Question 48

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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: 

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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