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

Answer:

The value of x is -2√2 or 2√2.

Step-by-step 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 :

$y = \frac{k}{ {x}^{2} }$

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

$3 = \frac{k}{ {7}^{2} }$

$3 = \frac{k}{49}$

$3 \times 49 = k$

$k = 147$

$y = \frac{147}{ {x}^{2} }$

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

$let \: y = 18.375$

$18.375 = \frac{147}{ {x}^{2} }$

$18.375 {x}^{2} = 147$

${x}^{2} = \frac{147}{18.375}$

${x}^{2} = 8$

$x = ± \sqrt{8}$

$x = - 2 \sqrt{2} \: \: or \: \: 2 \sqrt{2}$