x="43.5" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="251"/> </region> <region region-id="1355" left="78" top="3584.25" width="40.5" height="12" align-x="78" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1356" left="150" top="3585" width="24" height="12.75" align-x="161.25" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="252"/> </region> <region region-id="1357" left="198" top="3579" width="103.5" height="18.75" align-x="290.25" align-y="3594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="253"/> </region> <region region-id="1358" left="18" top="3615" width="54.75" height="12.75" align-x="32.25" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x1</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="254"/> </region> <region region-id="1359" left="90" top="3615" width="45" height="12.75" align-x="105.75" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="255"/> </region> <region region-id="1360" left="156" top="3615" width="43.5" height="12.75" align-x="170.25" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z1</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="256"/> </region> <region region-id="1361" left="30" top="3638.25" width="75.75" height="12" align-x="45" align-y="3648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Second solution</inlineAttr> </f> </text> </region> <region region-id="1362" left="18" top="3663" width="25.5" height="12.75" align-x="31.5" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="257"/> </region> <region region-id="1363" left="66" top="3662.25" width="40.5" height="12" align-x="66" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> trial value </text> </region> <region region-id="1364" left="138" top="3663" width="24" height="12.75" align-x="149.25" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="258"/> </region> <region region-id="1365" left="186" top="3657" width="103.5" height="18.75" align-x="278.25" align-y="3672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">X</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">X</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="259"/> </region> <region region-id="1366" left="18" top="3687" width="54.75" height="12.75" align-x="32.25" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x2</ml:id> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:id xml:space="preserve">X</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="260"/> </region> <region region-id="1367" left="90" top="3687" width="45" height="12.75" align-x="105.75" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">y2</ml:id> <ml:apply> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="261"/> </region> <region region-id="1368" left="156" top="3687" width="43.5" height="12.75" align-x="170.25" align-y="3696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">z2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">x2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="262"/> </region> <region region-id="1369" left="18" top="3722.25" width="109.5" height="13.5" align-x="74.25" align-y="3732" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Λ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">z1</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>-20.56536321475458</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="263"/> </region> <region region-id="1370" left="150" top="3722.25" width="104.25" height="13.5" align-x="206.25" align-y="3732" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffce" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Λ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>75.001428275672467</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="264"/> </region> <region region-id="1371" left="294" top="3723" width="84.75" height="18" align-x="321.75" align-y="3732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Procyon</ml:str> </result> </ml:eval> </math> <rendering item-idref="265"/> </region> <region region-id="1372" left="294" top="3741" width="75" height="18" align-x="321.75" align-y="3750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Pollux</ml:str> </result> </ml:eval> </math> <rendering item-idref="266"/> </region> <region region-id="1373" left="18" top="3746.25" width="99.75" height="13.5" align-x="74.25" align-y="3756" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x1</ml:id> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">z1</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>40.089546641206653</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="267"/> </region> <region region-id="1374" left="150" top="3746.25" width="99.75" height="13.5" align-x="206.25" align-y="3756" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffc6" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">Φ</ml:id> <ml:sequence> <ml:id xml:space="preserve">x2</ml:id> <ml:id xml:space="preserve">y2</ml:id> <ml:id xml:space="preserve">z2</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>35.010105477637019</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="268"/> </region> <region region-id="1375" left="24" top="3854.25" width="317.25" height="12" align-x="24" align-y="3864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">1. </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false">Positions, observed zenith angles for first pair of stars from Table1</inlineAttr> </f> </text> </region> <region region-id="1376" left="30" top="3885" width="24.75" height="12.75" align-x="42.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i1</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="269"/> </region> <region region-id="1377" left="84" top="3885" width="24.75" height="12.75" align-x="96.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i2</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="270"/> </region> <region region-id="1378" left="132" top="3885" width="93" height="18" align-x="159.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Aldebaran</ml:str> </result> </ml:eval> </math> <rendering item-idref="271"/> </region> <region region-id="1379" left="228" top="3885" width="75" height="18" align-x="255.75" align-y="3894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Star</ml:id> <ml:id xml:space="preserve">i2</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">Pollux</ml:str> </result> </ml:eval> </math> <rendering item-idref="272"/> </region> <region region-id="1380" left="18" top="3908.25" width="37.5" height="15.75" align-x="34.5" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">i1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="273"/> </region> <region region-id="1381" left="84" top="3908.25" width="37.5" height="15.75" align-x="100.5" align-y="3918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">α2</ml:id> <ml:apply> <ml:indexer/> <ml:id 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show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">λ2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>27.271531549750538</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="286"/> </region> <region region-id="1394" left="24" top="3998.25" width="149.25" height="12" align-x="24" align-y="4008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Calculate A-F variables, equations</inlineAttr> </f> </text> </region> <region region-id="1395" left="48" top="4022.25" width="56.25" height="13.5" align-x="63" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:sequence> <ml:id xml:space="preserve">λ1</ml:id> <ml:id xml:space="preserve">δ1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="287"/> </region> <region region-id="1396" left="126" top="4022.25" width="56.25" height="13.5" align-x="141" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a2</ml:id> 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height="13.5" align-x="135" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c2</ml:id> <ml:apply> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">δ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="292"/> </region> <region region-id="1401" left="198" top="4046.25" width="44.25" height="13.5" align-x="213.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="293"/> </region> <region region-id="1402" left="270" top="4046.25" width="44.25" height="13.5" align-x="285.75" align-y="4056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">ζ2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="294"/> </region> <region region-id="1403" left="24" top="4077" width="75.75" height="12.75" align-x="37.5" align-y="4086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">b2</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">a2</ml:id> <ml:id xml:space="preserve">b1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="295"/> </region> <region region-id="1404" left="132" top="4077" width="74.25" height="12.75" align-x="144" align-y="4086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">c1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">c2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="296"/> </region> <region region-id="1405" left="240" top="4082.25" width="51.75" height="12" align-x="240" align-y="4092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Equation 14 </text> </region> <region region-id="1406" left="24" top="4101" width="75.75" height="12.75" align-x="36" align-y="4110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b2</ml:id> <ml:id xml:space="preserve">p1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">b1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="297"/> </region> <region 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