A 273 -ft^3 pool is to be built with a square bottom of side length x. The sides are built with tiles and the bottom with cement. The cost per unit of tiles is $77 /ft2 while the cost of the bottom is $22 /ft2. Write the total cost C as a function of x.

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Mathematics

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23 August, 06:44

A 273 -ft^3 pool is to be built with a square bottom of side length x. The sides are built with tiles and the bottom with cement. The cost per unit of tiles is $77 /ft2 while the cost of the bottom is $22 /ft2. Write the total cost C as a function of x.

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Jasper · Answer 1

If the bottom is a square with sides equal to x then, the area is equal to x². The height of the pool is then equal to,

273/x²

Solving for the cost,

sides: (273/x²) (x) (4) (77) = $84084/x

bottoms: x² (22) = 22x²

Adding up all the cost will give us an answer of,

84084/x + 22x²