Question

If z=T (x,y)=1/2 (square root(20-5x^2-5y^2)) represents the temperature at any point on a flat plate (in the xy plane) and draws a contour map of the isotherms.

Answer 1

The given equation represents the temperature at any point on a flat plate. To draw a contour map of the isotherms, we can choose different values for T and solve for (x, y). Each value of T will represent a different contour line.

Step-by-step explanation:

The given equation is z = T(x,y) =
`1/2(sqrt(20-5x^2-5y^2))`re at any point on a flat plate in the xy plane. To draw a contour map of the isotherms, we can choose different values for T and solve for (x, y). Each value of T will represent a different contour line.

For example, let's say we choose T = 0, then we have 0 =
`1/2(sqrt(20-5x^2-5y^2)).`get
`20-5x^2-5y^2 = 0,`ion of a circle centered at (0, 0) with radius sqrt(4) = 2.

Similarly, we can choose other values of T and solve for (x, y) to obtain other contour lines on the plate.