Guse stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z) = 7yi + xzj + (x + y)k, c is the curve of intersection of the plane z = y + 9 and the cylinder x2 + y2 = 1. exp

By Stokes' theorem,

where is any oriented surface with boundary . We have

Take to be the ellipse that lies in the plane with boundary on the cylinder . Parameterize by

with and . Take the normal vector to to be

Then we have

the homeowners insurance cost for a 115,000 wood frame house is 80,500.

step-by-step explanation:

it is given that the coverage rate for wood frame house is 0.7.

the value of wood frame house is 115,000.

.

homeowners insurance cost for a 115,000 wood frame house is

therefore the homeowners insurance cost for a 115,000 wood frame house is 80,500.

363 square inches

step-by-step explanation:

surface area of a pyramid is b + 1/2ph

b is the area of the base: 11 x 11 = 121

p is the perimeter of the base: 11 + 11 + 11 + 11 = 44

h is the height of the pyramid: 11

121 + 1/2(44)(11)

121 + 242

363