Answer:
Let x represent the edge dimension of the square base in feet. Then the area of the base or lid is x², and the height of the box is 5/x². Total cost is then ...
... cost = cost of lid + 4×(cost of one side) + cost of bottom
... cost = 0.2x² + 4×(0.2x(5/x²)) + 0.5x²
... cost = 0.7x² + 4/x
We can differentiate this with respect to x and set that derivative to zero. This will give us the x-value at which the cost is a minimum.
... d(cost)/dx = 1.4x -4/x² = 0
... x³ = 4/1.4
... x = ∛(20/7) ≈ 1.419
Then the height of the box is
... height = 5/x² ≈ 5/2.01351 ≈ 2.483
The box is 1.491 ft square and 2.483 ft high.
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The average cost of the top and bottom is (0.2 +0.5)/2 = 0.35 per square foot. The overall cost will be minimized when the average cost of each face is the same. That is, the areas of the lateral faces will be equal and must be 0.35/0.2 = 1.75 times the area of the top or bottom to make the average cost of a lateral face equal to that of the top or bottom. Hence, the base will be square, and the box will be 1.75 times as high as it is wide or deep. The base edge dimension is then ∛(5/1.75) ≈ 1.419 ft.
Step-by-step explanation:
Answer:
15 dollars
Step-by-step explanation:
If you were to convert 3/4 and 4/5 to have the same denominator it would be 15/20 and 16/20.
Now we compare. This should be easy...
Its 4/5 or 16/20.
For the answer to the question above asking, how much gas will you have to buy i<span>f you drive 50 miles each week and your car gets 25 miles to the gallon with gas costing $4.00 per gallon?
</span>The car will use 2 gallons of gas per week at $4 per gallon so you will have to buy $8 per week.
i hope my answer helped you.
The answer with Be B good choice