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(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(52)/(2^2) \\ \text{Operating:} \\ 39=k\cdot(52)/(4) \\ 39=k\cdot13 \end{gathered}`

Solving for k:

`k=(39)/(13)=3`

The relationship is now:

`y=3\cdot(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(18)/(3^2) \\ y=3\cdot(18)/(9) \\ y=3\cdot2=6 \end{gathered}`

y = 2