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\noindent
\vfil \noindent
\large
\hfil Math 120 - Spring 2011 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil June 4, 2011 \hfil \pp
\hfil Answers \hfil \pp
\normalsize

\begin{enumerate}
\item 3.6457 hours
\item (a) 20.42 seconds (b) $x=R \cos (-2.4763439676+\frac{2\pi}{27}t),
y = R \sin (-2.4763439676 + \frac{2 \pi}{27} t)$
\item (a) $V(t)=10 \sin( \frac{2 \pi}{8} (t-3)) + 12$
(b) 4.5420068 hours
\item \[
\mbox{area}=\left \{
 \begin{array}{ll}
\frac{1}{2}x(21.8-0.778626x+21.8) & \mbox{if $0 \le x \le 13.1$,} \\
218.77+\frac{1}{2}(x-13.1)(11.6-2.761905(x-17.3)) & \mbox{if $13.1 \le x \le 17.3$.} 
\end{array}
\right.
\]

\item (a) \[
h(t) = \frac{89t+140}{t+28}
\]
(b) 32.30769 years from today

\item 53.23064 years after the year 2000

\item (a)
\[
f(g(x))=
 \left \{ \begin{array}{ll}
8x+19 & \mbox{if $ x \ge -5/2$,} \\
-4x-11 & \mbox{if $x < -5/2$.} 
\end{array}
\right.
\]
(b) 19/4 is the only solution



\end{enumerate}

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