Question

z varies directly with x and inversely with y^2. When x=2 and y=5, z=8. What is the value of z when x=4 and y=9

Answer 1

z varies directly with x and inversely with y^2

therefore
\[z = \frac{kx}{y^2}\]
when x = 2 and y = 5 then z = 8
\[8 = \frac{2k}{5^2}\]
\[8 = \frac{2k}{25}\]
\[200 = 2k\]
\[k = 100\]
when x = 4 and y = 9
\[z = \frac{kx}{y^2}\]
\[z = \frac{(100)(4)}{9^2}\]
\[z = \frac{400}{81}\]

Answer 2

got that?

Answer 3

Yea that makes sense! Thank you!

Answer 4

<tips hat>