The temperature in °C on the surface of a metal plate is given by T(x, y) = 20-4x - y, where x and y are measured in inches. a) In what direction from (2,-3) does the temperature increase most rapidly? What is this rate of increase? b) Provide a contour man and draw the
The temperature in °C on the surface of a metal plate is given by T(x, y) = 20-4x - y, where x and y are measured in inches. a) In what direction from (2,-3) does the temperature increase most rapidly? What is this rate of increase? b) Provide a contour man and draw the
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:8. The temperature in °C on the surface of a metal plate is given by T(x, y)= 20-4x² - y² , where x and y
%3D
are measured in inches.
a) In what direction from (2,-3) does the temperature increase most rapidly?
What is this rate of
increase?
b) Provide a contour map and draw the vector that indicates the direction of most rapid increase at (2,-3).
c) What is the hottest point on the plate? Note that the vector does not point toward the hottest point on the
plate. That is because the gradient provides only a local solution to finding a maximum increase.
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