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{\LARGE{
\hfil Math 120 A - Spring 2013 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 23, 2013 \hfil \pp
\hfil Answers \hfil \pp
}}

There were two versions of the exam.

Version A: In problem 1, Magdalena's height never exceeds 180 cm.

\begin{enumerate}

\item (a) $\dsps h(t)=\frac{180t-1560}{t-8}$ (b) $t=25.1428857$.

\item (a) $\dsps x=r \cos \left(-\frac{44 \pi}{95}+\frac{2 \pi}{95} t \right),
y=r \sin \left(-\frac{44 \pi}{95}+\frac{2 \pi}{95} t \right)$
(b) 125.0633 seconds

\item $104.82895$ years after 2000.

\item (a) $x=-\frac{3}{2}$ (b) $x=6$ and $x=2$ (c) $g(x)=\frac{2}{3}x+2$

\end{enumerate}

Version B: In problem 1, Magdalena's height never exceeds 200 cm.

\begin{enumerate}
\item (a) $\dsps h(t) = \frac{200t-\frac{2000}{9}}{t+\frac{55}{9}}$
(b) $t=66.11111111$ 

\item (a) $\dsps x = r \cos \left(-\frac{36\pi}{80} + \frac{2 \pi}{80} t \right),
y = r \sin \left(-\frac{36\pi}{80} + \frac{2 \pi}{80} t \right)$
(b) 85.71428 seconds

\item $40.2094$ years after 2000.

\item (a) $ x=-\frac{13}{10}$ (b) $x=3$ and $x=7$ (c) $g(x)=4x+2$

\end{enumerate}


\end{document}


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