If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show

Let
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that
.
So, we can write the given integral as

Splitting up terms and replacing
in the first integral, we get

Answer:
13.2 minutes or 13 minutes 12 seconds.
Step-by-step explanation:
1. Count how much water drains the first pump every minute. Let the volume of pool be D. Every minute first pump drains D/11 water.
2. Working together(6 minutes) First pump drains 6D/11 water, hence the second pump drains 5D/11 water.
3.Count how much water drains second pump per minute -> (5D/11)/6= 5D/66
4. It takes the second pump 66 minutes to drain pool 5 times, thus it takes 13.2(66/5) minutes to drain the pool, which is 13 minutes 12 seconds.
The answer is: -3y+9z
This is because you simply switch the sign for every number in the parentheses.
Hope this helps!
Answer:
The slope of the given two points is 
Step-by-step explanation:
Given two points are (-5,2) and (3,9)
To find the slope with these two points
Let
and
be the given points
By using Slope Formula:


( subtracting and adding the corresponding terms)

Therefore slope is 
The slope of the given two points is 
If I'm correct you should make a fraction first
5.4 3.6
----- to -----
4.8 ?
Now find the missing number
5.4 to 3.6 would be a difference of ÷ 1.5 so you must do the same for 4.8
÷<span>1.5 </span>
5.4 3.6
----- to -----
4.8 3.2
÷1.5
The tail length should be 3.2 feet