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3 years ago

Analyze the diagram below and complete the instructions that follow.

Mathematics

1 answer:

dolphi86 [110]3 years ago

3 0

Answer:

x = 50, y = 10

Step-by-step explanation:

$\\(5x-100)+(x-20) = 180 => 6x = 300 => x = 50\\(3y)+(y+140) = 180 => 4y = 40 => y = 10$

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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

Claudia is making a candle by pouring melted wax into a mold in the shape of a cylinder. The radius of the cylinder’s base is 4

Sati [7]

The formula of a cylinder is 2πr (r+h)

2π4 (4+9)

8π (13)

25.13 (13)

326.73

Cubes: area = a^3

3x3x3 = 27

326.73 / 27 = 12.1

Claudia would need to buy 13 wax cubes to fil the candle.

hope this helps k12 students :)

3 0

2 years ago

A 45-year-old client diagnosed with colon cancer states, "I do not want any treatment. I have not seen any family members in 25

Kruka [31]

Answer:

3,2,1,4

Step-by-step explanation:

I am a loner, I have not seen any of my family in 25 years, beside, i will decide when and how i want to die. I do not want any treatment.

7 0

4 years ago

Read 2 more answers

frosja888 [35]

B. D=0.25n + 25
D=total n=number of hours 0.25=price per hour 25=the one time fee

3 0

3 years ago

You have $35 to spend on candy and soda is $0.75 each. Assume x represents the amount of candy and y is the amount of sodas purc

sukhopar [10]

<h3>Answer:</h3>

x + 0.75y = ≤ 35

<h3>Explanation:</h3>

The amount of candy purchased, plus the amount of soda purchased times the amount per soda must be less than or equal to 35.

<em>I hope this helps, let me know if it's wrong though.</em>

7 0

3 years ago