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steposvetlana [31]
3 years ago
9

A rectangular box is to have a square base and a volume of 60 ft3. the material for the base costs 33¢/ft2, the material for the

sides costs 10¢/ft2, and the material for the top costs 20¢/ft2. letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
Mathematics
1 answer:
vodomira [7]3 years ago
5 0
The base and top have the same area, so we can add their costs.
.. cost of base + cost of top = (0.33 +0.20)*x^2 . . . . . . . . x measured in feet

The height of the box wil be (60/x^2), and the total length of all sides is the perimeter of the base, 4x. Then the cost of the sides is
.. cost of sides = (0.10)*(60/x^2)*(4x) = 24/x

The total cost of material for the box is
.. total cost = cost of base + cost of top + cost of sides
.. total cost = 0.53x^2 +24/x . . . . . . . . . . dollar cost for x in feet
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Water weighs 62.4 pounds per cubic foot. How much does the water in a tank that measures 7 ft × 4 ft × 9 in, weigh?
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Answer:

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Explanation:

<u>1) Calculate the volume of the water in the tank.</u>

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  • Height of the tank: H = 9 in = 9 in × 1 ft / 12 in = 0.75 ft
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<u>2) Calculate the weight of 21 ft³ of water.</u>

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So, rounding to the next integer, the water in the tank weighs 1,310 pounds, when it is full.

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