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

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204