A box is to be made where the material for the sides and the lid cost​ $0.20 per square foot and the cost for the bottom is $0.05 per square foot. Find the dimensions of a box with volume 20 cubic feet that has minimum cost.

Please answer in length , width and height in ft

Answers

Answer 1

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.

______

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:


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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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What is multiplication?

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes.

The symbols cross (×), asterisk (*), and dot (·) are used to denote multiplication. You most frequently utilize the cross when writing in your notebooks. In computer languages and algebra, the asterisk and dot are both utilized (higher mathematics).

Given:

When 2 pipes fill a pool together, they can finish in 5 hrs,

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1 / 2 of pool = 9 hrs as given

full pool = 9 × 2 = 18 hours

Therefore, The time taken to fill the pool if it were working alone is 18 hours.

To know more about multiplication:

https://brainly.com/question/1135170

#SPJ6

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____________________________________________________________________
༶•┈┈⛧┈♛ ♛┈⛧┈┈•༶༶•┈┈⛧┈♛ ♛┈⛧┈┈•༶v༶•┈┈⛧┈♛ ♛┈⛧┈┈•༶----

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Answer:

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Step-by-step explanation:

Answer:

A is your answer

Step-by-step explanation:

if you look you can see were the line stops. your welcome

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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A restaurant manager recorded the drinks ordered by 150 customers. Each customer ordered one drink. The results are shown in the circle graph below.

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

Answer:$49.33

Step-by-step explanation:

87.00 - 32.67

= 49.33

Remember to add the dollar sign :D

$49.33

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Step-by-step explanation:

             

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         _____________

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Answers

Answer:

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Step-by-step explanation:

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NEED ANSWER ASAP WILL GIVE BRAINLIEST
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Answers

Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answers

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Step-by-step explanation:

Elimination is combining equations to obtain an equation with just one variable. This is only possible if the coefficients of one variable in both equations are opposed and will cancel each other out when put together. Elimination is most effective when it occurs naturally in the equations, but equations may also be modified to produce typical coefficients by multiplying or dividing equations by a given value. The next step would be to utilize the equation we devised to determine the variable's worth and then insert that value back into the original equation to determine the remaining variable.

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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What i did was i first tried to do 17 x 20 x 10 which game 3400 but when i remembered that V=1/3 x base area x height which would be 1/3 x 17 x 20 = 113 1/3 but if the base was 10 it would be 1/3 x 10 x 20 = 66 2/3. so i think the base is 10 and the answer would be 66 2/3

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Answers

Answer:

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Step-by-step explanation:

i hope this helped you! :)

-2.6 or -8/3 would be your answer. You always have to isolate the x! Hope this helps!

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Answers

Answer:

Step-by-step explanation:

It uses 552 cubic feet of concrete
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07.01)

Which of the following sets shows all the numbers from the set {3, 4, 5, 6} that are part of the solution to the equation 5x + 4 < 29? (4 points)
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Answers

The answwwer Answer is c
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Answer:

Step-by-step explanation:

7. 6 + 1/2 + 1/2 = 7

8. shade it

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Answers

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Step-by-step explanation:

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