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Kipish [7]
3 years ago
9

Who ever gets it right first gets brainliest

Mathematics
1 answer:
sleet_krkn [62]3 years ago
7 0

Answer: Playing chess with Katie cause who'd play chess by themself right?

Step-by-step explanation:

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by
a_sh-v [17]

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

6 0
3 years ago
Lillian deposits $1,600 in an account at Excellence Bank. Find the total value of her account after 18 years. Total Value
Natasha2012 [34]

Answer:

28,800

Step-by-step explanation:

3 0
3 years ago
Lainey bought a set of 202020 markers for \$6$6dollar sign, 6.<br> What is the cost of 1 marker?
Galina-37 [17]

Answer:

$0.30

Step-by-step explanation:

6 / 20

0.3

Best of Luck!

4 0
3 years ago
Find the perimeter of the colored part of the figure. The figure is composed of small squares with side-length 1 unit and curves
harina [27]

Answer:

16.56 in

Step-by-step explanation:

4 sides of the squares are exposed

The radius of each semicircle is 1 since they are against 2 squares.

2pi*r=circumfrence

2pi*1=6.28

6.28/2=3.14 because it's a semicircle

3.14*4=12.56 because there are 4 equal semicircles

12.56+4=16.56

4 0
3 years ago
Vicki puts 10 books on a shelf.
nadezda [96]
the\ mean\ hickness\ of\ Vicki's\ books= \frac{28\ cm}{10} =2.8\ cm\\\\28\ cm\ \rightarrow\ 10\ boocks\\120\ cm\ \rightarrow\ x\\\\x= \frac{120\cdot 10}{28} \approx42.9\\\\Ans.\ Vicki\ can\ put\ 42\ books.
6 0
3 years ago
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