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}{ { ((1)/(4)) }^(2) } \\ \\ 64 = (k)/( (1)/(16) ) \\ \\ 64 = 16k \\ \\ k = (64)/(16) \\ \\ k = 4.`

Finding 'y'

`y = \frac{4}{ {7}^(2) } \\ \\ y = (4)/(49) .`