Question

Suppose you are climbing a hill whose shape is given by the equation $z = 1600 - 0.005x^2 - 0.01y^2$, where $x$, $y$, and $z$ are measured in meters, and you are standing at a point with coordinates $(120, 80, 1464)$. The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? ascend 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 direction begin? (Round your answer to two decimal places.)

          Suppose you are climbing a hill whose shape is given by the equation $z = 1600 - 0.005x^2 - 0.01y^2$, where $x$, $y$, and $z$ are measured in meters, and you are standing at a point with coordinates $(120, 80, 1464)$. The positive x-axis points east and the positive y-axis points north.
(a) If you walk due south, will you start to ascend or descend?
ascend
descend
At what rate?
vertical meters per horizontal meter
(b) If you walk northwest, will you start to ascend or descend?
ascend
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 direction begin? (Round your answer to two decimal places.)

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Suppose you are climbing a hill whose shape is given by the equation z = 1600 - 0.005x^2 - 0.01y^2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north.
(a) If you walk due south, will you start to ascend or descend?
ascend
descend
At what rate?
vertical meters per horizontal meter
(b) If you walk northwest, will you start to ascend or descend?
ascend
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 direction begin? (Round your answer to two decimal places.)

Added by Joel R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Qbs Educator

04/14/2022

Step 1

The partial derivative of the equation with respect to y at the point (120, 80, 1464) will give us the rate of change in the z direction (up or down the hill) as we move in the y direction. The partial derivative of the equation with respect to y is -0.02y. At the Show more…

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