Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization (u, v) = (u, v, 7565 -0.02u²-0.03v²) with u²+² s 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)= 37e(-7x² + 4y² + 22), Then the composition Q(u, v) = (P)(u, v) gives the pressure on the surface of the mountain in terms of the u and v Cartesian coordinat (a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.)
Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization (u, v) = (u, v, 7565 -0.02u²-0.03v²) with u²+² s 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)= 37e(-7x² + 4y² + 22), Then the composition Q(u, v) = (P)(u, v) gives the pressure on the surface of the mountain in terms of the u and v Cartesian coordinat (a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.)
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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please help with part a and b
Transcribed Image Text:Consider the mountain known as Mount Wolf, whose surface can be described by the parametrization
-0.024² -0.03²)
(u, v) = (u, v, 7565 -
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) = 37e(−7x² + 4y² + 2z).
Then the composition Q(u, v) =
(a) Use the chain rule to compute the derivatives. (Round your answers to two decimal places.)
aQ
au
მQ
Əv
(50, 25) = -18.30
(Por)(u, v) gives the pressure on the surface of the mountain in terms of the u and y Cartesian coordinates.
-(50, 25) = 5.12
X
X
(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.)
19.00
X
(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.)
û = <.96,-.27> ✓
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