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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2007 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 17, 2007 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hrulefill
\hspace{0.5in}
 Section: \hrulefill
\vfil
\begin{center}
{\large
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
Total & 40 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all questions. 
\item You may use a calculator during this
examination.  
Other electronic devices are not allowed, and should be
turned off for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method,
or read a numerical solution from a graph on your calculator
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.
\item Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item 
A probe lands on a distant planet at midnight.  
The temperature on the planet is a sinusoidal function of time.
At midnight, the temperature was decreasing, and it continued
decreasing until 5 AM, when the temperature reached the minimum, 20$^\circ$C.
The temperature then increased, reaching the maximum, 70$^\circ$C at 4 PM.

During the first 26 hours after the probe lands, for how much time was the temperature
above 59$^\circ$C?

\newp

\item A tree is growing in such a way that its height is always increasing
but never grows above 120 feet tall.  In 1998, the tree was 55 feet tall.
In 2006, it was 78 feet tall.  Assume that the tree's height is a linear-to-linear
rational function of time.  How many years after 1998 will the tree be 100 feet tall?

\newp

\item Malcolm is running around a circular track.  The track's radius is 50 meters.
Malcolm runs at a constant speed of 4 meters per second.
If he runs for 32 seconds, how far, in a straight line, will he be from his starting point?

\newp

\item Let 
\[
f(x) = \left\{ \begin{array}{ll}
				  2x & \mbox{if $x<5$,} \\
				  -5x & \mbox{if $x\ge 5$} 
			\end{array}
			\right.
\]
and
\[
g(x) = \left\{ \begin{array}{ll}
				 -3x & \mbox{if $x<0$,} \\
				 x-2 & \mbox{if $0 \le x \le 4$,} \\
				 -x & \mbox{if $x>4$} 
				 \end{array}
				 \right.
\]

Write the multipart rule for the function $h(x)=f(x)+g(x)$.


\end{enumerate}


\end{document}


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