# Thread: inversely proprtional to the square

1. ## inversely proprtional to the square

hi

i am struggling on the following. any help much appreciated

a is inversely proportional to the square of b. if a =3.6 x 10 -3 when b=2.5, determine the law of proportionality.

what is the value of a when b =1.8

what is the value of b when a = 4 x 10-3

thanks

2. Originally Posted by paulhr1976
hi

i am struggling on the following. any help much appreciated

a is inversely proportional to the square of b. if a =3.6 x 10 -3 when b=2.5, determine the law of proportionality.

what is the value of a when b =1.8

what is the value of b when a = 4 x 10-3

thanks
Hi paulrh1976,

If a varies inversely as the square of b, then

$\displaystyle a=\frac{k}{b^2}$ where k is the constant of proportionality.

If $\displaystyle a=3.6 \times 10^{-3}$ when $\displaystyle b=2.5$, then

$\displaystyle 3.6 \times 20^{-3}=\frac{k}{(2.5)^2}$

Solve the above equation for k.

$\displaystyle \boxed{k=2.25 \times 10^{-2}}$

(1) Find a when b = 1.8

$\displaystyle a=\frac{k}{b^2}$

Solve this: $\displaystyle a=\frac{2.25 \times 10^{-2}}{(1.8)^2}$

(2) Find b when $\displaystyle a=4 \times 10^{-3}$

$\displaystyle a=\frac{k}{b^2}$

Solve this: $\displaystyle 4 \times 10^{-3}=\frac{2.25 \times 10^{-2}}{b}$