Given that curl f = 2yi – 2zj + 3k, find the surface integral of the normal component of curl f (not f) over (a) the open hemispherical surface x2 + y2 + z2 = 9, z > 0. (b) the sphere x2 + y2 + z2 = 9. (in both parts, you should be able to write the answer down by inspection.)

Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.

a. The boundary of the hemisphere is the circle in the plane , where the curl is . Green's theorem applies here, so that

which means the value of the line integral is 3 times the area of the circle, or .

b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.

b. -7,185,024p6q5

step-by-step explanation:

find the 6th term of the expansion of (2p - 3q)11. a. -7,185,024p4q7 c. -7,185p4q7 b. -7,185,024p6q5 d. -7,185p6q5 select the best answer from the choices provided a b c d

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column