# How do you write the equation if R is inversely proportional to the square of I and I = 25 when R = 100?

Apr 14, 2018

$R = \frac{62500}{I} ^ 2$

#### Explanation:

$\text{the initial statement is } R \propto \frac{1}{I} ^ 2$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow R = k \times \frac{1}{I} ^ 2 = \frac{k}{I} ^ 2$

$\text{to find k use the given condition}$

$I = 25 \text{ when } R = 100$

$R = \frac{k}{I} ^ 2 \Rightarrow k = R {I}^{2} = 100 \times {25}^{2} = 62500$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{R = \frac{62500}{I} ^ 2} \textcolor{w h i t e}{\frac{2}{2}} |}}}$