\def\wsn{21}
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\item{1.}    My neighbors have a very loud stereo.  The volume knob
turns half a circle (angles $\theta$ between $0^\circ$ and
$180^\circ$) and the volume of the music (usually Prince) is given by
the function $V(\theta)=110\sin(\theta/2)$ decibels (dB).  One night
at 3:30 in the morning I notice the lyrics ``I wanna be your fantasy,
and you can be mine...'' increasing from a volume of 88 dB at a rate
of 1 decibel per second!  At what rate can I deduce that my neighbor
is turning his volume knob?

\smallskip
\item{}  (Note:  Since the time I wrote this problem, my neighbors
have been evicted.)

\bigskip
\item{2.}  Art and Val are on their annual hunting trip.  This time,
however, {\bf they} plan on outsmarting the deer!  Val is sitting to
Art's right (east) when the perfect buck appears 40 meters to the
north.  Art aims the gun, but Val sneezes.  The deer startles and
takes off straight southeast at 30 meters per second.  Art turns to
keep the deer centered in his sight, but can't get a clean shot.  At
the instant Art smacks Val in the head with the barrel of the gun, how
fast was he rotating?

\bigskip
\item{3.}    Brian got a new sand box over the weekend and took his
``friends,'' He-Man and Skeletor, out to play make-believe.  Skeletor
tied He-Man to a pole and began dumping sand on top of him at a rate
of 4 cubic inches per second.  He-Man is six inches tall.  At the
moment he is half buried, He-Man notices that the sand is rising at a
rate of 1/2 inch per second.  How much longer does Bri... I mean
He-Man have to come up with a way to escape before he is completely
buried?  

\bigskip
\item{4.}  Eleanor and Regina operate a tour service for people who
would like to travel from Austin to Shreveport to go riverboat
gambling.  The minimum size for a group is 50 people at \$200 per
person (it includes food, transportation, and a seminar on the
mathematics of gambling).  For each additional person, up to a maximum
of 80 people total, {\it everyone's} fare is reduced by \$2.  Given
that it costs them \$6000 (a fixed cost for their offices, the busses,
licenses, etc.) plus \$32 per person to conduct the tour, how many
people does it take to maximize their profits?

\smallskip
\item{}  What if property taxes increase, and their fixed costs rise
to \$7000?  What if that happens {\bf and} the Louisiana state
legislature puts an \$8 per person tax on gambling tours?

\bigskip
\item{5.}  Max has decided to try to get on Dr. Davis's good side by
building a life-size origami statue of her as a gift.  He begins with
a sheet of paper that is 40' long and 60' wide, and wants the first
fold to be particularly special.  Specifically, the bottom right
corner is to be folded to a point on the left side so that the length
of the crease is a minimum.  To what point should Max fold the corner
to achieve this incredibly symbolic feat?

\bigskip
\item{6.}  Brandie and Bat-Girl show up at Brian's new sand box.
Bat-Girl says that burying He-Man is boring and she would rather do
Calculus!  Help Bat-Girl and Skeletor do the following problem from
one of Kathy's old exams:

\smallskip
\item{}  Let $f(x)=\sin x+\cos x$ on the interval $[0,2\pi]$.

\itemitem{1)}  Differentiate and simplify.

\itemitem{2)}  Find all points $c$ where $f'(c)=0$ or $f'(c)$ does not
exist.

\itemitem{3)}  Use the first derivative test to classify the above
points.

\itemitem{4)}  Find all local and global extremes.

\bigskip
\item{7.}  Inspired by recently seeing ``Saturday Night Fever''
Melanie is redecorating her 16'x12' dorm room in a disco theme.  Her
roommate opens the door and is shocked by the sight of a disco ball
rotating once every 2 seconds from the center of the ceiling.  Her
horror is replaced by a trance-like state as she is hypnotized from
tracking one of the spots of light spinning around the room.  As this
spot of light enters a corner going from a long wall to a short wall,
how fast is it moving?


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