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source/calculus/RATs/RAT-AI.tex

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\item Recall that the pressure ($P$) asserted on a region of area $A$ is $$P=\frac{F}{A}$$ where $F$ is the force applied that region. If 10 lb/in$^2$ of pressure is applied uniformly across a 5 in by 5 in square, how much force is applied?
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\begin{enumerate}
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\item $2.5$ lb.
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\item $10$ lb.
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%\item $25$ lb.
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\item $50$ lb.
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\item $250$ lb. %correct
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\item $2.5$ lb
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\item $10$ lb
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%\item $25$ lb
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\item $50$ lb
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\item $250$ lb %correct
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\end{enumerate}
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source/calculus/exercises/outcomes/AI/AI7/template.xml

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</content>
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<outtro>
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<p>
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<me>\int_0^{ {{height}} } 62.4h\left( {{width}} \right)dh\ \text{lbs}.</me>
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<me>\int_0^{ {{height}} } 62.4h\left( {{width}} \right)dh\ \text{lb}</me>
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</p>
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</outtro>
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<!-- {{/dam}} -->

source/calculus/source/06-AI/05.ptx

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<activity xml:id="activity-TI4pyramidcentermass">
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<statement>
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<p>
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Consider that for the pyramid from <xref ref="activity-A4pyramidmass"/>, a cross section of height <m>h</m> is <m>A(h)=\pi\cdot \left( \frac{16-h}{2}\right)^2</m> ft<m>^2</m>. Also recall that the density of the pyramid is <m>\delta(h)=10+\cos{\pi h}</m> lb/feet<m>^3</m>, where <m>h</m> is the height in feet, and that we found the total mass to be about 3414.14.6 lbs.
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Consider that for the pyramid from <xref ref="activity-A4pyramidmass"/>, a cross section of height <m>h</m> is <m>A(h)=\pi\cdot \left( \frac{16-h}{2}\right)^2</m> ft<m>^2</m>. Also recall that the density of the pyramid is <m>\delta(h)=10+\cos{\pi h}</m> lb/feet<m>^3</m>, where <m>h</m> is the height in feet, and that we found the total mass to be about 3414.14.6 lb.
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</p>
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<p>
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Use <xref ref="fact-AI4centerofmass"/> to find the height where the center of mass occurs.

source/calculus/source/06-AI/07.ptx

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<introduction>
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<p>
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Consider a trapezoid-shaped dam that is 60 feet wide at its base and 90 feet wide at its top. Assume the dam is 20 feet tall with water that rises to its top.
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Water weighs 62.4 pounds per cubic foot and exerts <m>P=62.4d</m> lbs/ft<m>^2</m> of pressure at depth <m>d</m> ft. Consider a rectangular slice of this dam at height <m>h_i</m> feet and width <m>b_i</m>.
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Water weighs 62.4 pounds per cubic foot and exerts <m>P=62.4d</m> lb/ft<m>^2</m> of pressure at depth <m>d</m> ft. Consider a rectangular slice of this dam at height <m>h_i</m> feet and width <m>b_i</m>.
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</p>
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<image>
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<prefigure xmlns="https://prefigure.org" label="prefigure-AI7-graph3">

source/precalculus/exercises/outcomes/LF/LF7/template.xml

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</content>
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<outtro>
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<p>
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<m>{{amount1}}</m> lbs {{meat1}} and <m>{{amount2}}</m> lbs {{meat2}}
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<m>{{amount1}}</m> lb {{meat1}} and <m>{{amount2}}</m> lb {{meat2}}
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</p>
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</outtro>
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</knowl>

source/precalculus/source/01-EQ/02.ptx

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<p> Now solve for <m>N</m> and <m>S</m>, and put your answer in the context of the problem.
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<ol marker= "A.">
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<li>Ammie bought <m>2.5</m> lbs of Nerds Gummy Clusters and <m>4.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>3.5</m> lbs of Nerds Gummy Clusters and <m>3.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>4.5</m> lbs of Nerds Gummy Clusters and <m>2.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>5.5</m> lbs of Nerds Gummy Clusters and <m>1.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>2.5</m> lb of Nerds Gummy Clusters and <m>4.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>3.5</m> lb of Nerds Gummy Clusters and <m>3.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>4.5</m> lb of Nerds Gummy Clusters and <m>2.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>5.5</m> lb of Nerds Gummy Clusters and <m>1.5</m> lb of Starburst Jelly Beans.</li>
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</ol>
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</p>
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</statement>

source/precalculus/source/03-LF/07.ptx

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</p>
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<p>
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<ol marker= "A.">
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<li>Ammie bought <m>2.5</m> lbs of Nerds Gummy Clusters and <m>4.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>3.5</m> lbs of Nerds Gummy Clusters and <m>3.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>4.5</m> lbs of Nerds Gummy Clusters and <m>2.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>5.5</m> lbs of Nerds Gummy Clusters and <m>1.5</m> lbs of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>2.5</m> lb of Nerds Gummy Clusters and <m>4.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>3.5</m> lb of Nerds Gummy Clusters and <m>3.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>4.5</m> lb of Nerds Gummy Clusters and <m>2.5</m> lb of Starburst Jelly Beans.</li>
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<li>Ammie bought <m>5.5</m> lb of Nerds Gummy Clusters and <m>1.5</m> lb of Starburst Jelly Beans.</li>
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</ol>
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</p>

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