Suppose you go up a hill whose shape is given by the equation z = 1000 - 0.005x2 - 0.01y2, where x, y and z are measured in meters and you are at a point with coordinates (60,40,966). The positive x axis points east and the positive y axis points north. a) If you walk south, will you begin to ascend or descend? For what reason? b) If you walk northeast, will you begin to climb or descend? At what rate? c) In which direction is the slope greater? What is the rate of ascent in that direction? d) At what angle above the horizontal does the trajectory begin in that dir
Suppose you go up a hill whose shape is given by the equation
z = 1000 - 0.005x2 - 0.01y2, where x, y and z are measured in meters and you are at a point with coordinates (60,40,966). The positive x axis points east and the positive y axis points north.
a) If you walk south, will you begin to ascend or descend? For what reason?
b) If you walk northeast, will you begin to climb or descend? At what rate?
c) In which direction is the slope greater? What is the rate of ascent in that direction?
d) At what angle above the horizontal does the trajectory begin in that direction?
Note: To solve take into account the topics partial derivatives, directional derivative and the gradient
Note2: Answer all the items that are requested
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