If \(y \alpha \frac{1}{x^2}\) and \(y = 1\frac{1}{4}\) when x = 4, find the value of y when \(x = \frac{1}{2}\)

  • A \(2\frac{1}{2}\)
  • B 5
  • C 10
  • D 80
waec 2005mathematics

The correct answer is D. 80

\(y \propto \frac{1}{x^2} \Rightarrow y = \frac{k}{x^2} \Rightarrow k = yx^2\\

k = 1\frac{1}{4} \times 4^2 \Rightarrow k=\frac{5}{4}\times \frac{16}{1}=20\\

∴y = 20 \div \left(\frac{1}{2}\right)^2=20\times \frac{4}{1}=80\)

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