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, 2, 2) is 120 degrees. a. Find the rate of change of T at (1, 2, 2) in the direction toward the point (2, 1, 3).b. Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points at the origin
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, 2, 2) is 120 degrees. a. Find the rate of change of T at (1, 2, 2) in the direction toward the point (2, 1, 3).b. Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points at the origin
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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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, 2, 2) is 120 degrees.
a. Find the rate of change of T at (1, 2, 2) in the direction toward the point (2, 1, 3).
b. Show that at any point in the ball the direction of greatest increase in temperature is given by a
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