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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 100°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4). 320 3√5 X (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points towards 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 100°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4). 320 3√5 X (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points towards 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
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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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 100°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4). 320 3√5 X (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points towards the origin.
Transcribed Image Text: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 100°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4). 320 3√5 X (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points towards the origin.
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