If y varies inversely as x and y = -3 when x = 6, how do you find x when y is 36?

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If y varies inversely as x and y = -3 when x = 6, how do you find x when y is 36?

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Answer 1 · 2017-04-26T20:16:42

$x = - \frac{1}{2}$ $x=-1/2$

Explanation:

$Inverse means \frac{1}{variable}$ $color(blue)"Inverse"" means " 1/"variable"$

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

$to convert to an equation multiply by k, the constant of variation$ $"to convert to an equation multiply by k, the constant of variation"$

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

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

$y = - 3 when x = 6$ $y=-3" when "x=6$

$y = \frac{k}{x} \Rightarrow k = x y = 6 \times - 3 = - 18$ $y=k/xrArrk=xy=6xx-3=-18$

$the equation is y = \frac{- 18}{x}$ $"the equation is " y=(-18)/x$

$to find x when y = 36$ $"to find x when y = 36"$

$y = \frac{- 18}{x} \Rightarrow x = \frac{- 18}{y}$ $y=(-18)/xrArrx=(-18)/y$

$\Rightarrow x = \frac{- 18}{36} = - \frac{1}{2}$ $rArrx=(-18)/36=-1/2$

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If y varies inversely as x and y = -3 when x = 6, how do you find x when y is 36?

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