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The temperature at a point (x, y, z) is given by T(x, y, z) = 1000e-x²-2y-z2 where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -3,2) in the direction toward the point Q(3,-5, 3). Answer: D f(2,-3, 2) = (-16000*sqrt(6))/3)(e^(-26)) PQ 2. In what direction does the temperature increase fastest at P? Answer:

The temperature at a point (x, y, z) is given by T(x, y, z) = 1000e-x²-2y-z2 where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -3,2) in the direction toward the point Q(3,-5, 3). Answer: D f(2,-3, 2) = (-16000*sqrt(6))/3)(e^(-26)) PQ 2. In what direction does the temperature increase fastest at P? Answer:

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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I don't know how to get number two but I know it is a vector so can you express it in vector format. And what I calculated for z is incorrect so what did I do wrong?

The temperature at a point (x, y, z) is given by T(x, y, z) = 1000e 2-2y² –z² where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, –3, 2) in the direction toward the point Q(3, –5, 3). Answer: D f (2, –3, 2) = (-16000*sqrt(6))/3)(e^(-26)) PQ 2. In what direction does the temperature increase fastest at P? Answer:
Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, z) = 1000e 2-2y² –z² where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, –3, 2) in the direction toward the point Q(3, –5, 3). Answer: D f (2, –3, 2) = (-16000*sqrt(6))/3)(e^(-26)) PQ 2. In what direction does the temperature increase fastest at P? Answer:
If the gradient of f is Vf = y° j – xi + zyk and the point P f(x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. (-8, 6, 2) lies on the level surface = Z (8x/12-216y/12+1816/12)
Transcribed Image Text:If the gradient of f is Vf = y° j – xi + zyk and the point P f(x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. (-8, 6, 2) lies on the level surface = Z (8x/12-216y/12+1816/12)
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