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
Explicació
\(y \propto \frac{1}{x^2}\)
\(y = \frac{k}{x^2}\)
\(x^2 = \frac{k}{y}\)
\(x = \frac{\sqrt{k}}{\sqrt{y}}\)
Since k is a constant, then \(\sqrt{k}\) is also a constant.
\(\therefore x \propto \frac{1}{\sqrt{y}}\)