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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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.4: Combining And Decomposing Functions
Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...
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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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