Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = 2yi + xzj + (x + y)k, c is the curve of intersection of the plane z = y + 6 and the cylinder x2 + y2 = 1.

By Stokes' theorem, the line integral of over is given by the surface integral of the curl of over , where is the region of intersection of the plane and the cylinder with having positive/upward orientation.

Parameterize by

with and .

Take the normal vector to to be

The curl of is

Then the line integral is equivalent to

idk

step-by-step explanation:

payback

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.