# Whats the equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x= -0.5, z =4, and w = 5?

Nov 24, 2017

$y = - \frac{250 x z}{w} ^ 2$

#### Explanation:

$\text{the initial statement is } y \propto \frac{x z}{w} ^ 2$

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

$\Rightarrow y = k \times \frac{x z}{w} ^ 2 = \frac{k x z}{w} ^ 2$

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

$y = 20 \text{ when "x=-0.5,z=4" and } w = 5$

$y = \frac{k x z}{w} ^ 2 \Rightarrow k = \frac{y \times {w}^{2}}{x z} = \frac{20 \times {5}^{2}}{- 0.5 \times 4} = - 250$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{250 x z}{w} ^ 2} \textcolor{w h i t e}{\frac{2}{2}} |}}}$