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 3 years ago
The temperature at a point (x,y) on a flat metal plate is given by T(x,y)=19/(2+x^2+y^2), where T is measured in Celsuis and x,y in meters. Find the rate of change of temperature with respect to distance at the point (1,2) in the following directions.
(a) the xdirection
(b) the ydirection
 3 years ago
The temperature at a point (x,y) on a flat metal plate is given by T(x,y)=19/(2+x^2+y^2), where T is measured in Celsuis and x,y in meters. Find the rate of change of temperature with respect to distance at the point (1,2) in the following directions. (a) the xdirection (b) the ydirection

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3pwood
 3 years ago
Best ResponseYou've already chosen the best response.1Just need to take partial derivatives of the function with respect to x and y then plug in the point coordinates dT/dx = 38x/(2 + x^2 + y^2)^2 dT/dy = 38y/(2 + x^2 + y^2)^2 (only difference is the y in the numerator) so at point 1,2 dT/dx = 38/49 = 0.7755 dT/dy = 76/49 = 1.551
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