Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}

The area of the surface is the sum of all given areas.

Step-by-step explanation:

Adding Z to R,

(X^2 + Y^2) + (X^2 - Y^2 + 64) <= 64

"<=" represents "less than or equal to"

Opening brackets,

X^2 + X^2 + Y^2 - Y^2 + 64 <= 64

2X^2 + 64 <= 64

Divide through by 2;

X^2 + 32 <= 32

Hence X squared is less than or equal to zero.

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft

step-by-step explanation:

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