Jambmaths question:
T varies inversely as the cubes of R, when R =3, T = $\tfrac{2}{81}$, find T when R = 2
Option A:
$\tfrac{1}{24}$
Option B:
$\tfrac{1}{6}$
Option C:
$\tfrac{1}{12}$
Option D:
$\tfrac{1}{18}$
Jamb Maths Solution:
$\begin{align} & T\propto \frac{1}{{{R}^{3}}} \\ & T=\frac{K}{{{R}^{3}}} \\ & \text{when }R=2,T=\tfrac{2}{81} \\ & \frac{2}{81}=\frac{K}{{{3}^{3}}} \\ & K=\frac{2\times {{3}^{3}}}{81}=\frac{2}{3} \\ & \text{When }R=2 \\ & T=\frac{K}{{{R}^{3}}}=\frac{\tfrac{2}{3}}{{{2}^{3}}}=\frac{2}{3}\times \frac{1}{8}=\frac{1}{12} \\\end{align}$
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