# Y varies inversely with the square of x, Given that y= 1/3 when x= -2, how do you express y in terms of x?

Apr 6, 2017

$y = \frac{4}{3 {x}^{2}}$

#### Explanation:

Since $y$ varies inversely with the square of $x$, $y \propto \frac{1}{x} ^ 2$, or $y = \frac{k}{x} ^ 2$ where $k$ is a constant.

Since $y = \frac{1}{3} \mathmr{if} x = - 2$, $\frac{1}{3} = \frac{k}{- 2} ^ 2$. Solving for $k$ gives $\frac{4}{3}$.

Thus, we can express $y$ in terms of $x$ as $y = \frac{4}{3 {x}^{2}}$.

Apr 6, 2017

$y = \frac{4}{3 {x}^{2}}$

#### Explanation:

Inverse means $\frac{1}{\text{variable}}$

The square of x is expressed as ${x}^{2}$

$\text{Initially } y \propto \frac{1}{x} ^ 2$

$\Rightarrow y = k \times \frac{1}{x} ^ 2 = \frac{k}{x} ^ 2$ where k is the constant of variation.

To find k use the given condition $y = \frac{1}{3} \text{ when } x = - 2$

$y = \frac{k}{x} ^ 2 \Rightarrow k = y {x}^{2} = \frac{1}{3} \times {\left(- 2\right)}^{2} = \frac{4}{3}$

$\Rightarrow \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{4}{3 {x}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}} \leftarrow \text{ is the equation}$

Apr 6, 2017

$Y = \frac{4}{3 {x}^{2}}$

#### Explanation:

Y varies inversely with square of x means

$Y = k \left(\frac{1}{x} ^ 2\right)$ where $k$ is a constant

plug in $Y = \frac{1}{3}$ and $x = - 2$ in the above equation.

$\frac{1}{3} = k \left(\frac{1}{- 2} ^ 2\right)$

$\frac{1}{3} = k \left(\frac{1}{4}\right)$

multiply with $4$ to both sides.

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

therefore,
$Y = \frac{4}{3} \left(\frac{1}{x} ^ 2\right) = \frac{4}{3 {x}^{2}}$