by dy/dx, we'll be assuming that "y" is encapsulating a function, a function in terms of "x".

415800 gallons of water will be in the pool when it is 63% full
Well, the cos(∅) is negative in the second and third quadrants. If you are solving for theta, you would use the inverse of the cos or arccos

take the inverse of both sides to get:
x = arccos(-2/3) now evaluate the right
x = 131.8103149 degrees
to find your second solution, subtract your reference angle from 360 degrees.
360 - 131.8103149 = 228.1896851 degrees
Now the period of cos is 2π or 360 degrees. So if you want to consider all possible solutions, you would need to add/subtract 360n to both solutions above..
Not sure if this is what you're looking for, but thought I would leave it here for you just in case... As a side note, you could do this problem in radian measurement as well.
<h2>
Answer:</h2><h2 />
If we have two functions
such that
for every
in the domain of
, and
for every for every
in the domain of
. If we prove this, then
is the invers function of
and denoted by 
1. We need to prove whether
. So:


2. We need to prove whether
. So:

Since
, then:
are inverses to each other.
7,378,509,752,019 Is The Correct Answer!