Use the divergence theorem to compute the net outward flux of the following field across the given surface s. f = < x^2, y^2, z^2 > ; s is the sphere {(x, y, z) : x^2 + y^2 + z^2 = 25}

In this exercise we have to use the divergent theorem to calculate the flow of the given equation, so we will find that:

So from the given equation, we will find that:

where the region with as its boundary. Convert to spherical coordinates, taking:

Then the volume integral is:

See more about Divergence Theorem at link

By the divergence theorem,

where the region with as its boundary. Convert to spherical coordinates, taking

Then the volume integral is

c

step-by-step explanation:

c

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15