Jambmaths question:
The weight W kg of a metal varies jointly as its length L metres and the squares of its diameter d metres. If W =140kg when d =$4\tfrac{2}{3}metres$and L =54. Find d in terms of W and L
Option A:
$\frac{42W}{5L}$
Option B:
$\sqrt{\frac{42W}{5L}}$
Option C:
$\frac{5L}{42W}$
Option D:
$\sqrt{\frac{5L}{42W}}$
Jamb Maths Solution:
$\begin{align} & W=140,\text{ }d=4\tfrac{2}{3}=\tfrac{14}{3},\text{ }L54 \\ & W\propto L{{d}^{2}} \\ & W=kL{{d}^{2}}----(i) \\ & 10=k\times 54\times {{\left( \frac{14}{3} \right)}^{2}} \\ & k=\frac{140\times 9}{14\times 14\times 54}=\frac{5}{42} \\ & {{d}^{2}}=\frac{kL}{W}\text{ }\text{from equation}(i) \\ & d=\sqrt{\frac{kL}{W}}=\sqrt{\frac{5L}{42W}} \\\end{align}$
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