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

Question

3 years ago

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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 x-direction
(b) the y-direction

Mathematics

1 answer:

jok3333 [9.3K] · Answer 1 · 2022-03-12T11:46:35+03:00

Just 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)^2dT/dy = -38y/(2 + x^2 + y^2)^2 (only difference is the y in the numerator)
so at point 1,2dT/dx = -38/49 = -0.7755dT/dy = -76/49 = -1.551