If y varies directly as x and inversely as the square of z and if y=20  when x=50 and z=5 how do you find y when x=3 and z=6?

May 9, 2018

$y = \frac{5}{6}$

Explanation:

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

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

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

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

$y = 20 \text{ when "x=50" and } z = 5$

$y = \frac{k x}{z} ^ 2 \Rightarrow k = \frac{y {z}^{2}}{x} = \frac{20 \times 25}{50} = 10$

"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(10x)/z^2)color(white)(2/2)|))

$\text{when "x=3" and "z=6" then}$

$y = \frac{10 \times 3}{36} = \frac{30}{36} = \frac{5}{6}$