Question

Suppose y varies inversely as x², and y = 64 when x = 1/4. Find y when x = 7.

Answer 1

Finding the proportionality constant :

• y = k/x²
• 64 = k/(1/4)²
• k = 4

Finding y when x = 7 :

• y = 4/(7)²
• y =  4/49

The value of y is 4/49 when x = 7.

Answer 2

$y = \frac{k}{ {x}^{2} } \\ \\ 64 = \frac{k}{ { (\frac{1}{4}) }^{2} } \\ \\ 64 = \frac{k}{ \frac{1}{16} } \\ \\ 64 = 16k \\ \\ k = \frac{64}{16} \\ \\ k = 4.$

Finding 'y'

$y = \frac{4}{ {7}^{2} } \\ \\ y = \frac{4}{49} .$