Question 14

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waecmaths question: 

If $p=\tfrac{3}{5}\sqrt{\tfrac{q}{r}}$ express q in term of p and r

Option A: 

$\tfrac{9}{25}p{{r}^{2}}$  

Option B: 

$\tfrac{9}{25}{{p}^{2}}r$

Option C: 

$\tfrac{25}{9}{{p}^{2}}r$

Option D: 

$\tfrac{25}{9}p{{r}^{2}}$

waecmaths solution: 

$\begin{align}  & p=\frac{3}{5}\sqrt{\frac{q}{r}} \\ & \frac{5p}{3}=\sqrt{\frac{q}{r}} \\ & {{\left( \frac{5p}{3} \right)}^{2}}=\frac{q}{r} \\ & \frac{25{{p}^{3}}}{9}=\frac{q}{r} \\ & q=\frac{25{{p}^{2}}r}{9} \\\end{align}$

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