Question

Find the average value of the function f ( x , y , z ) = 5 x 2 z + 5 y 2 z over the region enclosed by the paraboloid z = 9 x 2 y 2 and the plane z = 0.

Answer 1

Answer:

y=−z100z2+36

Step-by-step explanation:

5 x 2 z + 5 y 2 z

10yz + 10z + 9 x 2 y 2 + z + z = 0

10yz(10)z+(9)(2)y(2)+z=0

Step 1: Add -z to both sides.

100yz2+36y+z+−z=0+−z

100yz2+36y=−z

Step 2: Factor out variable y.

y(100z2+36)=−z

Step 3: Divide both sides by 100z^2+36.

y(100z2+36)100z2+36=−z100z2+36

y=−z100z2+36