The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e-x²-3y²-9z² (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). -10400 6 43 °C/m (b) In which direction does the temperature increase fastest at P? -18 <-2, 3 (c) Find the maximum rate of increase at P. -43√337 400e

The temperature at a point (x, y, z) is given by the following equation where T is measured in °C and x, y, z in meters. T(x, y, z) = 200e-x²-3y²-9z² (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -3, 3). -10400 6 43 °C/m (b) In which direction does the temperature increase fastest at P? -18 <-2, 3 (c) Find the maximum rate of increase at P. -43√337 400e

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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