Question

. y is inversely proportional to the square of (x + 2).

When x = 3, y = 2. Find y when x = 8.​

Answer 1

Question :

y is inversely proportional to the square of (x + 2). When x = 3, y = 2. Find y when x = 8.​

Answer :

     y = 0.5 when x = 8

Given :

• y is inversely proportional to the square of (x + 2)
• When x = 3, y = 2

To find :

• value of y when x = 8

Solution :

 It is given,

=> y is inversely proportional to the square of (x + 2)

            $y \ \propto \ \frac{1}{(x+2)^2} \\\\ y \ = \ \frac{constant}{(x+2)^2}$

Now we know the relation between x and y,

i.e.,      $\boxed{\bf y \ = \ \frac{constant}{(x+2)^2} }$

=> When x = 3, y = 2

         substitute the values of x and y,

           $y=\frac{\text{constant}}{(x+2)^2} \\\\ 2=\frac{\text{constant}}{(3+2)^2} \\\\ 2=\frac{constant}{5^2} \\\\ 2=\frac{constant}{25} \\\\ constant = 2\times 25 \\\\ \boxed{\bf constant=50}$

Now, we got the value of constant.

=> To find y, when x = 8

          substitute the values of x and constant

          $y \ = \ \frac{constant}{(x+2)^2} \\\\ y=\frac{50}{(8+2)^2} \\\\ y=\frac{50}{10^2} \\\\ y=\frac{50}{100} \\\\y=\frac{1}{2} \\\\ \bf{y=0.5}$

∴ y = 0.5 when x = 8

Answer 2

Answer:

0.5

Step-by-step explanation:

Constant method is used