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Suppose the function f (x, y, z) = 2x – 3y + z – 20 gives the temperature, in degrees Fahrenheit, at a point (x, y, z). (a) Describe the isothermal surfaces of f. (b) Calculate and interpret f- (0, 0,0). (c) If you are standing at the point (0, 0, o), in what direction should you move to increase your temperature the fastest? (d) Is f (x, y) = -2x + 3y + 17 an isothermal surface of f? If so, what is the temperature on this isotherm?

Suppose the function f (x, y, z) = 2x – 3y + z – 20 gives the temperature, in degrees Fahrenheit, at a point (x, y, z). (a) Describe the isothermal surfaces of f. (b) Calculate and interpret f- (0, 0,0). (c) If you are standing at the point (0, 0, o), in what direction should you move to increase your temperature the fastest? (d) Is f (x, y) = -2x + 3y + 17 an isothermal surface of f? If so, what is the temperature on this isotherm?

Advanced Engineering Mathematics
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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19. Suppose the function f (x, y, z) = 2x – 3y + z – 20 gives the temperature, in degrees Fahrenheit, at a point (x, y, z). (a) Describe the isothermal surfaces of f. (b) Calculate and interpret fz (0, 0,0). (c) If you are standing at the point (0, 0, 0), in what direction should you move to increase your temperature the fastest? (d) Is f (x, y) = -2x + 3y + 17 an isothermal surface of f? If so, what is the temperature on this isotherm?
Transcribed Image Text:19. Suppose the function f (x, y, z) = 2x – 3y + z – 20 gives the temperature, in degrees Fahrenheit, at a point (x, y, z). (a) Describe the isothermal surfaces of f. (b) Calculate and interpret fz (0, 0,0). (c) If you are standing at the point (0, 0, 0), in what direction should you move to increase your temperature the fastest? (d) Is f (x, y) = -2x + 3y + 17 an isothermal surface of f? If so, what is the temperature on this isotherm?
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