Difference between revisions of "Proportion/Intermediate"
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==Problem== | ==Problem== | ||
| − | <math>x</math> is directly proportional to the sum of the squares of <math>y</math> and <math>z</math> and inversely proportional to <math>y</math> and the square of <math>z</math>. If <math>x = 8</math> when <math>y = 1/2</math> and <math>z = \sqrt {3}/2</math>, find <math>y</math> when <math>x = 1</math> and <math>z = 6</math>. | + | <math>x</math> is directly proportional to the sum of the squares of <math>y</math> and <math>z</math> and inversely proportional to <math>y</math> and the square of <math>z</math>. If <math>x = 8</math> when <math>y = 1/2</math> and <math>z = \sqrt {3}/2</math>, find <math>y</math> when <math>x = 1</math> and <math>z = 6</math>. (Thanks to Bicameral of the AoPS forum for this one) |
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==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
Revision as of 17:02, 9 October 2007
Problem
is directly proportional to the sum of the squares of 
and 
and inversely proportional to and the square of . If 
when 
and 
, find when 
and 
. (Thanks to Bicameral of the AoPS forum for this one)
Solution
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