Suppose you are climbing a hill whose shape is given by theequation
z = 1400 ?0.005x2 ?0.01y2,
where x, y, and z are measured inmeters, and you are standing at a point with coordinates (60, 40,1366). The positive x-axis points east and the positivey-axis points north.
(a) If you walk due south, will you start to ascend ordescend?
At what rate?
vertical meters per horizontal meter
(b) If you walk northwest, will you start to ascend or descend?
At what rate? (Round your answer to two decimal places.)
vertical meters per horizontal meter
(c) In which direction is the slope largest?
What is the rate of ascent in that direction?
vertical meters per horizontal meter
At what angle above the horizontal does the path in that directionbegin? (Round your answer to two decimal places.)
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