If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?

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If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?

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Answer 1 · 2017-04-29T12:58:41

$y = 20$ $y=20$

Explanation:

$varies inversely means \frac{1}{variable}$ $"varies inversely means " 1/("variable")$

$the initial statement is y \propto \frac{1}{x}$ $"the initial statement is " yprop1/x$

To convert to an equation, multiply by k, the constant of variation.

$\Rightarrow y = k \times \frac{1}{x} = \frac{k}{x}$ $rArry=kxx1/x=k/x$

$to find k, use the condition given$ $"to find k, use the condition given"$

$that is y = 8 when x = 5$ $"that is " y=8" when " x=5$

$y = \frac{k}{x} \Rightarrow k = x y = 5 \times 8 = 40$ $y=k/xrArrk=xy=5xx8=40$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=40/x)color(white)(2/2)|)))$

$"when "x=2toy=40/2=20$

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If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?

1 Answer

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