proportionality

Proportionality

Unit 4.3 Ratio and proportion

y is inversely proportional to $d^{2}$ .

When d =10, y =4

d is directly proportional to $x^{2}$

When x = 2, d = 24

Find a formula for y in terms of x . Give your answer in its simplest form.

$y α \frac{1}{d^{2}} \Rightarrow y = \frac{k}{d^{2}}$ $4 = \frac{k}{10^{2}} = 4 x 100 = k$ ( given y = 4 and d = 10 )

$y = \frac{400}{d^{2}} \to (1$ )

b) $d α x^{2} \Rightarrow d = k x^{2}$

$\begin{array}{l} d = 24, x = 2 \\ 24 = k {(2)}^{2} \Rightarrow 24 = 4 k \end{array}$

$\begin{array}{l} K = \frac{24}{4} = 6 \\ d = 6 x^{2} \to (2) \end{array}$

$y = \frac{400}{d^{2}}; d = 6 x^{2}$ ( substitute $d = 6 x^{2}$ in equation 1 )

$y = \frac{400}{6 x^{2}} \Rightarrow \frac{200}{3 x^{2}}$

$y = \frac{200}{3 x^{2}}$

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