You are on a hike. The altitude nearby is
described by the function \(f(x, y)= k x^{2}y\), where \(k=20 \mathrm{\frac{m}{km^3}}\)
is a constant, \(x\) and \(y\) are east and north coordinates,
respectively, with units of kilometers. You're standing at the spot
\((3~\mathrm{km},2~\mathrm{km})\) and there is a cottage located at \((1~\mathrm{km}, 2~\mathrm{km})\). You drop your water bottle and the water spills out.
- Plot the function \(f(x, y)\) and also its level curves in your favorite plotting software. Include images of these graphs.
Special note: If you use a computer program written by someone else, you must reference that appropriately.
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In which direction in space does the water flow?
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At the spot you're standing, what is the slope of the ground in the direction of the cottage?
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Does your result to part (c) make sense from the graph?