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alexandr402 [8]
3 years ago
9

An open box is to be made from a rectangular piece of material 9 inches by 12 inches by cutting equal squares from each corner a

nd turning up the sides.
Mathematics
1 answer:
grigory [225]3 years ago
7 0
The questions for this problem would be:
1. What is the dimensions of the box that has the maximum volume?
2. What is the maximum volume of the box?

Volume of a rectangular box = length x width x height

From the problem statement,
length = 12 - 2x
width = 9 - 2x
height = x

where x is the height of the box or the side of the equal squares from each corner and turning up the sides

V = (12-2x) (9-2x) (x)
V = (12 - 2x) (9x - 2x^2)
V = 108x - 24x^2 -18x^2 + 4x^3
V = 4x^3 - 42x^2 + 108x

To maximize the volume, we differentiate the expression of the volume and equate it to zero.

V = 4x^3 - 42x^2 + 108x
dV/dx = 12x^2 - 84x + 108
12x^2 - 84x + 108 = 0x^2 - 7x + 9 = 0

Solving for x,
x1 = 5.30 ;      Volume = -11.872  (cannot be negative)
x2 = 1.70 ;      Volume = 81.872

So, the answers are as follows:

1. What is the dimensions of the box that has the maximum volume?
length = 12 - 2x = 8.60
width = 9 - 2x = 5.60
height = x = 1.70 

2. What is the maximum volume of the box?

Volume = 81.872
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Ierofanga [76]

Answer:

A

Step-by-step explanation:

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Repeat this with the components in the second row of A with the corresponding components of the second column in B, that is

AB

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6 0
3 years ago
What is the surface area of the cylinder with height 4m and radius 2m? Round your answer to the nearest thousandth.
Artyom0805 [142]

Answer:

50.265m^3

Step-by-step explanation:

because the formula for solving this problem is πr^2•height and then to finish solving it would have to be put into cubed as it's 3d

3 0
3 years ago
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
11Alexandr11 [23.1K]

Answer:

None

Step-by-step explanation:

Let’s graph the points first.

Look at the image below.

And by looking at the image we can tell that none of the points lay on the same horizontal line.

<em>Thus,</em>

<em>none of the points lay on the same horizontal line.</em>

<em />

<em>Hope this helps :)</em>

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8 0
3 years ago
The scale on the map is 2 inches = 50 miles. If the distance between the two cities is 175 miles, how many
iVinArrow [24]

Answer:

7 inches

Step-by-step explanation:

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3 years ago
Directions: Solve for the surface area of the following figures using the formula.
Lina20 [59]

Answer:

3^3 x 3.14

9 x 3.14 = 28.26

28.26  x 2 = 56.52

2 x 3.14 x 3 = 18.84

18.84 x 10 = 188.4

Now lets add all given areas:

56.52 + 188.4 = 244.92 m^2 for question 1

4 x 3.14 x 12^2

4 x 3.14 x 144 = 1,808.64 cm^2 is your answer for question 2

14^2 x 3.14

196 x 3.14 = 615.44

3.14 x 14 x 33 = 1450.68

1450.68 + 615.44 = 2,066.12 cm^2 is your answer for question 3 I think

7 0
3 years ago
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