Question

y varies directly as x and inversely as the square of z. y = 39 when x = 52 and z=2. Find y when x= 18 and z = 3.y=

Answer 1

Proportions

We are told that y varies directly as x and inversely as the square of z. This can be written as:

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

Where k is the constant of proportionality. The value of k can be found by using the given point: y = 39 , x = 52 , z = 2

Substituting:

$\begin{gathered} 39=k\cdot\frac{52}{2^2} \\ \text{Operating:} \\ 39=k\cdot\frac{52}{4} \\ 39=k\cdot13 \end{gathered}$

Solving for k:

$k=\frac{39}{13}=3$

The relationship is now:

$y=3\cdot\frac{x}{z^2}$

Now we use the equation to know the value of y when x=18 and z=3:

$\begin{gathered} y=3\cdot\frac{18}{3^2} \\ y=3\cdot\frac{18}{9} \\ y=3\cdot2=6 \end{gathered}$

y = 2