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?

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Answer 1 · 2016-04-15T10:55:20

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

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#