If y varies directly as x and inversely as the square of z and if $y = 20$ $y=20$ when $x = 50$ $x=50$ and $z = 5$ $z=5$ how do you find y when $x = 3$ $x=3$ and $z = 6$ $z=6$ ?

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If y varies directly as x and inversely as the square of z and if $y = 20$ $y=20$ when $x = 50$ $x=50$ and $z = 5$ $z=5$ how do you find y when $x = 3$ $x=3$ and $z = 6$ $z=6$ ?

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Answer 1 · 2018-05-09T19:27:35

$y = \frac{5}{6}$ $y=5/6$

Explanation:

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

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

$\Rightarrow y = k \times \frac{x}{z^{2}} = \frac{k x}{z^{2}}$ $rArry=kxx x/z^2=(kx)/z^2$

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

$y = 20 when x = 50 and z = 5$ $y=20" when "x=50" and "z=5$

$y = \frac{k x}{z^{2}} \Rightarrow k = \frac{y z^{2}}{x} = \frac{20 \times 25}{50} = 10$ $y=(kx)/z^2rArrk=(yz^2)/x=(20xx25)/50=10$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(10x)/z^2)color(white)(2/2)|))$

$"when "x=3" and "z=6" then"$

$y=(10xx3)/36=30/36=5/6$

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If y varies directly as x and inversely as the square of z and if $y = 20$ $y=20$ when $x = 50$ $x=50$ and $z = 5$ $z=5$ how do you find y when $x = 3$ $x=3$ and $z = 6$ $z=6$ ?

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Explanation:

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Math

Humanities

... and beyond

If y varies directly as x and inversely as the square of z and if y=20y=20y=20 when x=50x=50x=50 and z=5z=5z=5 how do you find y when x=3x=3x=3 and z=6z=6z=6?

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Explanation:

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Impact of this question

If y varies directly as x and inversely as the square of z and if $y = 20$ $y=20$ when $x = 50$ $x=50$ and $z = 5$ $z=5$ how do you find y when $x = 3$ $x=3$ and $z = 6$ $z=6$ ?