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

  • A x varies inversely as y2
  • B x varies inversely as √y
  • C x varies directly as y2
  • D x varies directly as y
waec 1999mathematics

The correct answer is B. x varies inversely 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.

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

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