Question

HELP ME!!! y is inversely proportional to square of x. Given that y=3 when x=7, find the value of x when y=18.375 TYSM!

Answer 1

The value of x is -2√2 or 2√2.

Explanation:

Given that y is inversely proportion to x², y ∝ 1/x². So the formula will be y = k/x² where k is the constant. In order, to find the value of k, you have to substitute the values of x and y into the formula :

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

`let \: x = 7 \\ let \: y = 3`

`3 = \frac{k}{ {7}^(2) }`

`3 = (k)/(49)`

`3 * 49 = k`

`k = 147`

`y = \frac{147}{ {x}^(2) }`

Next, you have to substitute the y value into the equation to find x :

`let \: y = 18.375`

`18.375 = \frac{147}{ {x}^(2) }`

`18.375 {x}^(2) = 147`

`{x}^(2) = (147)/(18.375)`

`{x}^(2) = 8`

`x = ± √(8)`

`x = - 2 √(2) \: \: or \: \: 2 √(2)`