Question

Suppose that y varies inversely as the square of x, and that y = 9 when x = 15. What is y when x 2? Round your answer to two decimal places if necessary.

Answer 1

Y varies inversely as the square of x. This relationship can be expressed as

$y=\frac{k}{x^2}$

where k is a constant. we need to find the value of k

To do that, we use the provided data, y = 9 when x = 15. Substituting in the above equation:

$9=\frac{k}{15^2}$

Solving for k:

$k=9\cdot15^2=2,025$

The equation is, then:

$y=\frac{2,025}{x^2}$

We finally need to find the value of y when x = 2:

$y=\frac{2,025}{2^2}=\frac{2,025}{4}=506.25$

y is 506.26 when x = 2