# The force, f, between two magnets is inversely proportional to the square of the distance x between them. when x=3 f=4. How do you find an expression for f in terms of x and calculate f when x=2?

Jan 30, 2017

$f = \frac{36}{x} ^ 2$

$f = 9$

#### Explanation:

Break down the question into sections

The basic relationship as stated

$\text{ (1) The force" f " between two magnets}$ is
$\text{inversely proportional to the square of the distance "x}$

$\implies f \text{ "alpha" } \frac{1}{x} ^ 2$

$\text{ change to an eqn.}$

$\implies f = \frac{k}{x} ^ 2 \text{ where " k " is the constant of proportionality}$#

find the constant of proportionality

$\text{ (2) when } x = 3 , f = 4.$

$4 = \frac{k}{3} ^ 2$

$\implies k = 36$

$\therefore f = \frac{36}{x} ^ 2$

Now calculate $f$ given the $x$ value

$\text{ (3) } x = 2$

$f = \frac{36}{2} ^ 2 = \frac{36}{4} = 9$