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7.3 Heavy Metal(#differentiation) The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,3,2) is 100°C. (a) Derive a function T(x, y, z) that gives the temperature in the ball at the point (x, y, z). (b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0, 4, 2). (c) Show that at any point in the ball the direction of greatest increase in temper- ature is given by a vector that points toward the origin.

7.3 Heavy Metal(#differentiation) The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,3,2) is 100°C. (a) Derive a function T(x, y, z) that gives the temperature in the ball at the point (x, y, z). (b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0, 4, 2). (c) Show that at any point in the ball the direction of greatest increase in temper- ature is given by a vector that points toward the origin.

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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7.3 Heavy Metal(#differentiation) The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,3, 2) is 100°C. (a) Derive a function T(x, y, z) that gives the temperature in the ball at the point (x, y, z). (b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0,4, 2). (c) Show that at any point in the ball the direction of greatest increase in temper- ature is given by a vector that points toward the origin.
Transcribed Image Text:7.3 Heavy Metal(#differentiation) The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,3, 2) is 100°C. (a) Derive a function T(x, y, z) that gives the temperature in the ball at the point (x, y, z). (b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0,4, 2). (c) Show that at any point in the ball the direction of greatest increase in temper- ature is given by a vector that points toward the origin.
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