Suppose that y varies inversely as the square of x, and that y=4 when x=2. What is y when x=4? (Round to 2 decimal places)

Question

Suppose that y varies inversely as the square of x, and that y=4 when x=2. What is y when x=4? (Round to 2 decimal places)

Answer 1

y ∝ 1/x²

 

We can establish an equation using this equation.

 

y = K/x²

 

where K is constant.   We need to solve for K using the initial conditions.

 

K = yx²

   = 4(2)²

   = 4(4)

   = 16

 

Now we can use this value of K to find y when x = 4.

 

y = K / x²

y = 16 / (4)²

y = 16 / 16

y = 1