# How do you find an equation of variation: y varies inversely as the square of x, and y = 0.15 when x= 0.1?

Apr 5, 2016

$y = \frac{0.0015}{x} ^ 2$

Or if you prefer $y = \frac{15}{10000 {x}^{2}}$

Or as scientific notation: $y = \frac{15}{{x}^{2}} \times {10}^{- 4}$

#### Explanation:

Splitting the question down into its component parts:

y varies inversely as: ->y=1/?

the square of ->y=1/(?^2)

$x \text{ } \to y = \frac{1}{{x}^{2}}$

But we need a constant of variation
Let the constant of variation be $k$ then we have:

$y = k \times \frac{1}{{x}^{2}}$
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$\textcolor{b l u e}{\text{Determine the value of } k}$

Known condition: at $y = 0.15 \text{; } x = 0.1$

So by substitution we have

$0.15 = k \times \frac{1}{{\left(0.1\right)}^{2}}$

$\implies k = 0.15 \times {\left(0.1\right)}^{2}$

$k = 0.15 \times 0.01$

To calculate this directly think of $0.01 \text{ as } \frac{1}{100}$

Then we have:

$k = \frac{0.15}{100} = 0.0015$

So the equation becomes:

$y = \frac{0.0015}{x} ^ 2$

Or if you prefer $y = \frac{15}{10000 {x}^{2}}$
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