Question

14. Write a specific formula to describe the variation: x varies inversely with the square of y; X = 6 when y = 4.

Answer 1

We are told that "x" varies inversely with the square of "y". This means that the value of "x" must be given by the following relationship:

`x=(k)/(y^2)`

Inverse variation implies that when one variable increases the other decreases. Since "x" varies inversely with the square of "y" this means that when the square of "y" increases "x" must decrease, that is why we put the square of "y" in the denominator.

Now we need to determine the value of the constant "k". To do this we use the fact that when x 0 6 then y =4. We plug in those values in the previous relationship and we get:

`6=(k)/((4)^2)`

Now we solve the square:

`6=(k)/(16)`

Now we multiply both sides by 16:

`96=k`

Now we replace the value of "k" in the relationship:

`x=(96)/(y^2)`

And thus we got our formula.