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

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours