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quantity-name="magnetic_flux"/> <unit unit-name="tesla" quantity-name="magnetic_flux_density"/> <unit unit-name="watt" quantity-name="power"/> <unit unit-name="pascal" quantity-name="pressure"/> <unit unit-name="ohm" quantity-name="resistance"/> <unit unit-name="liter" quantity-name="volume"/> </derivedUnits> </customUnitSystem> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="true" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1170" 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="804" left="36" top="8.25" width="416.25" height="13.5" align-x="53.25" align-y="18" 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">PV Sizing.xmcd<sp count="3"/>Charles Kim 2013</p> </text> </region> <region region-id="902" left="24" top="38.25" width="660" height="151.5" align-x="27.75" align-y="48" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(Background) An energy efficient house in Fresno, CA (Latitude at 22 degrees) is to ve fitted with a rooftop PV array that will annually replace all of the 3600 kWh/year of electricty that the home uses.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(Assumption): </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(1) Roof is south facing with a moderate tilt angle.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(2) Annual Insolation for L-15 is 5.7 kWh/m<sup>2</sup>-day ----> (5.7 Peak Sun Hours)</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(3) DC-to-AC conversion efficiency is 75%</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(4) PV array average 1-sun efficiency (or Capacifty Factor, CF)is 12.5%</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>(Q): How many<sp count="2"/>kW (DC rating) of PV panels will be required and what are will be needed?</b> </p> </text> </region> <region region-id="1095" left="30" top="204" width="254.25" height="323.25" align-x="30" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="252.75" display-height="321.75"/> </picture> <rendering item-idref="3"/> </region> <region region-id="1092" left="312" top="212.25" width="315" height="13.5" align-x="327.75" align-y="222" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Annual Energy Production Equation (for PV)</p> </text> </region> <region region-id="1090" left="300" top="240" width="382.5" height="35.25" align-x="300" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="4" display-width="381" display-height="33.75"/> </picture> <rendering item-idref="5"/> </region> <region region-id="1098" left="312" top="282" width="331.5" height="249" align-x="312" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="6" display-width="330" display-height="247.5"/> </picture> <rendering item-idref="7"/> </region> <region region-id="1099" left="36" top="542.25" width="67.5" height="13.5" align-x="65.25" align-y="552" 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">SOLUTION </p> </text> </region> <region region-id="1100" left="36" top="566.25" width="375" height="13.5" align-x="39" align-y="576" 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">1. Annual Energy (AC) Required is 3600 kWh (Eann):</p> </text> </region> <region region-id="1105" left="438" top="564.75" width="69" height="15.75" align-x="472.5" align-y="576" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Eann</ml:id> <ml:real>3600</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="1107" left="522" top="566.25" width="60" height="13.5" align-x="533.25" align-y="576" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kWh/year</p> </text> </region> <region region-id="1108" left="60" top="582.75" width="57" height="15.75" align-x="91.5" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">PSH</ml:id> <ml:real>5.7</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1110" left="132" top="584.25" width="97.5" height="13.5" align-x="143.25" align-y="594" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Peak sun hour</p> </text> </region> <region region-id="1102" left="36" top="620.25" width="405" height="13.5" align-x="39" align-y="630" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Required AC Power Generation from PV system (Pac): </p> </text> </region> <region region-id="1104" left="60" top="640.5" width="150" height="33.75" align-x="87" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Pac</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Eann</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">PSH</ml:id> <ml:real>365</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.7303532804614275</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1112" left="222" top="650.25" width="22.5" height="13.5" align-x="230.25" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kW </p> </text> </region> <region region-id="1114" left="36" top="692.25" width="390" height="13.5" align-x="39.75" align-y="702" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">3. Required DC Power Generation from PV array (Pdc):</p> </text> </region> <region region-id="1116" left="450" top="690.75" width="63.75" height="15.75" align-x="482.25" align-y="702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D2A</ml:id> <ml:real>0.75</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1118" left="534" top="692.25" width="142.5" height="27" align-x="542.25" align-y="702" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">DC to AC Conversion Efficiency</p> </text> </region> <region region-id="1115" left="66" top="712.5" width="120.75" height="33.75" align-x="93" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Pdc</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Pac</ml:id> <ml:id xml:space="preserve">D2A</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.3071377072819033</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1120" left="204" top="722.25" width="22.5" height="13.5" align-x="212.25" align-y="732" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kW </p> </text> </region> <region region-id="1139" left="246" top="732" width="400.5" height="61.5" align-x="246" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="13" display-width="399" display-height="60"/> </picture> <rendering item-idref="14"/> </region> <region region-id="1122" left="36" top="758.25" width="157.5" height="13.5" align-x="39.75" align-y="768" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">4. PV Array Area (A):</p> </text> </region> <region region-id="1140" left="60" top="782.25" width="142.5" height="13.5" align-x="66.75" align-y="792" 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">PV Efficiency (η): </p> </text> </region> <region region-id="1141" left="222" top="786.75" width="54" height="15.75" align-x="238.5" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">η</ml:id> <ml:real>0.125</ml:real> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1129" left="84" top="814.5" width="119.25" height="33.75" align-x="101.25" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Pdc</ml:id> <ml:apply> <ml:mult/> <ml:real>1</ml:real> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>18.457101658255226</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="1131" left="216" top="821.25" width="20.25" height="16.5" align-x="222.75" align-y="834" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">m<sup>2</sup> <sp/> </p> </text> </region> <region region-id="1133" left="36" top="878.25" width="187.5" height="13.5" align-x="39.75" align-y="888" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">5. Selection of PV Module</p> </text> </region> <region region-id="1137" left="414" top="878.25" width="232.5" height="13.5" align-x="417.75" align-y="888" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">6. Selection of Inverter Module</p> </text> </region> <region region-id="1142" left="54" top="894" width="242.25" height="231.75" align-x="54" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="17" display-width="240.75" display-height="230.25"/> </picture> <rendering item-idref="18"/> </region> <region region-id="1138" left="414" top="900" width="249" height="210.75" align-x="414" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="19" display-width="247.5" display-height="209.25"/> </picture> <rendering item-idref="20"/> </region> <region region-id="1147" left="96" top="1128.75" width="79.5" height="15.75" align-x="138" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Prated</ml:id> <ml:real>0.158</ml:real> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="1162" left="228" top="1128.75" width="70.5" height="15.75" align-x="267" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">PVlen</ml:id> <ml:real>1.29</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1163" left="336" top="1128.75" width="72" height="15.75" align-x="376.5" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">PVwid</ml:id> <ml:real>0.99</ml:real> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1169" left="504" top="1182" width="192" height="150" align-x="504" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="24" display-width="190.5" display-height="148.5"/> </picture> <rendering item-idref="25"/> </region> <region region-id="1170" left="6" top="1200" width="483" height="114" align-x="6" align-y="1200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="26" display-width="481.5" display-height="112.5"/> </picture> <rendering item-idref="27"/> </region> <region region-id="1144" left="36" top="1460.25" width="255" height="13.5" align-x="39.75" align-y="1470" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">6. Number of Modules Needed (Npv):</p> </text> </region> <region region-id="1145" left="324" top="1450.5" width="139.5" height="33.75" 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:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Npv</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Pdc</ml:id> <ml:id xml:space="preserve">Prated</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>14.602137387860147</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1146" left="486" top="1458.75" width="162.75" height="15.75" align-x="516" 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 warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Npv</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:id xml:space="preserve">round</ml:id> <ml:id xml:space="preserve">Npv</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>15</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="1151" left="102" top="1490.25" width="255" height="27" align-x="104.25" align-y="1500" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">3 strings:<sp count="2"/>23.2 [V] *3 = 69.6 [V]</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">5 rows</p> </text> </region> <region region-id="1152" left="60" top="1530" width="414" height="211.5" align-x="60" align-y="1530" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="30" display-width="412.5" display-height="210"/> </picture> <rendering item-idref="31"/> </region> <region region-id="1154" left="36" top="1766.25" width="112.5" height="13.5" align-x="39.75" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">7. Verification</p> </text> </region> <region region-id="1155" left="60" top="1788.75" width="168.75" height="15.75" align-x="95.25" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">PdcV</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Prated</ml:id> <ml:id xml:space="preserve">Npv</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2.37</ml:real> </result> </ml:eval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="1157" left="240" top="1790.25" width="22.5" height="13.5" align-x="248.25" align-y="1800" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">kW </p> </text> </region> <region region-id="1158" left="60" top="1806.75" width="265.5" height="21.75" align-x="102.75" align-y="1824" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">EannV</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">PdcV</ml:id> <ml:id xml:space="preserve">D2A</ml:id> </ml:apply> <ml:id xml:space="preserve">PSH</ml:id> </ml:apply> <ml:real>365</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>3698.08875</ml:real> </result> </ml:eval> </ml:define> </math> <rendering 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