1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elixir [45]
3 years ago
5

Arnold is trying to make packing boxes out of 6 foot by 6 foot pieces of cardboard from the local grocer. Help Arnold decide how

much he should cut from each corner of the cardboard to make an open box for moving.
Part I: Determining Dimensions
Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with the same size variable cut from each corner.

*You don't have to draw one, just explain what it would look like*










Part II: Analyze
How does each variable expression relate to the length, width, and height of the box when folded?














Part III: Extend your Findings
a. Based upon the variables you used in Part II, write a product for the volume.







b. Expand the product to write a volume function.








c. What domain makes sense for the volume?








d. Guess and check values to find the size cut that produces a maximum volume.
*Six guesses are required*
Mathematics
1 answer:
lions [1.4K]3 years ago
7 0
<span>Part I: Determining Dimensions

Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with the same size variable cut from each corner.

*You don't have to draw one, just explain what it would look like*


Answer:

Base of the box:

     it is a square
     side of the base = 6 foot - x - x. = 6 - 2x

Height of the box: x

Part II: Analyze

How does each variable expression relate to the length, width, and height of the box when folded?

Answer:

length = width = 6 - 2x
height = x


Part III: Extend your Findings
a. Based upon the variables you used in Part II, write a product for the volume.

Answer:

Volume = area of the base × height


Volume = (6 - 2x)² x

b. Expand the product to write a volume function.

Answer:

Volume = (36 - 24x + 4x²)x

Volume = 36x - 24x² + 4x³


c. What domain makes sense for the volume?

Answer:

Since x is a physical dimension x is greater than 0

Since the lenght of the cardboarc sheet is 6 and two squares are cut off, x has to be less than 3

So, the domain is (0, 3)


d. Guess and check values to find the size cut that produces a maximum volume.
*Six guesses are required*

Answer:

x              </span>Volume = 36x - 24x² + 4x³

0.1           36(0.1) - 24(0.1)² + 4(0.1)³ = 3.36
0.5           36(0.5) - 24(0.5)² + 4(0.5)³ = 12.5
1.0           36 - 24 + 4 = 16
1.5           36(1.5) - 24(1.5)² + 4(1.5)³ = 13.5
2.0           36(2) - 24(2)² + 4(2)³ = 8
1.7           36(1.7) - 24(1.7)² + 4 (1.7)³ = 11.49
1.2           36(1.2) - 24(1.2)² + 4(1.2)³ = 15.55

Then you can guess that the maximum volume is pretty close to 16 and it is whenx is close to 1.
2.9

You might be interested in
Which term is a perfect square of the root 3x4?<br>​
KiRa [710]

Answer:

2√3

Step-by-step explanation:

√3x4 = √12 = 2√3

5 0
3 years ago
Read 2 more answers
SO Problem -3.62 + 18.57 =
Whitepunk [10]

Answer:

<h2> 18.57</h2><h2>- 3.62</h2>

___________________

<h2> 14.95</h2>
5 0
3 years ago
At 5 am, the temperature was -10°F. By noon the temperature was 7°F, What Integer
True [87]

Answer:

The integer that represents the change in temperature is 17.

Step-by-step explanation:

6 0
2 years ago
Find the number of miles per hour in each of the following cases,
inysia [295]

100 miles

100 miles

100 miles

100 miles 100 miles

100 miles ok?

4 0
3 years ago
Is it ok this way guys
AleksAgata [21]

Answer:

No

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the trigonometric ratio for cos C?
    12·1 answer
  • In a randomly generated list of numbers from 0 to 6, what is the chance that each number will occur?
    6·2 answers
  • A city is built on a grid in which each block is 300 feet wide. Anwar walks all the way around a park. His route takes him 1 blo
    10·1 answer
  • What is the distance between the points (10, -7) and ( 10, 9) on the coordinate plane?
    7·1 answer
  • A metal strip is being installed around a workbench that is 12 feet long and 3 feet wide. If the stripping costs ​$4 per​ foot,
    15·1 answer
  • I am part of a whole. I am greater than three fourths but less than nine tenths. I am a decimal with a 3 in its hundredth place.
    13·2 answers
  • Hello everyone I need serious help!!!
    12·2 answers
  • The original price of a pair of shoes is $36.00. Edward buys the shoes for 13% off its original price. Two weeks later Chad buys
    13·2 answers
  • SOMEONE PLSSS HELPP MEE
    12·1 answer
  • The cost of two books is ₹126.If the cost of one book is twice the other, the find the cost of books.​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!