# How do you write a specific formula to describe the variation: S varies jointly with the inverse of the square of P and inversely with the cube of L; S=6 when P=8, L=10?

May 10, 2017

Variation equation is $S = 384000 \cdot \frac{1}{{P}^{2} \cdot {L}^{3}}$

#### Explanation:

$S \propto \frac{1}{P} ^ 2 \mathmr{and} S \propto \frac{1}{L} ^ 3$ When varies jointly,

$S \propto \frac{1}{{P}^{2} \cdot {L}^{3}} \mathmr{and} S = k \cdot \frac{1}{{P}^{2} \cdot {L}^{3}} \therefore k = S \cdot {P}^{2} \cdot {L}^{3}$ "k" is a constant.

$S = 6 , P = 8 , L = 10 \therefore k = 6 \cdot {8}^{2} \cdot {10}^{3} = 384000$

So variation equation is $S = 384000 \cdot \frac{1}{{P}^{2} \cdot {L}^{3}}$ [Ans]