What's an expression with a value of 12
2 answers:
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Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
The amount of drinks is a linear function of the number of drinks. The maximum amount that can be purchased is 100 soft drinks.
Let
amount of drinks
number of drinks
For drinks not more than 50
For drinks more than 50.
For a purchase of $85, it means that:
So, we solve for x in both equations.
Collect like terms
Divide through by 0.8
--- approximated
Collect like terms
Divide by 0.7
By comparing both values:
Hence, the maximum amount that can be purchased is 100
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