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The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). 200 √3e86 X °C/m (b) In which direction does the temperature increase fastest at P? 200 e86 <4,- 5,36 > X (c) Find the maximum rate of increase at P.

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). 200 √3e86 X °C/m (b) In which direction does the temperature increase fastest at P? 200 e86 <4,- 5,36 > X (c) Find the maximum rate of increase at P.

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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The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). 200 √3e86 X °C/m (b) In which direction does the temperature increase fastest at P? 200 e86 <4,- 5,36 > (c) Find the maximum rate of increase at P.
Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x² - 5y² - 9z² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -3, 6). 200 √3e86 X °C/m (b) In which direction does the temperature increase fastest at P? 200 e86 <4,- 5,36 > (c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by 300e-x²-3y² - 9z² T(x, y, z) = where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 3) in the direction towards the point (5, -3, 4). 3700 6 €100 °C/m S (b) In which direction does the temperature increase fastest at P? 600 €100 X (-4,3, -27) S X (c) Find the maximum rate of increase at P. 600 754 €100 S X
Transcribed Image Text:The temperature at a point (x, y, z) is given by 300e-x²-3y² - 9z² T(x, y, z) = where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 3) in the direction towards the point (5, -3, 4). 3700 6 €100 °C/m S (b) In which direction does the temperature increase fastest at P? 600 €100 X (-4,3, -27) S X (c) Find the maximum rate of increase at P. 600 754 €100 S X
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