8. Let F = (4xyz + ay², 2r²z+ bry, 2r2y), where a and b are real-valued constants, be the velocity field of a fluid. (a) Find div F. the sphere (b) Use the Divergence Theorem to evaluate fF.dS, where S is the surface of the portion of radius R with y 20 and z 20. All three surfaces of the solid are included in S, and S is oriented outward. Your answer should contain a and b. (c) Is the net flow into the surface, out of the surface, or zero? Why? 1) Use curl F to determine all values of a and b for which F is conservative. If a and b have these values, how does this effect for your answers for (b) and (c) (if at all)?

Q: f c = 12, what is 4 + c?

A: given,  c=12 let  A=4+c

Q: How do you complete part g for this question

A:

Q: Solution for h?

A:

Q: 8 in images

A: It is an important part of statistics . It is widely used .

Q: Preliminary work Evaluate Vx? + 6x dr.

A:

Q: Your missing the part d solution

A: First three parts are as solved before.

Q: c/6 = 18

A:

Q: thank you! could you show me how to do d

A: We will be using the Washer method to find the volume of the solid generated when R is revolved…

Q: Entegrate. your reark dx 4+25,2

A:

Q: Mulitipication or cross products property    96  = b 45    20

A: We have, By cross multiplication,

Q: What is the value of r?

A: Calculated values :  N1 = 200  dN1/dt = 100    N2 = 400  dN2/dt = 160

Q: Solve. (a-4)(a+7)=0

A: We need to solve the equation (a−4)(a+7)=0