Question

Suppose that y varies inversely as the square of x, and that y = 3 when x = 17. What is y when x = 3? Round your answer to two decimal places if necessary.

Answer 1

we know that

If y varies inversely as the square of x

then

the equation is equal to

$yx^2=k$

where

k is the contant of proportionality

step 1

Find the constant k

For y=3, x=17

substitute the given values

$\begin{gathered} 3(17^2)=k \\ k=867 \end{gathered}$

we have the equation

$yx^2=867$

step 2

Find the value of y when the value of x=3

substitute in the equation

$\begin{gathered} y3^2=867 \\ y=\frac{867}{9} \\ y=96.33 \end{gathered}$