Question

If y varies inversely as the square of x and y = 8 when x = 2, then what is the value of y when x = -1?

Answer 1

The answer is `32`, based on an inverse proportionality model.

Explanation:

According to the statement,

`y prop 1/x^2`

This expression takes us to the exact formula:

`y = alpha / x^2`

where `alpha` is a constant of proportionality. To find it, we need a numerical value: `y(x=2) = 8`. By substituting:

`8 = alpha / 2^2 rightarrow alpha = 32`

So our formula is:

`y = 32 / x^2`

Now, let us calculate `y(x=-1)`:

`y = 32 / (-1)^2 = 32`