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Svet_ta [14]
3 years ago
15

Answer the photo below thanks!! —Explain your answer please—

Mathematics
1 answer:
UkoKoshka [18]3 years ago
8 0
(17X22)+((12X19)/2)=488cm^2
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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

h = 3/x²

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

x³ = 30/24

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

#SPJ1

5 0
2 years ago
Plz Help!!!! <br>Solve for x<br>3y = 4x+ 1 ​
astraxan [27]

Answer:

Step-by-step explanation:

STEPS FOR SOLVING LINEAR EQUATION

3y=4x+1

Swap sides so that all variable terms are on the left hand side.

4x+1=3y

Subtract 1 from both sides.

4x=3y−1

Divide both sides by 4.

4

4x

​

=  

4

3y−1

​

 

Dividing by 4 undoes the multiplication by 4.

x=  

4

3y−1

​

 

7 0
3 years ago
Help I’ll mark brain list
Marat540 [252]

Answer:

23

Step-by-step explanation:

i think i hope it help

7 0
3 years ago
47.9 less than k is -21.6
Law Incorporation [45]
K is equal to -69.5 K=69.5 You put it in an equation 47.9-K=-21.6Then you subtract 47.9 from both sides and you get K=69.5 
3 0
3 years ago
What is the solution to the equation 3 square root x+4+3 square root 2x+8=0? x = –12 x = –4 x = 4 x = 12
Gre4nikov [31]

Answer:

x=-4

Step-by-step explanation:

3 0
3 years ago
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