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

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕