Question

How do you find the variation constant and an equation of variation where y varies inversely as x and y = 6 when x = 14?

Answer 1

Variation constant is `84`

Explanation:

The maths symbol for proportional to is:`" "alpha`

Given that `" "y color(white)(.) alpha color(white)(.) 1/x`

Let `k` be the constant of variation giving

`y" "=" "kxx1/x" "=" "k/x`
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Given condition `color(blue)(" if "x=14" then "y=6)`

So by substitution

`color(brown)(y=k/x" "->" "color(blue)(6)=k/(color(blue)(14))`

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Multiply both sides by `color(green)(14)`

`=>color(blue)(6color(green)(xx14) color(brown)(=) (color(brown)(k))/14color(green)(xx14))`

`=>84=kxx14/14`
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But `14/14=1`

`84=kxx1`

`color(magenta)(k=84 -> "variation constant")`

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So `" "color(brown)(y color(white)(.) alpha color(white)(.) 1/x)" "->" "color(blue)(y=84/x)`