Question

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

Answer 1

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

Answer 2

The change in the temperature.

As per the question, the temperatures at the point of x and y on a flat plate of metal is put by the formula of T(x, y)=19 and(2+x^2+y^2). The T represents the measure of Celsius and the X, Y are given in meters.  The temperature of the points x, y  proves.

The answer is based in the changes in properties of metallic plate. Hence function of coordinates gives us  -1.551

• As the temperature of the points x and y are found to be on a flat metal plate they can be a partial derivative of functions according to x and y at a point of coordinates

• The 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). Thus the point 1,2dT/dx is  -38/49 = -0.7755dT/d y = -76/49 or -1.551.

Find out more information about the changes in temperature

brainly.com/question/3672197.