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?
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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 7: Mountain Climbing and Elevation Change**
On a certain mountain range, the elevation \( z \) above a point \( (x, y) \) in the xy-plane at sea level is given by:
\[ z = 1200 - 0.02x^2 - 0.04y^2 \]
In this scenario:
- The positive x-axis points east.
- The positive y-axis points north.
The climber is currently at the point \( (80, 100, 672) \).
**Questions:**
a. If the climber begins to walk northeast, will they be ascending or descending the mountain? At what rate?
b. If the climber wants to descend as quickly as possible from the point \( (80, 100, 672) \), in what direction should they begin to move? At what rate will their altitude change in that direction?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14851614-7f15-4b21-be9e-fda332bc9b7d%2F6d6d04cf-2edd-47e3-885b-cc1da900eb2d%2Fe9vuxtwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7: Mountain Climbing and Elevation Change**
On a certain mountain range, the elevation \( z \) above a point \( (x, y) \) in the xy-plane at sea level is given by:
\[ z = 1200 - 0.02x^2 - 0.04y^2 \]
In this scenario:
- The positive x-axis points east.
- The positive y-axis points north.
The climber is currently at the point \( (80, 100, 672) \).
**Questions:**
a. If the climber begins to walk northeast, will they be ascending or descending the mountain? At what rate?
b. If the climber wants to descend as quickly as possible from the point \( (80, 100, 672) \), in what direction should they begin to move? At what rate will their altitude change in that direction?
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