# How do you write a specific formula to describe the variation:x varies directly with the cube root of y; x=3 when y = 125?

The variation formula may be written as $125 {x}^{3} = 27 y$
$x \propto \sqrt[3]{y} \mathmr{and} x = k \cdot \sqrt[3]{y}$ ; k= constant of proportionality
$x = 3$ when $y = 125 \therefore 3 = k \cdot \sqrt[3]{125} \mathmr{and} 3 = k \cdot 5 \mathmr{and} k = \frac{3}{5}$ So the variation formula may be written as $x = \frac{3}{5} \cdot \sqrt[3]{y} \mathmr{and} {x}^{3} = \frac{27}{125} \cdot y \mathmr{and} 125 {x}^{3} = 27 y$[Ans]