Question 38

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Jambmaths question: 

If p varies inversely as cube of q and q varies directly as square of r. What is the relationship between p and r

Option A: 

p varies directly as r3

Option B: 

p varies inversely as r

Option C: 

p varies inversely as $\sqrt[6]{r}$

Option D: 

p varies directly as r6

Jamb Maths Solution: 

$\begin{align}  & p\propto \frac{1}{{{q}^{3}}} \\ & p=\frac{k}{{{q}^{3}}}----(i)\text{   (}k\text{ is the constant of proportionality)} \\ & q\propto {{r}^{2}} \\ & q=x{{r}^{2}}----(ii)\text{  (}x\text{ is the constant of proportionality)} \\ & \text{substitute }x{{r}^{2}}\text{ for }q\text{ in equation(}i\text{)} \\ & p=\frac{k}{{{(x{{r}^{2}})}^{3}}}=\frac{k}{{{x}^{3}}{{r}^{6}}}=\frac{k}{{{x}^{3}}}\left( \frac{1}{{{r}^{6}}} \right) \\ & \text{Where }\frac{k}{{{x}^{3}}}=z\text{   (}z\text{ is the constant of proportionality}) \\ & p=\frac{z}{{{r}^{6}}} \\ & p\propto \frac{1}{{{r}^{6}}} \\ & p\text{ varies inversely as }{{r}^{6}} \\\end{align}$

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