SOLUTION: ``Given that X is inversely proportional to the square of Y. It is known that x = 8 for a particular value of Y. When Y is increased by 200%, find (a) the value of X, (b) the per

Algebra ->  Equations -> SOLUTION: ``Given that X is inversely proportional to the square of Y. It is known that x = 8 for a particular value of Y. When Y is increased by 200%, find (a) the value of X, (b) the per      Log On


   

Question 1038500: ``Given that X is inversely proportional to the square of Y. It is known that x = 8 for a particular value of Y. When Y is increased by 200%, find
(a) the value of X,
(b) the percentage change in the value of X''.
Answer by Othel(27) About Me  (Show Source):
You can put this solution on YOUR website!
We are told that X is inversely proportional to the square of Y. So...
Y%5E2=%281%2FX%29 or...X=%281%2FY%5E2%29
Let us use the first of the two options.
If x=8, then Y%5E2=%281%2F8%29
And...

Now we will raise our value of Y by 200%...
%28%282%2Asqrt%282%29%29%2F4%29=%281%2FX%29
Now just a little algebra...
%282%2AX%2Asqrt%282%29%29=4
Then..

After raising Y by 200%, the value of X is...
X=sqrt%282%29
And comparing this to our first value of x, we find that when X=8, and then Y is raised by 200%, X is DECREASED by Approximately 82.3 %.
1-%28sqrt%282%29%2F8%29=.8232233047
Check your answer!
I hope this helps! Learn on!
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