Question

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

Answer 1

Step-by-step explanation:

$x = \frac{k}{y}$

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:

$x = \frac{k}{y}$

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.

$x = \frac{k}{y} \\ 2 = \frac{k}{20} \\ k = 2(20) = 40$

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

$x = \frac{k}{y} \\ = \frac{40}{5} \\ = 8$

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