# How do you write a general formula to describe each variation if T varies jointly with the cube root of x and the square of d; T=18 when x=8 and d=3?

Sep 6, 2017

$T = {d}^{2} \sqrt[3]{x}$

#### Explanation:

$\text{the initial statement can be expressed as}$

$T \propto {d}^{2} \sqrt[3]{x}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow T = k {d}^{2} \sqrt[3]{x}$

$\text{to find k use the given condition}$

$T = 18 \text{ when "x=8" and } d = 3$

$T = k {d}^{2} \sqrt[3]{x} \Rightarrow k = \frac{T}{{d}^{2} \sqrt[3]{x}} = \frac{18}{9 \times 2} = 1$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{T = {d}^{2} \sqrt[3]{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$