Question

It is given that y is inversely proportional to the square of x and that y=48 when x=$\frac{1}{2}$.
Find;
(a), the formula for y in terms of x,
(b), the values of x when y=3.

Answer 1

Answer:

$a. y = 12\times \frac{1}{x^2} \\b. x = 2 , when \ y =3$

Step-by-step explanation:

$y \ is\ inversely \ proportional \ to \ square \ of \ x \ means , y \ \alpha \ \frac{1}{x^2}$

$Therefore, y = k \times \frac{1}{x^2}$

Given y = 48, x = 1/2. We will find k.

                 $y = k \times \frac{1}{x^2}\\\\48 = k \times \frac{1}{\frac{1}{4}}}\\\\k = 48 \times \frac{1}{4} =12$

Find x.

$y = k \times \frac{1}{x^2} \\\\3 = 12 \times \frac{1}{x^2}\\\\\frac{3}{12} = \frac{1}{x^2}\\\\x^2 = \frac{12}{3}\\\\x^2 = 4 \\\\x = 2$