Question

If x varies inversely as y 2, and x = 2 when y = 20, find x when y = 5.

Answer 1

Explanation:

`x = (k)/(y)`

x varies inversely as y. This means that x is equal to the inverse of y which can be translated as x = 1/y but the problem said that x is not exactly equal to the inverse of y. Therefore, we need to introduce a factor k. Factor k will represent the word "varies" in the problem.

To illustrate:

`x = (k)/(y)`

Since we don't have the value of k, we have to solve for it by using the first values of x and y which was given as x=2 and y=20.

`x = (k)/(y) \\ 2 = (k)/(20) \\ k = 2(20) = 40`

Now that we have the value of k, we can now solve for the value of x when y=5.

`x = (k)/(y) \\ = (40)/(5) \\ = 8`

Therefore, when y is 5, the value of x is 8.