Use stokes' theorem to evaluate s ∫ f · ds. f(x, y, z) = x2 sin(z)i + y2j + xyk, s is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.

Look at the image,

Step-by-step explanation:

This is an explanation of the same exercise but when the paraboloid is z = 9 − x2 − y2.  In that case you just have to replace 9 by 4 and follow the same steps :).

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,