Use the divergence theorem to compute the net outward flux of the following field across the given surface s.

f = < 8y^2 - 3x, -9x+4y, -2y^3 +z >

s is the sphere {(x, y,z): x^2 + y^2 + z^2 = 9}

find net outward flux across the surface.

Flux across S = 72π

Step-by-step explanation:

First we need to calculate the divergence of the vector field:

Div F =

Where

Fx = 8y^2 - 3x

Fy = -9x+4y

Fz = -2y^3 +z

Then

Div F = -3 +4 + 1  = 2

And how the vector field’s divergence is a constant, we can calculate the flux across of the surface how:

Flux across S = Div F * Volume of Sphere

Fluz acroos S = 2(4/3)π

                 r : Sphere’s radio

Flux across S = (2)(4/3)π

                       = 72π

1) the property is   ixi = a ⇔x = a   o x = -a

4(x-5)+3= 15⇒4x-20+3 = 15⇒4x-17= 15⇒4x = 15+17⇒4x = 32⇒x =32/4= 8

4(x-5) +3= -15⇒4x-20 +3 = -15⇒4x-17= -15⇒4x =-15+17⇒4x = 2⇒x =2/4= 1/2

the values are x =8 and x = 0,5

17,000 is the correct answer.