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Vera_Pavlovna [14]
3 years ago
12

At your local farmers market, it cost $10 to rent a stand, and $7 for every hour you stay there. If you paid a total of $38, how

many hours did you stay at the farmers market
Mathematics
2 answers:
anyanavicka [17]3 years ago
7 0

Answer:

4 Hours

Step-by-step explanation:

38 - 10 = 28

28 / 7 = 4

amm18123 years ago
3 0

Answer:

4 hours

Step-by-step explanation:

You paid a total of $38, in which $10 was a one-time payment.

Subtract 10 from 38: 38 - 10 = 28

You have to pay $7 for every hour. Divide 7 from 28:

28/7 = 4

You stayed at the farmers market for 4 hours.

~

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A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3
zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

  • l represents the length.
  • w represents the width.
  • h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

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For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

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x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

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2 years ago
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so once again the ordered pair is a solution.


Hoped this helped.

5 0
3 years ago
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