If varies inversely as the cube root of , then, if are the initial values of the variables and are the final values,

Substitute and find :

Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:

20*6=24*x

120=24x

x=120/24

x=5

In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.

If varies inversely as the square of , then, if are the initial values of the variables and are the final values,

.

Substitute and find :

This rounds to 3.5.

If varies inversely as the cube of , then, if are the initial values of the variables and are the final values,

Substitute and find :

This rounds to 2.3.

If varies inversely with the square root of , then, if are the initial values of the variables and are the final values,

.

Substitute and find :

To find the inverse of a function we need to first switch the and . Therefore, becomes

We now solve for y by subtracting 1 from each side

From here we divide both sides by 2 which results in

To find the inverse we first switch the variables then solve for y.

Then we subtract from each side

Now we divide by to get our final answer. When we divide by we are left with . When we divide by we are left with . Thus resulting in:

To find the inverse we first switch the x and y variables

Now we add 4 to each side

From here to isolate y we need to multiply each side by 2

By distributing the 2 we get our final solution:

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

1. Switch the and variables in the above equation.

2. Solve for :