Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,

Then

Then
x ≈ 21
Answer:
Roger can earn $510 at most.
Step-by-step explanation:
We are given the function

Which gives the earnings of Roger when he sells v videos. Since the play’s audience consists of 230 people and each one buys no more than one video, v can take values from 0 to 230, i.e.

That is the practical domain of E(v)
If Roger is in bad luck and nobody is willing to purchase a video, v=0
If Roger is in a perfectly lucky night and every person from the audience wants to purchase a video, then v=230. It's the practical upper limit since each person can only purchase 1 video
In the above-mentioned case, where v=230, then

Roger can earn $510 at most.
Make a change of coordinates:


The Jacobian for this transformation is

and has a determinant of

Note that we need to use the Jacobian in the other direction; that is, we've computed

but we need the Jacobian determinant for the reverse transformation (from

to

. To do this, notice that

we need to take the reciprocal of the Jacobian above.
The integral then changes to
