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\centerline{\bf GAUSS'S LAW}
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Suppose you are standing on a hill. You have a topographic map, which uses rectangular coordinates (x; y) measured in miles. Your global positioning system says your present location is at one of the following points (pick
one):

\large
A: (1, 4) \hs  B: (4, 9) \hs  C: (4, 9)

D: (1, 4) \hs  E: (2, 0) \hs  F: (0, 3)
\normalsize

Your guidebook tells you that the height h of the hill, in feet above sea level
is given by:

$$h(x, y) = (2xy - 3x^{2} - 4y^{2} - 18x + 28y + 1200)$$

\begin{itemize}
\item Where is the top of the hill located?
\item How high is the hill?
\item Draw a topographic map of the hill (your map should have at least 3
level curves; label your location on the map). What is your height?
\item Starting at your present location, in what compass direction (2-D unit
vector) do you need in order to climb the hill as steeply as possible?
\item How steep is the hill in you start at your present location and go in
this direction?
\item In what direction in space (3-d vector) would you actually be mov-
ing if you started at your present location and walked in the compass
direction you found in the previous problem?
\end{itemize}

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