Question

Suppose z varies directly with x and inversely with the square of y. If z = 18 when I = 6 and y = 2, what is z when I 7 and y = 7? Z =

Answer 1

It is given that z varies directly with x and inversely with the square of y so it follows:

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

It is also given that z=18 when x=6 and y=2 so it follows:

$\begin{gathered} 18=k\frac{6}{2^2} \\ k=\frac{18\times4}{6} \\ k=12 \end{gathered}$

So the equation of variation becomes:

$z=12\frac{x}{y^2}$

Therefore the value of z when x=7 and y=7 is given by:

$\begin{gathered} z=\frac{12\times7}{7^2} \\ z=\frac{12}{7} \\ z\approx1.7143 \end{gathered}$

Hence the value of z is 12/7 or 1.7143.