WAEC - Mathematics (1999 - No. 18)

If y varies inversely as x\(^2\), how does x vary with y?

x varies inversely as y²

x varies inversely as √y

x varies directly as y²

x varies directly as y

\(y \propto \frac{1}{x^2}\)

\(y = \frac{k}{x^2}\)

\(x^2 = \frac{k}{y}\)

\(x = \frac{\sqrt{k}}{\sqrt{y}}\)

Since k is a constant, then \(\sqrt{k}\) is also a constant.

\(\therefore x \propto \frac{1}{\sqrt{y}}\)