A thin metal plate located in the center of the xy plane has a temperature T(x, y) at the point(x,y) given by T(x, y) = 100/(1 + x^2 + y^2) . (a) What is the temperature on the plate at point (1, 2), approximately? (b) At what point is the temperature as high as possible? (c) If a particle moves away from the origin, moving along the positive x axis, Will the temperature increase or decrease?
A thin metal plate located in the center of the xy plane has a temperature T(x, y) at the point(x,y) given by T(x, y) = 100/(1 + x^2 + y^2) . (a) What is the temperature on the plate at point (1, 2), approximately? (b) At what point is the temperature as high as possible? (c) If a particle moves away from the origin, moving along the positive x axis, Will the temperature increase or decrease?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A thin metal plate located in the center of the xy plane has a temperature T(x, y) at the point(x,y) given by
T(x, y) = 100/(1 + x^2 + y^2) .
(a) What is the temperature on the plate at point (1, 2), approximately? (b) At what point is the temperature as high as possible? (c) If a particle moves away from the origin, moving along the positive x axis, Will the temperature increase or decrease? (d) At what points is the temperature 50? (e) The contour lines of T are called isotherms (because all points on a of these curves have the same temperature). Sketch some isotherms of that function.
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