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Please help quick. 9. Let F...

Please help quick.

9. Let F be any vector field of the form F(x,y, z) = f (x) i+g(y) j+h(z)k

and let G be any vector field of the form G(x,y, z) = f (y, z) i+g(x, z) j+h(x,y)k.

Indicate whether the following statements are true or false by placing ”T” or ”F” to

the left of the statement.

1. G is incompressible

2. F is incompressible

3. F is irrotational

4. G is irrotational

10.

A vector field gives a geographical description of the flow of money in a society. In the neighborhood of a political convention,

the divergence of this vector field is:

• A. negative

• B. positive

• C. zero

11. Evaluate Double_Integral_S sqrt(1+x^2+y^2) dS where S is the helicoid:

r(u,v) = ucos(v)i+usin(v)j+vk, with 0 <= u <= 1,0 <= v <= 3pi

12. Let S be the part of the plane 3x+3y+z = 4 which

lies in the first octant, oriented upward. Find the flux of the

vector field F = 2i+3j+3k across the surface S.

13. Suppose F is a radial force field, S1 is a sphere of

radius 9 centered at the origin, and the flux integral

Double_Integral_S1 F·dS= 2.

Let S2 be a sphere of radius 36 centered at the origin, and consider

the flux integral

Double_integral_S2 F·dS.

(A) If the magnitude of F is inversely proportional to the

square of the distance from the origin,what is the value of

Double_Integral_S2 F·dS?

(B) If the magnitude of F is inversely proportional to the cube

of the distance from the origin, what is the value of

Double_integral_S2 F·dS?

Please I need the answers as quick as possible

9. Let F be any vector field of the form F(x,y, z) = f (x) i+g(y) j+h(z)k

and let G be any vector field of the form G(x,y, z) = f (y, z) i+g(x, z) j+h(x,y)k.

Indicate whether the following statements are true or false by placing ”T” or ”F” to

the left of the statement.

1. G is incompressible

2. F is incompressible

3. F is irrotational

4. G is irrotational

10.

A vector field gives a geographical description of the flow of money in a society. In the neighborhood of a political convention,

the divergence of this vector field is:

• A. negative

• B. positive

• C. zero

11. Evaluate Double_Integral_S sqrt(1+x^2+y^2) dS where S is the helicoid:

r(u,v) = ucos(v)i+usin(v)j+vk, with 0 <= u <= 1,0 <= v <= 3pi

12. Let S be the part of the plane 3x+3y+z = 4 which

lies in the first octant, oriented upward. Find the flux of the

vector field F = 2i+3j+3k across the surface S.

13. Suppose F is a radial force field, S1 is a sphere of

radius 9 centered at the origin, and the flux integral

Double_Integral_S1 F·dS= 2.

Let S2 be a sphere of radius 36 centered at the origin, and consider

the flux integral

Double_integral_S2 F·dS.

(A) If the magnitude of F is inversely proportional to the

square of the distance from the origin,what is the value of

Double_Integral_S2 F·dS?

(B) If the magnitude of F is inversely proportional to the cube

of the distance from the origin, what is the value of

Double_integral_S2 F·dS?

Please I need the answers as quick as possible

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