Evaluate ∫∫s z ds, where s is the surface whose sides s1 are given by the cylinder x2 + y2 = 81, whose bottom s2 is the disk x2 + y2 ≤ 81 in the plane z = 0, and whose top s3 is the part of the plane z = 9 + x that lies above s2.

The integral of over is equal to the sum of the integrals of over .

Parameterize the surface by

with and . Take the normal vector to to be

Then the integral of over is

Parameterize by

with and . Since , the integral over is also 0.

Parameterize by

with and . The normal to is

so that the integral over is

Putting the results together, the integral of over is

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

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step-by-step explanation: