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\begin{document}

\noindent
\vfil \noindent
{\LARGE
\hfil Math 120 A - Spring 2018\hfil \pp
\hfil Final Exam\hfil  \pp
\hfil June 2, 2018 \hfil \pp
}
\normalsize
\vfil
\medskip
\hfil Student's name: \hrulefill \hrulefill \hspace{0.25in} Student ID no. : \hrulefill

\vfil \vfil

\hfil Student's signature: \hrulefill \hrulefill \hrulefill \hspace{0.25in} 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
6 &  10 &    \\ \hline
7 &  10 &    \\ \hline
Total & 70 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Fill in all information above.  Unsigned exams will not be graded.
\item Complete all questions. 
\item You may use a TI30XIIS calculator during this
examination.  
No other electronic devices are not allowed, and they should be
turned off and put away for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 inch by 11 inch sheet of notes.  Write
your name on your notesheet and turn it in with your exam.
\item Show all work for full credit.  
\item You have 170 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Edwina is suffering from Sinsoidal fever.
Her body temperature is a sinusoidal function of time.
Today, at 5 AM, her temperature was at its maximum, 104 degrees Fahrenheit.
Her temperature then dropped, reaching its minimum of 97 degrees Fahrenheit
at 9:30 AM.  

How much time today (from midnight to midnight) will her temperature be
above 101 degrees Fahrenheit?

\newp

\item The height of a certain tree is a linear-to-linear rational function of time.  
 One year from today, the tree will be $7$ feet tall.
Six years from today, the tree will be $18.5$ feet tall.

The height of the tree will always increase, but will never be more then $30$ feet tall.

When will the tree be $27$ feet tall?

\newp

%\item You have a piece of cloth shaped as shown in the figure below.
%You wish to cut the cloth into two pieces with a vertical cut parallel
%to the left edge.  You will make the cut a distance $x$ from the left edge.
%
%Express the area of cloth to the left of the cut as a multipart function of $x$.
%
%FIGURE NEEDED
%
%%\epsfig{file=pizza01.eps, 
%% width=9cm,
%% angle=0 }
%
%\newp



\item Let $f(x)=3x+2$ and $\displaystyle g(x)=(x-4)^{2}-5$.

\begin{enumerate}

\item Let $h(x)=f(g(x))$ restricted to the domain $x \le 4$.  Find $h^{-1}(x)$.

\vfill

\item Solve the following equation for x:
 $\, \displaystyle \frac{g(x+4)-g(x)}{6} = 10$

\vfill

\end{enumerate}

\newpage


\item You have 500 meters of fencing with which to make two enclosures.

One enclosure will be in the shape of a square, and the other will have
the shape of an isosceles right triangle.  

For example, the enclosures might look like this:


\begin{tikzpicture}[auto,scale=0.5]
\draw (0,0) -- (4,0) -- (4,4) -- (0,4) -- cycle;
\draw (6,5) -- (6,0) -- (11,0) -- cycle;
\end{tikzpicture}


How long should the legs of the triangular enclosure be to minimize
the combined area of the two enclosures?

\newp

%\item Dora and Diego start jogging in the coordinate plane at the same time.  They both exhibit \textbf{uniform linear motion}. \\
%Dora starts at the point (-10,0).  She jogs on a straight line path
%through the point (2,6) which she reaches in 4 seconds. \\
%Diego starts at the point (1,0) and jogs on a straight line path
%through the point (-3,3) at a constant speed of 6 ft/sec.  (All
%coordinates are in feet). 
%
%\begin{enumerate}
%\item Find the linear parametric equations for Dora's motion.
%\vfil \vfil
%\item Find the linear parametric equations for Diego's motion.
%\vfil \vfil
%\item Find the time when the distance between Dora and Diego is minimum.
%\vfil \vfil \vfil
%\end{enumerate}
%
%\newpage

%\item You will use 80 feet of fencing to make three enclosures.  
%Two will be squares with identical dimensions, and one will be 
%a rectangle that is twice as long as it is
%wide.
%
%What is the \emph{minimum} possible combined area of the three enclosures?
%
%\newpage

\item You are climbing a pole some distance from a tall building.
When you reach a point $20$ meters above the ground, you measure the angle of elevation of the
building (i.e., the angle that the top of the building makes with the horizontal)
and find this angle is $60^{\circ}$.

You then climb $10$ meters farther up the pole, and measure the angle again.
This time the angle is $57^{\circ}$.

How tall is the building?

 %\epsfig{file=balloon01.eps, 
 %width=9cm,
 %angle=0 }

\newp




\item Boris and Stella are walking on a circular path which has
a radius of 1000 meters.  They start walking at the same time.
Boris starts at the northernmost point of the path, and Stella starts at
the easternmost point.  Boris walks clockwise.
Stella walks counterclockwise, and she walks three times as fast as Boris walks.  
They pass each other for the first
time after 300 seconds.

How far (in a straight line) is Boris from his staring point when he has been
running for 1500 seconds?

\newp

%\item The populations of city X and city Y are growing exponentially.
%The population of city X triples every 100 years.  The population of
%city Y was half that of city X in the year 1900, but city Y had twice the
%population of city X in the year 1950.
%
%\begin{enumerate}
%
%\item The population of city X was 20,000 in the year 1925.  What was the
%population of city X in 1890?
%
%\vfil
%
%\item When will the population of city Y be six times the population of 
%city X?  Express your answer in years after 1900.
%
%\end{enumerate}
%
%\newp

\item Imogene is sailing near a buoy with a radar antenna on it.
She sails at a constant 4 miles per hour.
The buoy's radar can detect her boat when she is within 5 miles of it.
Imogene starts sailing from a point 9 miles EAST and 2 miles NORTH
of the buoy.  She sails due WEST for 1.5 hours, then turns and
sails due directly to a point $16$ miles NORTH and $4$ miles WEST
of the buoy.

How much time did Imogene spend within 5 miles of the buoy?


\end{enumerate}

\end{document}


% \epsfig{file=pizza01.eps, 
% width=11cm,
% angle=0 }

