Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization r(u, v) = (u, v, 7565 -0.02u² -0.03v²) with u² + v² ≤ 10,000, where distance is measured in meters. The air pressure P(x, y, z) in the neighborhood of Mount Wolf is given by P(x, y, z) = 31e(-7x² + 4y² + 2z) Then the composition Q(u, v) = (Por)(u, v) gives the pressure on the surface of the mountain in terms of the u and y Cartesian coordinates. (a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.) მQ მu aq Əv -(50, 25) = (50, 25) = (b) What is the greatest rate of change of the function Q(u, v) at the point (50, 25)? (Round your answer to two decimal places.) û = (c) In what unit direction û = (a, b) does Q(u, v) decrease most rapidly at the point (50, 25)? (Round a and b to two decimal places. (Your instructors prefer angle bracket notation <> for vectors.)
Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization r(u, v) = (u, v, 7565 -0.02u² -0.03v²) with u² + v² ≤ 10,000, where distance is measured in meters. The air pressure P(x, y, z) in the neighborhood of Mount Wolf is given by P(x, y, z) = 31e(-7x² + 4y² + 2z) Then the composition Q(u, v) = (Por)(u, v) gives the pressure on the surface of the mountain in terms of the u and y Cartesian coordinates. (a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.) მQ მu aq Əv -(50, 25) = (50, 25) = (b) What is the greatest rate of change of the function Q(u, v) at the point (50, 25)? (Round your answer to two decimal places.) û = (c) In what unit direction û = (a, b) does Q(u, v) decrease most rapidly at the point (50, 25)? (Round a and b to two decimal places. (Your instructors prefer angle bracket notation <> for vectors.)
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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Transcribed Image Text:Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization
r(u, v) = (u, v, 7565 -0.02u² - 0.03v²)
with u² + v² ≤ 10,000, where distance is measured in meters. The air pressure P(x, y, z) in the neighborhood of Mount Wolf is given by
P(x, y, z) = 31e(-7x² + 4y² +
Then the composition Q(u, v) = (Por)(u, v) gives the pressure on the surface of the mountain in terms of the u and ✓ Cartesian coordinates.
(a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.)
aQ
au
მი
Əv
-(50, 25)
2z)
-(50, 25) =
û =
(b) What is the greatest rate of change of the function Q(u, v) at the point (50, 25)? (Round your answer to two decimal places.)
(c) In what unit direction û = (a, b) does Q(u, v) decrease most rapidly at the point (50, 25)? (Round a and b to two decimal places. (Your instructors prefer angle bracket notation <> for vectors.)
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