This problem has been solved! see the answerverify that the line intergral and the surface integral of stokes theorem are equal for the following vector field, surface s and closed curve c. assume that c has counterclockwise orientation and s has a consistent orientation. f= < x, y,z> ; s is the paraboloid z = 13 - x^2 - y^2, for 0 less than or equal z less than or equal 13 and c is the circle x^2 + y^2 = 13 in the xy plane.

Line integral: Parameterize by

with . Then

Surface integral: By Stokes' theorem, the line integral of over is equivalent to the surface integral of the curl of over :

The curl of is 0, so the value of the surface integral is 0, as expected.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.