SOLUTION: Y varies inversely as the square of x. When y is 10, x is 0.5. Find y when x is 4

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Question 1098164: Y varies inversely as the square of x. When y is 10, x is 0.5. Find y when x is 4
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Formally, you can represent this inverse variation with either
y+=+k%2Fx%5E2 or x%5E2y+=+k

I think inverse variation problems are easier to solve informally by thinking of the second of these forms as saying that the product of x^2 and y is a constant. If the product of two numbers is a constant, then if one goes up by a factor of x, the other has to go down by a factor of x.

In your example, the value of x went up by a factor of 8 (4/0.5 = 8); so the value of x^2 went up by a factor of 8^2=64. That means y has to go down by a factor of 64. So the new value of y is 10%2F64+=+5%2F32%29