waecmaths question:
If $y\propto \frac{1}{{{x}^{2}}}$ and y = 1¼ when x = 4. Find the value of y when x = ½
Option A:
2½
Option B:
5
Option C:
10
Option D:
80
waecmaths solution:
$\begin{align} & y\propto \frac{1}{{{x}^{2}}} \\ & y=\frac{k}{{{x}^{2}}} \\ & \frac{5}{4}=\frac{k}{{{4}^{2}}} \\ & k=\frac{8\times {{4}^{2}}}{4}=20 \\ & \text{When }x=\frac{1}{2} \\ & y=\frac{k}{{{x}^{2}}}=\frac{20}{{{(\tfrac{1}{2})}^{2}}}=20\times 4=80 \\ \end{align}$
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