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b) Determine the rate of change in temperature at point A, in the direction from A to point B (2,1,3).

b) Determine the rate of change in temperature at point A, in the direction from A to point B (2,1,3).

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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Suppose that the temperature T (x, y, z) of a spherical metal part satisfies, for each point (x, y, z) on its surface, which is inversely proportional to the distance from the point to the origin of coordinates (that is, T = k/D). Furthermore, it is known that The temperature at point A (1,2,2) is 120 ° C. a) Determine the value of the constant k. b) Determine the rate of change in temperature at point A, in the direction from A to point B (2,1,3). c) In which direction does the temperature increase faster in the point A? d) Verify that at any point (x, y, z) on the sphere, the direction towards which the temperature increases most rapidly is given by a vector pointing toward the coordinate origin.
Transcribed Image Text:Suppose that the temperature T (x, y, z) of a spherical metal part satisfies, for each point (x, y, z) on its surface, which is inversely proportional to the distance from the point to the origin of coordinates (that is, T = k/D). Furthermore, it is known that The temperature at point A (1,2,2) is 120 ° C. a) Determine the value of the constant k. b) Determine the rate of change in temperature at point A, in the direction from A to point B (2,1,3). c) In which direction does the temperature increase faster in the point A? d) Verify that at any point (x, y, z) on the sphere, the direction towards which the temperature increases most rapidly is given by a vector pointing toward the coordinate origin.
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