Answer:
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Length x width x height</h2>
Step-by-step explanation:
This is how you get the area of a shape.
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Explanation:</h2><h2>
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Here we need to write a function that models each variation, so we know that:
![x = \frac{1}{3} \\ \\ y = \frac{1}{5} \\ \\ r = 3 \\ \\ z = \frac{1}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20%5C%5C%20y%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%5C%5C%20%5C%5C%20r%20%3D%203%20%5C%5C%20%5C%5C%20%20z%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
We also know that z varies directly with x and inversely with the product of r² and y. In other words, we can write z as follows:
![z=k\frac{x}{r^2y} \\ \\ \\ \text{Where k is a real constant.} \\ \\ \\ \text{By substituting x,y,r and z into the equation we can get k:} \\ \\ \\ \frac{1}{2}=k\frac{\frac{1}{3}}{3^2(\frac{1}{5})^2} \\ \\ \frac{1}{2}=k\frac{\frac{1}{3}}{\frac{9}{25}} \\ \\ \frac{1}{2}=k(\frac{25}{27}) \\ \\ k=\frac{27}{50}](https://tex.z-dn.net/?f=z%3Dk%5Cfrac%7Bx%7D%7Br%5E2y%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BWhere%20k%20is%20a%20real%20constant.%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BBy%20substituting%20x%2Cy%2Cr%20and%20z%20into%20the%20equation%20we%20can%20get%20k%3A%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%3Dk%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B3%5E2%28%5Cfrac%7B1%7D%7B5%7D%29%5E2%7D%20%5C%5C%20%5C%5C%20%20%5Cfrac%7B1%7D%7B2%7D%3Dk%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B9%7D%7B25%7D%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%3Dk%28%5Cfrac%7B25%7D%7B27%7D%29%20%5C%5C%20%5C%5C%20k%3D%5Cfrac%7B27%7D%7B50%7D)
Therefore, the model is:
![\boxed{z=\frac{27}{50}\frac{x}{r^2y}}](https://tex.z-dn.net/?f=%5Cboxed%7Bz%3D%5Cfrac%7B27%7D%7B50%7D%5Cfrac%7Bx%7D%7Br%5E2y%7D%7D)
The equation would be 6x+x=63. Not sure how the models play out, but good luck