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Gnesinka [82]
3 years ago
12

What is the answer to this problem

Mathematics
2 answers:
Kruka [31]3 years ago
6 0
 The answer would be 24x10 to the fourth

cluponka [151]3 years ago
5 0
It would be 24^10_{4}
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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
1 year ago
What is the sum of 6 7/8 + 4 5/8
erica [24]
6\frac{7}{8}+4\frac{5}{8}\\----------------\\6+4=10\\\\\frac{7}{8}+\frac{5}{8}=\frac{7+5}{8}=\frac{12}{8}=1\frac{4}{8}=1\frac{1}{2}\\\\10+1\frac{1}{2}=11\frac{1}{2}\\\\====================\\\\6\frac{7}{8}+4\frac{5}{8}=11\frac{1}{2}
8 0
2 years ago
Read 2 more answers
Please can someone help? As i'm not confident this is right for factorising 4b^2 + 8b + 3 ​
SIZIF [17.4K]

Answer:

your answer is correct

Step-by-step explanation:

4b² + 8b + 3

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term.

product = 4 × 3 = 12 and sum = + 8

The factors are 2 and 6

Use these factors to split the b- term

4b² + 2b + 6b + 3 ( factor the first/second and third/fourth terms )

= 2b(2b + 1) + 3(2b + 1) ← factor out (2b + 1) from each term

= (2b + 1)(2b + 3)

5 0
2 years ago
What are the factors of 3x2 + 10x + 8?
DaniilM [7]
(3x+4) (x+2)
This gives you 3x^2 + 6x + 4x + 8
Which simplifies to 3x^2 + 10x + 8
4 0
2 years ago
I need help someone help me please &lt;3
ElenaW [278]

Answer:

y=-\frac{3}{2}x-2

Step-by-step explanation:

using the y=mx+b equation, where m=slope and b=y-intercept, we can place our known slope and y-intercept to form our answer, y=-\frac{3}{2}x-2 :-) hope this helped!

4 0
2 years ago
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