The temperature T at a point (x,y,z) in space is inversely proportional to the square of thedistance from (x,y,z) to the origin. It is known that 7(0,0,1)=500. Find the rate of change of Tat (2,3,3) in the direction of (3,1,1). In which direction from (2,3,3) does the Temperature Tincrease most rapidly? At (2,3,3) what is the maximum rate of change of T?

The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1)=500. Find the rate of change of T at (2,3,3) in the direction of (3,1,1). In which direction from (2,3,3) does the Temperature T increase most rapidly? At (2,3,3) what is the maximum rate of change of T?

The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1)=500. Find the rate of change of T at (2,3,3) in the direction of (3,1,1). In which direction from (2,3,3) does the Temperature T increase most rapidly? At (2,3,3) what is the maximum rate of change of T?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...

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