Proportion/Intermediate

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Problem

$x$ is directly proportional to the sum of the squares of $y$ and $z$ and inversely proportional to $y$ and the square of $z$ . If $x = 8$ when $y = 1/2$ and $z = \sqrt {3}/2$ , find $y$ when $x = 1$ and $z = 6$ . (Thanks to Bicameral of the AoPS forum for this one)

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Proportion/Intermediate

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