20x 10 to the third power equals 20000
The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.
The dimensions of your box will be 8 ft square by 4 ft high.
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If the base dimension is x ft, the area (quantity of material) is
... a = x² + 4x(256/x²)
... a = x² + 1024x⁻¹
Then the derivative of area with respect to x is
... a' = 2x -1024x⁻²
Setting this derivative to zero and solving for x gives the value of x for minimum area.
... 0 = 2x -1024/x²
... 512 = x³
... x = 8 . . . . . . . . same as above.
Answer:
Tip: $2.61
Total: $17.11
Step-by-step explanation:
tip = total cost * rate of tip
Add the tip to the original bill, that's the total.
I hope this helped.
Answer:
31.177 m
Step-by-step explanation:
So the formula of a hexagon is Area = (3√3 s^2)/ 2
s = side in this problem. A hexagon is made up of 6 equilateral triangles, so the distance from the center is equal to each of the sides.
For this problem, plug and chug. Plug your knowns into equation and you will find the answer.
s^2 = (2√3)^2 = 12
Area = (3√3 x 12)/2 = 31.1769 m
I am not sure how many decimals you are supposed to round, probably 3 so in that case 31.177 m
