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\begin{document}
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\begin{center}
{\Large TEST 3

Math 202}
\end{center}

\begin{itemize}
\item  Do your work on separate paper.  Show all your work and make your work neat.  You will be graded on this!
\item  You can use a calculator and book, but I must be able to follow your work as if you had no calculator and book.  No notes!
\item  You will be graded on both your answer and the work done to get that answer.
\item  You have one hour to finish the questions on the exam.
\end{itemize}



\begin{enumerate}

\item  (10 points)  James Bond has been thrown into a swimming pool with a bunch of sharks.
	There are men with guns ready to shoot him if he leaves the pool from above, but there
	is a triangular gate at the bottom of the pool that opens to air and will drain the pool as in the figure.
	The water is 6 meters deep at the bottom of the pool.
	How much force does Bond have to exert on the gate to open it and escape?

\epsfysize=8 cm
\begin{figure}[htb]
\center{
\leavevmode
\epsfbox{pool.eps}
%\caption{JamesAppears as Fig. Caption under the Drawing}
}
\end{figure}


\newpage


\item  Consider the parametric equations
\[
x = t^3-4t  \qquad y = -t^2
\]
\begin{enumerate}
\item  For the Sketch the curve given below, determine the direction of the curve.
\item  Determine all the $t$ and $x$ and $y$ values of the intersection points on the $y$-axis.
\item  Determine where ($x$ and $y$ values as well as $t$ values) there are horizontal and vertical tangent lines.
\item  Set up an integral that represents the area enclosed by the loop.
\item  Set up an integral that represents the length of the loop.
\item  Set up an integral that represents the surface area obtained by rotating the loop around the $y$-axis.
\end{enumerate}

\epsfysize=5.2 cm
\begin{figure}[htb]
\center{
\leavevmode
\epsfbox{graph1.eps}
%\caption{JamesAppears as Fig. Caption under the Drawing}
}
\end{figure}

\newpage

\item  Consider the polar equation:
\[
r = \sin \theta \cos^2 \theta
\]
\begin{enumerate}
\item  Find a Cartesian equation for the curve.
\item  Find an integral representing the total area that is enclosed by this curve.
\item  Find an integral representing the total length of this curve.
\end{enumerate}

\epsfysize=5.2 cm
\begin{figure}[htb]
\center{
\leavevmode
\epsfbox{graph2.eps}
%\caption{JamesAppears as Fig. Caption under the Drawing}
}
\end{figure}


\end{enumerate}

\end{document}