Mathcad Professional 14.0 <description/> <author>Kaushik</author> <company/> <keywords/> <revisedBy>Kaushik</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>04B9E145-22EF-47E1-9F21-06B178E761AC</documentID> <versionID>130CB2AC-16D8-4428-AA42-5542F27C24D2</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="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2" base-style="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Verdana" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#000080"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="dot" derivative="derivative" literal-subscript="small" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Geneva" font-charset="1" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" 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<dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="86.4" right="27.6" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </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="mks" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"> <tabs> <tab show-guide="true" position="36"/> <tab show-guide="true" position="360"/> </tabs> </ruler> <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="137" 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="131" left="6" top="20.25" width="126.75" height="12" align-x="18" align-y="30" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Using Units in X-Y Plots</p> </text> </region> <region region-id="136" left="6" top="54.75" width="263.25" height="14.25" align-x="12.75" align-y="66" 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">Set up the function you want to plot and a range if desired.</p> </text> </region> <region region-id="89" left="6" top="82.5" width="73.5" height="33.75" align-x="31.5" 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/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">g</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="128" left="6" top="138.75" width="123.75" height="15.75" align-x="17.25" align-y="150" show-border="false" show-highlight="false" 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">t</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:id xml:space="preserve">min</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</ml:real> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:sequence> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:id xml:space="preserve">min</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="91" left="6" top="162.75" width="279.75" height="14.25" align-x="21" align-y="174" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The variable t is defined as the range 0 minutes to 10 minutes. </p> </text> </region> <region region-id="98" left="6" top="198.75" width="404.25" height="14.25" align-x="18" align-y="210" 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">Insert a QuickPlot and add the variables t and f(t) to the placeholders on the x and y axes:</p> </text> </region> <region region-id="107" left="24" top="240" width="215.25" height="145.5" align-x="24" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="4"/> <rendering item-idref="5"/> </region> <region region-id="106" left="6" top="402.75" width="309.75" height="14.25" align-x="14.25" align-y="414" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">By default, the horizontal axis goes from 0 seconds to 600 seconds.</p> </text> </region> <region region-id="115" left="0" top="432" width="6000" height="6" align-x="0" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="108" left="6" top="444.75" width="102" height="14.25" align-x="8.25" align-y="456" 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">Look at the variable t :</p> </text> </region> <region region-id="137" left="150" top="429.75" width="69" height="225.75" align-x="160.5" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>60</ml:real> <ml:real>120</ml:real> <ml:real>180</ml:real> <ml:real>240</ml:real> <ml:real>300</ml:real> <ml:real>360</ml:real> <ml:real>420</ml:real> <ml:real>480</ml:real> <ml:real>540</ml:real> <ml:real>600</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="6"/> </region> <region region-id="109" left="6" top="702.75" width="332.25" height="28.5" align-x="15" align-y="714" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Note that, as always, the variable t is displayed in terms of its base unit, seconds. This is the default internal definition of t. </p> </text> </region> <region region-id="119" left="6" top="756.75" width="279.75" height="14.25" align-x="10.5" 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="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">To display the units in minutes, divide t by minutes.</p> </text> </region> <region region-id="120" left="42" top="792" width="200.25" height="155.25" align-x="42" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="7"/> <rendering item-idref="8"/> </region> <region region-id="125" left="0" top="966" width="6000" height="6" align-x="0" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="130" left="12" top="990.75" width="395.25" height="57" align-x="21.75" 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">To see an output table in minutes, change the unit in the unit placeholder to min by clicking on the unit, until you see an unit placeholder (small black rectangle) and insert the unit you want from the <b>Insert Unit</b> menu, or type in the correct abbreviation if you know it.<sp count="2"/> </p> </text> </region> <region region-id="121" left="36" top="1053.75" width="66.75" height="225.75" align-x="46.5" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>60</ml:real> <ml:real>120</ml:real> <ml:real>180</ml:real> <ml:real>240</ml:real> <ml:real>300</ml:real> <ml:real>360</ml:real> <ml:real>420</ml:real> <ml:real>480</ml:real> <ml:real>540</ml:real> <ml:real>600</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="9"/> </region> <region region-id="132" left="162" top="1053.75" width="65.25" height="225.75" align-x="172.5" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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