If $y$ $y$ varies inversely as the square of $x$ $x$ and $y = 4$ $y=4$ when $x = 5$ $x=5$ , what is $y$ $y$ when $x$ $x$ is $2$ $2$ ?

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If $y$ $y$ varies inversely as the square of $x$ $x$ and $y = 4$ $y=4$ when $x = 5$ $x=5$ , what is $y$ $y$ when $x$ $x$ is $2$ $2$ ?

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Answer 1 · 2017-06-06T08:24:47

$y = 25$ $y=25$

Explanation:

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

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

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

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

$y = 4 when x = 5$ $y=4" when " x=5$

$y = \frac{k}{x^{2}} \Rightarrow k = x^{2} y = 5^{2} \times 4 = 100$ $y=k/x^2rArrk=x^2y=5^2xx4=100$

$"the equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=100/(x^2))color(white)(2/2)|)))$

$"when "x=2$

$rArry=100/(2^2)=100/4=25$

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If $y$ $y$ varies inversely as the square of $x$ $x$ and $y = 4$ $y=4$ when $x = 5$ $x=5$ , what is $y$ $y$ when $x$ $x$ is $2$ $2$ ?

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If yyy varies inversely as the square of xxx and y=4y=4y=4 when x=5x=5x=5, what is yyy when xxx is 222?

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If $y$ $y$ varies inversely as the square of $x$ $x$ and $y = 4$ $y=4$ when $x = 5$ $x=5$ , what is $y$ $y$ when $x$ $x$ is $2$ $2$ ?