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The temperature T in a metal ball is inversely proportional to the distance from the center...

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Basic Math

The temperature T in a metal ball is inverselyproportional to the distance from the center of the ball, which wetake to be the origin. The temperature at the point (1, 2, 2) is160°.

(a) Find the rate of change of T at (1, 2, 2) in thedirection toward the point (3, 1, 4).

(b) Show that at any point in the ball the direction of greatestincrease in temperature is given by a vector that points towardsthe origin.

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