Question

The value of y varies inversely as the square of x, and y = 16, when I = 3.

Find the value of x when y = 1.​

Answer 1

x = 12

Explanation:

The statement

The value of y varies inversely as the square of x is written as

`y = \frac{k}{ {x}^(2) }`

where k is the constant of proportionality

To find the value of x when y = 1 first find the formula for the variation

y = 16 x = 3

k = yx²

k = 16(3)²

k = 16 × 9

k = 144

The formula for the variation is

`y = \frac{144}{ {x}^(2) }`

when y = 1

We have

`1 = \frac{144}{ {x}^(2) }`

Cross multiply

x² = 144

Find the square root of both sides

We have the final answer as

x = 12

Hope this helps you