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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 B and C - Autumn 2005 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 17, 2005 \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
5 & 10 & \\ \hline
Total & 50 & \\ \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 Maria is climbing a vertical cliff wall.  

Alice is observing Maria from a straight road that extends horizontally away from the
base of the wall.
Some distance away from the wall, Alice observes that from her position, 
Maria is 39 degrees above the horizontal.
Alice moves 200 feet further away from the wall, and notices that Maria has climbed
12 feet higher.  At this point Maria makes an angle of 35 degrees with the horizontal.

How high is Maria now?

\newp




\item George and Paula are running around a circular track.
George starts at the westernmost point of the track, and Paula starts at the easternmost point.
The illustration below shows their starting positions and running directions.
They start running toward each other at constant speeds.
George runs at 9 feet per second.
Paula takes 50 seconds to run a lap of the track.
George and Paula pass each other after 11 seconds.

\epsfig{file=george01.eps,width=8cm,angle=0}

After running for 3 minutes, how far east of his starting point is George?

\newp

\item Over time, Frank's accuracy at the game of darts gets better and better.
When Frank was 15 years old, he was only 74 percent accurate.
When he was 25 years old, he was 90 percent accurate.
Assume that his accuracy will always increase, and will approach arbitrarily close
to 100 percent if he lives long enough.

Suppose Frank's accuracy percentage is a linear-to-linear function of his age.

How old will Frank be when he is 98 percent accurate?

\newp



\item Matilda is planning a walk around the perimeter of Wedge Park, which is
shaped like a circular wedge, as shown below.
The walk around the park is 2.1 miles, and the park has an area of 0.25 square miles.

If $\theta$ is less than 90 degrees, what is the value of the radius, $r$?

\epsfig{file=wedge01.eps,width=6cm,angle=0}


\newp

\item Let $u(t)$ be the basic step function
 \[
 u(t) = \left \{ \begin{array}{ll}
 					0 & \mbox{ if $t<0$, } \\
 					1 & \mbox{ if $0 \le t \le 1$, } \\
 					0 & \mbox{ if $t>1$ }
 				 \end{array}
 \right.			
 \]

Write the mult-part rule for the function
\[
g(t) = u(t-5) + u(2t-3) + 3t.
\]

\end{enumerate}




\end{document}


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