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<ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="9"/> </region> <region region-id="562" left="744" top="737.25" width="31.5" height="23.25" align-x="744" align-y="756" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" 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undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">m</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="a">m</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="811" left="36" top="987.75" width="28.5" height="18" align-x="36" align-y="1002" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(09)</f> </p> </text> </region> <region region-id="168" left="102" top="956.25" width="454.5" height="69" align-x="146.25" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="a">m</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="11"/> </region> <region region-id="812" left="36" top="1083.75" width="28.5" height="18" align-x="36" align-y="1098" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(10)</f> </p> </text> </region> <region region-id="169" left="102" top="1038.75" width="438" height="88.5" align-x="146.25" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> <ml:symResult> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="12"/> </region> <region region-id="563" left="750" top="1103.25" width="31.5" height="23.25" align-x="750" align-y="1122" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">[03]</f> </p> </text> </region> <region region-id="163" left="0" top="1152" width="6000" height="6" align-x="0" align-y="1152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="564" left="744" top="1169.25" width="31.5" height="23.25" align-x="744" align-y="1188" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">[04]</f> </p> </text> </region> <region region-id="815" left="36" top="1203.75" width="28.5" height="18" align-x="36" align-y="1218" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(11)</f> </p> </text> </region> <region region-id="485" left="198" top="1170.75" width="462.75" height="88.5" align-x="253.5" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="814" left="36" top="1323.75" width="28.5" height="18" align-x="36" align-y="1338" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(11)</f> </p> </text> </region> <region region-id="486" left="198" top="1292.25" width="547.5" height="69" align-x="253.5" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" 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<ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="813" left="36" top="1395.75" width="28.5" height="18" align-x="36" align-y="1410" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(12)</f> </p> </text> </region> <region region-id="156" left="12" top="1446" width="900.75" height="71.25" align-x="134.25" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>80</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> <ml:id 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subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="15"/> </region> <region region-id="428" left="0" top="1536" width="6000" height="6" align-x="0" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="819" left="36" top="1581.75" width="28.5" height="18" align-x="36" align-y="1596" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(13)</f> </p> </text> </region> <region region-id="429" left="168" top="1550.25" width="682.5" height="69" align-x="248.25" align-y="1596" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="430" left="162" top="1664.25" width="528.75" height="69" align-x="287.25" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:command> <ml:id xml:space="preserve">collect</ml:id> </ml:command> <ml:command> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">m</ml:id> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>1600</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>60</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="17"/> </region> <region region-id="818" left="36" top="1701.75" width="28.5" height="18" align-x="36" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(14)</f> </p> </text> </region> <region region-id="817" left="36" top="1761.75" width="28.5" height="18" align-x="36" align-y="1776" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(15)</f> </p> </text> </region> <region region-id="431" left="162" top="1730.25" width="489.75" height="69" align-x="242.25" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">m</ml:id> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">V</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="816" left="36" top="1845.75" width="28.5" height="18" align-x="36" align-y="1860" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(16)</f> </p> </text> </region> <region region-id="432" left="156" top="1820.25" width="534" height="69" align-x="281.25" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:command> <ml:id xml:space="preserve">collect</ml:id> </ml:command> <ml:command> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>1600</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">a</ml:id> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>60</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="19"/> </region> <region region-id="565" left="762" top="1847.25" width="31.5" height="23.25" align-x="762" align-y="1866" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">[05]</f> </p> </text> </region> <region region-id="171" left="0" top="1896" width="6000" height="6" align-x="0" align-y="1896" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="823" left="48" top="1953.75" width="28.5" height="18" align-x="48" align-y="1968" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(17)</f> </p> </text> </region> <region region-id="433" left="162" top="1921.5" width="660.75" height="75.75" align-x="357.75" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:minus/> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:apply> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>1600</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> </math> <rendering item-idref="20"/> </region> <region region-id="822" left="48" top="2049.75" width="28.5" height="18" align-x="48" align-y="2064" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(18)</f> </p> </text> </region> <region region-id="434" left="156" top="2011.5" width="612.75" height="75.75" align-x="297.75" align-y="2064" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="A name is required here." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:minus/> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">V</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="821" left="48" top="2145.75" width="28.5" height="18" align-x="48" align-y="2160" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(19)</f> </p> </text> </region> <region region-id="435" left="156" top="2113.5" width="624.75" height="75.75" align-x="309.75" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:minus/> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:apply> </ml:chem> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="м">a</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">V</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="820" left="48" top="2235.75" width="28.5" height="18" align-x="48" align-y="2250" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(20)</f> </p> </text> </region> <region region-id="436" left="156" top="2223" width="603.75" height="56.25" align-x="309.75" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:chem> <ml:apply> <ml:minus/> <ml:chem> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:lambda> </ml:apply> </ml:chem> <ml:chem> <ml:apply> <ml:derivative style="derivative"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> <ml:id xml:space="preserve">T</ml:id> </ml:lambda> </ml:apply> </ml:chem> </ml:apply> </ml:chem> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">a</ml:id> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">V</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="566" left="762" top="2267.25" width="31.5" height="23.25" align-x="762" align-y="2286" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">[06]</f> </p> </text> </region> <region region-id="437" left="0" top="2316" width="6000" height="6" align-x="0" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="567" left="762" top="2333.25" width="31.5" height="23.25" align-x="762" align-y="2352" show-border="true" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="20">[07]</f> </p> </text> </region> <region region-id="828" left="48" top="2379.75" width="28.5" height="18" align-x="48" align-y="2394" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(21)</f> </p> </text> </region> <region region-id="501" left="312" top="2367.75" width="151.5" height="45" align-x="361.5" align-y="2394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="a">y</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">y</ml:id> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="a">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="502" left="306" top="2427" width="252.75" height="47.25" align-x="352.5" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Π</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="a">m</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="a">y</ml:id> <ml:id xml:space="preserve" subscript="м">y</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="м">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="м">y</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="829" left="48" top="2457.75" width="28.5" height="18" align-x="48" align-y="2472" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(22)</f> </p> </text> </region> <region region-id="503" left="306" top="2493" width="270" height="50.25" align-x="378.75" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval 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</ml:apply> <ml:id xml:space="preserve">Y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">g</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="a">m</ml:id> <ml:id xml:space="preserve" subscript="м">m</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">V</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="833" left="42" top="2895.75" width="28.5" height="18" align-x="42" align-y="2910" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16">(26)</f> </p> 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