1) Whistler, very popular ski hill in B.C., welcomes lots of skiers in the winter season. a) A skier's height z at (x, y), measured from the ground, is modeled by = f(x,y) = 2 – x² + 3xy – y³ + e(-1)². If the skier starts at the point (1,1), in which direction should the skier ski if he wants to move downhill the fastest? What is the rate of descent in this direction? b) When the skier moves downhill, his blood pressure is modeled by the function of three variables P(x, y, z) at every point (x, y, z) on the hill. If his path is described by w = x = 2 sin(t), y = 2 cos(t), z = T – t. find the rate of change of the skier's blood pressure at t = * using the data below: P«(2,0, T/2) = 4, Pr(0,2, 1/2) = 1 P,(2,0, 7/2) = 2, P,(0,2, /2) = 1 P:(2,0, 7 /2) = 1, P:(0,2, 7/2) = 2.
1) Whistler, very popular ski hill in B.C., welcomes lots of skiers in the winter season. a) A skier's height z at (x, y), measured from the ground, is modeled by = f(x,y) = 2 – x² + 3xy – y³ + e(-1)². If the skier starts at the point (1,1), in which direction should the skier ski if he wants to move downhill the fastest? What is the rate of descent in this direction? b) When the skier moves downhill, his blood pressure is modeled by the function of three variables P(x, y, z) at every point (x, y, z) on the hill. If his path is described by w = x = 2 sin(t), y = 2 cos(t), z = T – t. find the rate of change of the skier's blood pressure at t = * using the data below: P«(2,0, T/2) = 4, Pr(0,2, 1/2) = 1 P,(2,0, 7/2) = 2, P,(0,2, /2) = 1 P:(2,0, 7 /2) = 1, P:(0,2, 7/2) = 2.
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:1) Whistler, very popular ski hill in B.C., welcomes lots of skiers in the winter season.
a) A skier's height z at (x, y), measured from the ground, is modeled by
= f(x, y) = 2 – x² + 3xy – y3 + e(x-1)?.
Z =
If the skier starts at the point (1,1), in which direction should the skier ski if he wants to move downhill
the fastest? What is the rate of descent in this direction?
b) When the skier moves downhill, his blood pressure is modeled by the function of three variables
w = P(x, y, z) at every point (x, y, z) on the hill. If his path is described by
x = 2 sin(t),
y = 2 cos(t),
z = T – t.
find the rate of change of the skier's blood pressure at t = , using the data below:
Pa(2,0, T/2) = 4, P#(0,2, 7/2)
1
Py(2,0, 7/2) = 2, P,(0,2, T/2) = 1
P:(2,0, 1/2) = 1, P:(0,2, /2) = 2.
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