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Masteriza [31]
3 years ago
15

A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.36/ft2, the material fo

r the sides costs $0.05/ft2, and the material for the top costs $0.14/ft2, determine the dimensions of the box that can be constructed at minimum cost.length ftwidth ftheight ft
Mathematics
1 answer:
blagie [28]3 years ago
6 0

Answer:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

Step-by-step explanation:

The total cost of the top and bottom is $0.36 + 0.14 = $0.50 per square foot.

The total cost of a pair of opposite sides is $0.05 +0.05 = $0.10 per square foot.

A minimum-cost box will have the cost of any pair of opposite sides be the same. Here, that means the box will have a side area that is 5 times the area of the top or bottom.

Since the base is square, that means the box is the shape of 5 cubes stacked one on the other. Each of those would be 8 ft³, so would have edge dimensions of ∛8 = 2 feet. The height is 5 times that, or 10 ft.

The box is 2 feet square by 10 feet high:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

_____

If you feel the need to write an equation, you can let x represent the edge length of the base. Then the cost of the top and bottom will be ...

  top&bottom cost = 0.50·x²

The height of the box is 40/x², so the cost of the four sides will be ...

  side cost = (0.05)(4x)(40/x²) = 8/x

This is minimized when the derivative of the sum of these costs is zero:

  cost = top&bottom cost + side cost

  cost = 0.50x² + 8/x

  d(cost)/dx = 1.00x -8/x² = 0

Multiplying by x², we get ...

  x³ -8 = 0

  x = ∛8 = 2 . . . . . . as above

  height = 40/x² = 40/4 = 10 . . . . . as above

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netineya [11]

Answer:

D; D

Step-by-step explanation:

The common difference of the first sequence is 10, so the coefficient is 10. The first term minus the common difference is -8, so that is the constant

The common difference of the second sequence is 3, so the coefficient is 3. The first term minus the common difference is -9, so that is the constant.

7 0
2 years ago
PLZ HELP AND EXPLAIN !! Arron borrowed $200 from his cousin. He promised to repay the loan in 2 years at a simple annual interes
Dmitriy789 [7]
The first thing you have to do is know the equation. The equation is a(1+p)^t.
a= the amount of money p= the percent represented as a decimal and t=time ( the t is raised as an exponent)
so, in this case, it is represented as 200(1+0.05)^2\
200(1.05)^2
200(1.1025)
220.5 That is how much extra he would owe in interest fee's

5 0
3 years ago
Giving brainliest to the answer who gives step by step examples clearly!
Anarel [89]

<em>Hi there!</em>

<em>This should be easy,lol!</em>

<em>Answer:</em>

<em />\sqrt[3]{-128} = \boxed{-128 \sqrt{3} }<em> (Decimal: -221.702503)</em>

<em />\sqrt[3]{162} = \boxed{162 \sqrt{3} }<em> (Decimal: 280.592231)</em>

<em />\sqrt[3]{-1000x^4} = \boxed{-1732.050808x^4}<em />

<em>Sorry bout the explanation thingy. Their really long -.-!</em>

<em>But the last one is short so i'll put it for you!</em>

<em>Step-by-step explanation:</em>

<em>∴!For the last one!∴</em>

<em />\sqrt[3]{-1000x^4}<em />

<em>Simplifies to:</em>

<em />= - 1732.050808 * x^4<em />

<em />= - 1732.050808 * ( x * x * x * x)<em> </em>

<em />= - 1732.050808x^4<em />

<em>Have a great day/night!</em>

7 0
3 years ago
Read 2 more answers
-6x-7=4x-2. Can you show step by step explanation. thank u.
monitta

Answer:

x=-1/2

Step-by-step explanation:

-6x-7=4x-2

-6x-7+6x=4x+6x-2

-7=10x-2

-7+2=10x-2+2

-5=10x

-5/10=10x/10

x=-1/2

Hope this helps!

8 0
2 years ago
Which expression represents the employees take home pay after deductions
Juliette [100K]

The expression 0.15(x-350) would be the proper equation.

7 0
3 years ago
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