Dont understand how this works

**brianfisher1208** · Feb 26th 2010, 08:23 PM

Suppose y varies directly as the square of x and inversly as the cube of w. We know that y=9 when x=2 and w=1. Find y when x=4 and w=2.

**pflo** · Feb 26th 2010, 08:45 PM

Originally Posted by brianfisher1208

Suppose y varies directly as the square of x and inversly as the cube of w. We know that y=9 when x=2 and w=1. Find y when x=4 and w=2.

The first sentence is telling you the following formula is correct (where k is the 'constant of variation'): $y=k\frac{x^2}{w^3}$

Use the information in the second sentence to solve for k. Once you know that, you can use the equation to get the answer to the third sentence.

**Prove It** · Feb 26th 2010, 08:46 PM

Originally Posted by brianfisher1208

Suppose y varies directly as the square of x and inversly as the cube of w. We know that y=9 when x=2 and w=1. Find y when x=4 and w=2.

$y \propto x^2$ , so $y = k_1x^2$ .

Substitute $x$ and $y$ to find $k_1$ .

$y \propto \frac{1}{w^3}$ , so $y = \frac{k_2}{w^3}$ .

Substitute $w$ and $y$ to find $k_2$ .

Then you should be able to finish the question.

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