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jeka57 [31]
2 years ago
6

Find all values of x that satisfy the equation

Mathematics
1 answer:
zlopas [31]2 years ago
6 0
Factor an x^2 out,
x^2 ( 5x^2 -7x -4)
Can't factor the quadratic, but graphing or quadratic formula yields,
the zeroes are 0, -0.4358, 1.8358
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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
Evaluate 3+n-5×2 for n=4​
xxTIMURxx [149]

Answer:

-3 is the answer

Step-by-step explanation:

distribute the value of n

3+4-5×2

=7-10

=-3

6 0
3 years ago
Read 2 more answers
What is 5/8 times 4/5?​
Genrish500 [490]

Answer:

1/2 and 0.5 is right

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Please helm me
spin [16.1K]
<span>Area of circular metal=πr^2 =3.14 x 3.5 x 3.5 m^2 now, total cost=area x rate =3.14 x 3.5 x 3.5 x 3.25 $ =125.01 $</span>
4 0
3 years ago
Read 2 more answers
Rounded to hundred how can I round to hundred
Gwar [14]
If you are talking about any number then.....
imagine a mountain, any number less than 5 is only the left and any number greater than 5 is on the right
      
Here, for example, let's try 13 

look at 13 on the pyramid .... since it's not a the top of the mountain so it falls back down to 10... it rounds down to 10
Now let's try 18 ...hmmm.... 18 is not at the top either so it falls as well. It falls down to 20 it rounds up to 20 

how about 15 u might be asking...it is at the top...15 is a little different ...make sure no one is looking and push it off the right side and falls to 20. Also rounding up to 20

              5
           4    6 
        3          7 
     2                8 
   1                      9 
0                           10
7 0
3 years ago
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