Q44 the temperature function T(x, y) = 100/(3x^2 + y^2) represents the temperature of a point (x,y) on a rectangular metal plate, solve the following: (a) Determine the rate of change of T at the point (5, 8) in the direction of the vector (-3,-4). Round your answer to 6 decimal places (b) Find a unit vector in the direction of the maximum increase of T at the point (5, 8). Write your answer symbolically with no decimal places. (c) Calculate the maximum rate of change of T at the point (5, 8). Round your answer to 6 decimal places.
Q44 the temperature function T(x, y) = 100/(3x^2 + y^2) represents the temperature of a point (x,y) on a rectangular metal plate, solve the following: (a) Determine the rate of change of T at the point (5, 8) in the direction of the vector (-3,-4). Round your answer to 6 decimal places (b) Find a unit vector in the direction of the maximum increase of T at the point (5, 8). Write your answer symbolically with no decimal places. (c) Calculate the maximum rate of change of T at the point (5, 8). Round your answer to 6 decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q44
the temperature function T(x, y) = 100/(3x^2 + y^2) represents the temperature of a point (x,y) on a rectangular metal
plate, solve the following:
(a) Determine the rate of change of T at the point (5, 8) in the direction of the vector (-3,-4). Round your answer to 6
decimal places
(b) Find a unit vector in the direction of the maximum increase of T at the point (5, 8). Write your answer symbolically with
no decimal places.
(c) Calculate the maximum rate of change of T at the point (5, 8). Round your answer to 6 decimal places.
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