If y varies inversely as the square of x and y=144 when x=4, find y when x=12
Please explain the steps to me I'd really like to understand!!

Step-by-step explanation:

In inverse variation, as increase in the value of variable causes a corresponding decrease in the value of the other variable and a decrease in the value of that variable causes a corresponding increase in the value of the other variable.

Since y varies inversely as the square of x, we would introduce k, the constant of variation. It becomes

y = k/x

When x = 4, y = 144

Therefore

144 = k/4

k = 4 × 144 = 576

The expression becomes

y = 576/x

Therefore, when x = 12,

y = 576/12 = 48

48

Step-by-step explanation:

y varies inversely as the square of x

y ∝ 1/x

y =k/x

yx=k k is the unit of constant

y=144, x=4

144x4 = k = 576

the constant k is 576 when y =144 and x=4

to find y when x=12

y =k/x= 576/12 = 48