If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

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If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

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Answer 1 · 2017-05-02T18:55:45

$y = 324$ $y=324$

Explanation:

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

$\Rightarrow the initial statement is y \propto \frac{1}{x^{2}}$ $rArr"the initial statement is " yprop1/(x^2)$

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

$\Rightarrow y = k \times \frac{1}{x^{2}} = \frac{k}{x^{2}}$ $rArry=kxx1/x^2=k/x^2$

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

$y = \frac{k}{x^{2}} \Rightarrow k = x^{2} y$ $y=k/x^2rArrk=x^2y$

$given x = 9 when y = 64$ $"given " x=9" when " y=64$

$\Rightarrow k = 9^{2} \times 64 = 5184$ $rArrk=9^2xx64=5184$

$rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5184/x^2)color(white)(2/2)|)))$

$"when x = 4 then"$

$y=5184/16=324$

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If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

1 Answer

Explanation:

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