7. On a certain mountain range, the level is z = 1200 -0.02x² -0.04y². points north. The climber is at the p a. If he begins to walk northeast, wi mountain? At what rate? b. If he wants to descend as quickly direction should he begin to move? direction?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 38E
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7. On a certain mountain range, the elevation z above a point (x,y) in the xy-plane at sea
level is z = 1200 -0.02x² -0.04y2. The positive x-axis points east, and the positive y-axis
points north. The climber is at the point (80, 100, 672). [5]
a. If he begins to walk northeast, will he be ascending the mountain or descending the
mountain? At what rate?
b. If he wants to descend as quickly as possible from the point (80, 100, 672), in what
direction should he begin to move? At what rate will his altitude change in that
direction?
Transcribed Image Text:7. On a certain mountain range, the elevation z above a point (x,y) in the xy-plane at sea level is z = 1200 -0.02x² -0.04y2. The positive x-axis points east, and the positive y-axis points north. The climber is at the point (80, 100, 672). [5] a. If he begins to walk northeast, will he be ascending the mountain or descending the mountain? At what rate? b. If he wants to descend as quickly as possible from the point (80, 100, 672), in what direction should he begin to move? At what rate will his altitude change in that direction?
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