If y varies inversely as x\(^2\), how does x vary with y?
MATHEMATICS
WAEC 1999
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
Correct Answer: B. x varies inversely as ?y
Explanation
\(y \propto \frac{1}{x^2}\)
\(y = \frac{k}{x^2}\)
\(x^2 = \frac{k}{y}\)
\(x = \frac{\sqrt{k}}{\sqrt{y}}\)
Since k is a constant, then \(\sqrt{k}\) is also a constant.
\(\therefore x \propto \frac{1}{\sqrt{y}}\)
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