<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
Answer:
L-6 test results measure the amount of IL-6 circulating in the blood, and are used as one sign of systemic inflammation. A normal level of IL-6 may represent people who do not have an infection or inflammation. A low level of IL-6 may be expected for most patients with a less severe inflammatory response.
Step-by-step explanation:
Answer:
39.99 is the correct answer.
The correct answer is, ABCD has four congruent angles.
Answer:
hi! this is (insert your name) what does this sybol/mathematical term mean?
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Step-by-step explanation:
