y varies inversely

Question

If y varies inversely with the square of? x, and
y=14
when
x=5
find y when
x=0.2

Answer 1

Jessica,

An inverse relationship means essentially that as one gets bigger, the other gets smaller. The way we set that up is with the equation  y = k/x, where k is a constant to be determined. In your problem, since y varies inversely with the square of x, we use:

 

y = k/x²  

 

We plug in the first set of givens to determine the value of k:

 

14 = k/5²              multiply by 25

 

14*25 = k             solve

 

k = 350  

 

Now use k to find the y that corresponds to x = .2

 

y = 350/.2 = 1750

 

I hope that helps

Answer 2

Hi Jessica,

The statement y varies inversely with the square of x in mathematical terms is      y = k/x² .  Substitute 14 for y and 5 for x which results in 

                                   14 = k/5²

Multiply both sides by 25 gives us the value of k = 350. When x = 0.2, then  y = 350/ (0.2)² = 8750