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.
Properly identifying and assigning the proper variables to each part of the problem before attempting to solve it
One way to solve this is by changing the mixed numbers to improper functions.
3 1/3 = 10/3
2 2/5 = 12/5
The next step I would take is to find a common denominator.
10/3 = 50/15
12/5 = 36/15
Now we can solve the original equation:
50/15 - 36/15 = 14/15
Since 14/15 is already simplified this is your final answer.
Answer:
y=a/(9+3x)
Step-by-step explanation:
Reverse: 9y+3xy=a
y(9+3x)=a
y=a/(9+3x)
