Question

If $A$ varies as $B$ and $C$ jointly, while $B$ varies as $D^2$, and $C$ varies inversely as $A$, show that $A$ varies as $D$.

Answer 1

According to question let,

$A=k\left(BC\right)$

$B=l\left(D^2\right)$

$C=\frac{m}{D}$

where $k,l,m$ are constants

Putting the values of $B,C$ in first equation

$A=k.l.D^2.\frac{m}{D}=\left(klm\right)D=nD$

where $n=klm$ a constant.

Hence proved