3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of
cardboard that is 10 inches by 18 inches. The box will be formed by making cuts as shown in
the diagram and folding up the sides.
a) Write a function that models the volume of the box.
b) What are the dimensions of the box with the maximum volume? Round to the nearest tenth.
el
at
c) What is the maximum volume of the box?

3) Postcards: Marcie Wants To Make A Box To Hold Her Postcard Collection From A Piece Ofcardboard That

Answers

Answer 1

The volume of the box is the amount of space in it.

The dimension of the postcard is:

[tex]\mathbf{Length = 10}[/tex]

[tex]\mathbf{Width = 18}[/tex]

Let x represents the length of the cut.

So, the dimension of the box is:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

(a) The function that represents the volume of the box

This is calculated as:

[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

(b) The dimension that maximizes the volume

We have:

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 7.3,2.1}[/tex]

The value x = 7.3 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 2.1}[/tex]

Recall that:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]

[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]

[tex]\mathbf{Height = 2.1}[/tex]

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]

[tex]\mathbf{Volume = 168.1}[/tex]

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

https://brainly.com/question/17056191


Related Questions

Old Faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height of a nearby tree that casts a shadow 63 feet long? Assume the triangles are similar.

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It will be 90 feet considering the water triangle as shown as the figure

Explain how to use a model to represent the division of two fractions.
Please help with this it's due in 20 mins!

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Answer:

You can use the model to show the fractions alongside each other.

Step-by-step explanation:

help! Scroll to see image!

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mhorn seems to be correct

Step-by-step explanation:

yshahaa

Assume there are 20 people in a room, including you. You must shake hands with everyone else in the room. How many hands will you shake

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Answer:

19, I'm pretty sure?

..................................

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….there’s nothing here?…

[tex]\sqrt{5}+\sqrt{5}=?[/tex]

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[tex]\sqrt 5 + \sqrt 5 \\\\=\sqrt 5(1+1) \\\\= 2 \sqrt 5[/tex]

who goes to Catonsville middle school pls answer

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Answer:

Uh not me but I don't think you should leak your schools name...

The nth term of a sequence is n^2 + 5.

Find the first three terms and show that 261 is a term in this sequence.

Answers

Answer:

first 3 terms: 6, 9, 14

16^2+5=261

Step-by-step explanation:

1^2+5= 6

2^2+5= 9

3^2+5= 14

what would 2 x (x-3) sum be

Answers

Answer:

2x-6 I think

Step-by-step explanation:

A company is considering purchasing the mineral rights to two different mountains. The probability that it will purchase the mineral rights to the first mountain is 0.55. The probability that it will purchase the mineral rights to the second mountain is 0.4. Assuming the decisions to purchase the mineral rights to each mountain are made independently, what is the probability that it will purchase the mineral rights to exactly one of the two mountains?
a. 0.4
b. 0.45
c. 0.51
d. 0.49

Answers

Using probability of independent events, it is found that the probability that it will purchase the mineral rights to exactly one of the two mountains is given by:

c. 0.51

If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, these following two events result in the rights of exactly one of the two mountains being bought:

First bought(0.55 probability), second not(0.6 probability).First not bought(0.45 probability), second bought(0.4 probability).

Hence:

[tex]p = 0.55(0.6) + 0.45(0.4) = 0.51[/tex]

Thus, option c is correct.

A similar problem is given at https://brainly.com/question/24174994

In an experiment, the temperature of a sample is measured as 16 degrees Celsius.

If the percent error is 0.75%, how can you report the temperature of the sample using the absolute error and the actual temperature value in degrees Celsius?

-16±0.12
-16±12
-16±0.047
-16±4.7

Answers

Answer: T=16 ± 0.12 ° CA Aw

Step-by-step explanation:

Helpppppppppppppppppppp

Answers

Answer:

x = -5

Step-by-step explanation:

f(x) = [tex]\frac{x+5}{4}[/tex]

Okay, so in order to find the zeroes of the equation, we need to find the values of x for which f(x) = 0.

[tex]\frac{x+5}{4}[/tex] = 0

We can start by multiplying both sides by 4.  Anything multiplied by 0 equals 0, so we have the following:

x + 5 = 0

Now, subtracting 5 from both sides in order to isolate x, we have:

x = -5

To check our work, let's substitute -5 into our equation:

f(-5) = [tex]\frac{-5+5}{4}[/tex] = [tex]\frac{0}{4}[/tex]

0 divided by anything equals 0, so f(-5) = 0.

Apply the Triangle Sum Theorem to find the sum of the angles in the pentagon. A pentagon can be divided into three triangles.​

Answers

Step-by-step explanation:

according to angle sum property of triangle

sum of all 3 angles of triangle is 180°

and here it is given that the Pentagon is divided in 3 triangles,

now,

3×180 = 540°

therefore, option C 540° is correct

hope this answer helps you dear! take care

Answer:

540

Step-by-step explanation:

Each triangle only has 180 degrees

We have 3 triangle, 180 + 180 + 180 = 540 degrees

0.314 x 100 = help me pls

Answers

0.314 x 100 = 31.4 (Checked easily using calculator). ✌️

Answer:

your answer would be 31.4 :)

Step-by-step explanation:


Help Please please please

Answers

The answer is b
…………….

Simplify 38 - 32
-
A. 34
B. 36
c. 310
D. 3-6

Answers

Answer:

38 - 32 = 6

Step-by-step explanation:

subtract the question

Which fraction is larger? 2/3, 3/4, 3/5, 5/7

A: 2/3 B: 3/4 C: 3/5 D: 5/7​

Answers

I think it is A not 100% sure tho!

A true/false test consists of 100 questions. A student knows the correct answer to 40 of the questions. She guesses each of the other answers independently based on the toss of a coin.

Answers

Answer:

whats the question

Step-by-step explanation:

1 define and give an example for: rate:

2 define and give an example for unit rate
pls help I'm struggling​

Answers

Step-by-step explanation:

1. quantity, amount, or degree of something measured per unit of something else her typing rate was 80 words per minute. b : an amount of payment or charge based on another amount specifically : the amount of premium per unit of insurance.

2.A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

Find x and y. Give reasons to justify your solution. Pleaseee help

Answers

Answers:

x = 40 and y = 40

========================================================

Explanation:

The three angles involving x add up to 180 since they form a straight line or straight angle.

3x+0.5x+x = 180

4.5x = 180

x = 180/(4.5)

x = 40

Then note how the 0.5x and 0.5y angles are vertical angle pairs. Vertical angles form when we have two lines cross to form an X shape, and vertical angles are always opposite one another. Also, vertical angles are always the same measure.

0.5x = 0.5y

x = y

40 = y

y = 40

In the second step, I multiplied both sides by 2. Then I plugged in x = 40 we found earlier.

If A:B = 5:9 and B:C = 3:7, find A:B:C.

Answers

Answer:

15:27:63

Step-by-step explanation:

solve by multiplying the ratio by the opposing number.

a b b c

5 9 3 7

multiply 5 x 3 = 15

multiply 9 x 3 = 27

mutliply 9 x 7 = 63

what is 3 square root of 64

Answers

Answer:

24

Step-by-step explanation:

1. John is going to join a gym. He must pay a one-time membership fee of $75 and a monthly fee of $30. Let m = the number of months John has his membership. Write an expression to represent this situation How much will John pay for 6 months of membership?

2. Madison is having a party. She went to the store and bought a cake for $18.50 and 20 balloons. Her total bill was $63.50. How much did each balloon cost if they all cost the same? Write and solve an equation. Please look over these again. Webmail your answers to get your points back.

Answers

John's membership in the gym and Madison's party are illustrations of linear equations.

1. John's equation

The given parameters are:

[tex]\mathbf{Base = 75}[/tex]

[tex]\mathbf{Monthly = 30}[/tex]

The monthly expression is:

[tex]\mathbf{f(m) = Base + Monthly \times m}[/tex]

So, we have:

[tex]\mathbf{f(m) = 75+ 30 \times m}[/tex]

[tex]\mathbf{f(m) = 75+ 30m}[/tex]

For 6 months, we have:

[tex]\mathbf{f(6) = 75+ 30 \times 6}[/tex]

[tex]\mathbf{f(6) = 255}[/tex]

Hence, the expression that represents the situation is [tex]\mathbf{f(m) = 75+ 30m}[/tex], and the amount for 6 months of membership is $255

2. Madison's party

The given parameters are:

[tex]\mathbf{Cake = 18.50}[/tex]

[tex]\mathbf{Balloon = 20}[/tex]

[tex]\mathbf{Total = 63.50}[/tex]

Let n represent the cost of each balloon.

So, the equation is:

[tex]\mathbf{Cake + Balloon \times n = Total}[/tex]

This gives:

[tex]\mathbf{18.50 + 20 \times n = 63.50}[/tex]

Subtract 18.50 from both sides

[tex]\mathbf{ 20 \times n = 45}[/tex]

Divide both sides by 20

[tex]\mathbf{ n = 2.25}[/tex]

Hence, the expression that represents the situation is [tex]\mathbf{18.50 + 20 \times n = 63.50}[/tex], and the cost of each balloon is $2.25

Read more about linear equations at:

https://brainly.com/question/11897796

What percent of 80 is 112? Please hurry!

Answers

Answer:

140

Step-by-step explanation:

Here you go. Hope it helps you

If you reported to work at 18.00 on Wednesday and you get off at 02.50 on a Thursday, which day of pay period week are you working?

Answers

Answer:

Only Wednesday and Thursday

Step-by-step explanation:

Can some one help me

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Answer:

16.95

Step-by-step explanation:

because when you add 14.95 and 2 together you get 16.95

Answer:

Step-by-step explanation:

Area of  Big circle = πr² = 3.14 * 6.5*6.5  = 132.67 cm²

Area of small circle = 3.14 * 2.3*2.3 = 16.61 cm²

Area of shaded region = area of big circle - area of small circle

         = 132.67 - 16.61  = 116.06 cm²

Karly used 3.5cans of tomato sauce to make lasagna. Each can contains 10.5 ounces. How many ounces of tomato sauce is in the lasagna?

Answers

Answer:

31.75

Step-by-step explanation:

if there are 3.5 (or 3 and a half) cans in the lasagna and each holds 10.5 oz, you can use 3.5x10.5 to solve it.

sand is falling off a conveyor in a conical pile at a constant rate of 2 cubic yards per minute. The height of the sand is equal to the radius of the pile of sand on the ground. If the cone-shaped pile is 3 feet tall now, how tall will it be in one hour?​

Answers

The volume of a cone is (1/3)πr2h.

In this problem r=2h or h=(1/2)r

Hence V = (1/6)πr3

dV/dt = (1/2)πr2 dr/dt

With this information you should now be able to answer the question. Remember the relation between r and h!

never mind i was right

im also so sorry if you dont understand or its not one of the answers

Answer:

t a sand and gravel plant, sand is falling off a conveyor, and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?

Step-by-step explanation:

which number is closest to 0.02
A. 0.019
B. 0.04
C. 0.1
D. 0

Answers

Answer: 0.019

Step-by-step explanation: 0.019 is the only closest number to 0.020, others are much less than 0.020.

Kiley had a piece of bamboo skewer that measured 14 Three-fifths inches long. She wanted to cut it into toothpicks that were each 3 One-fifth inches long. How many toothpicks can she make?

Answers

4.5 or 5(rounded)
Since 73/5 divided by 16/5 = 4.5625
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