<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:
144i + 81
Step-by-step explanation:
(-3*9i)(-5 + 3i) + 9i
-27i (-5 + 3i) + 9i
FOIL
135i + 81 + 9i
144i + 81
Answer:
30/(2x^2-x)
Step-by-step explanation:
5/(2x-1) * 6/x
Multiply the numerators
5*6 = 30
Multiply the denominatos
(2x-1) *x = 2x^2 -x
5/(2x-1) * 6/x = 30/x(2x-1) = 30/(2x^2-x)
First, let's find out how much the 6 boxes weigh. If one box of clay weighs 17.4 ounces, then how much does 6 boxes weigh? Well, let's multiply.
17.4 × 6 = 104.4
Next, let's find out how much clay each student get. Since there are 18 students and only 6 boxes, let's find this out by dividing the ounces.
104.4 ÷ 18 = 5.8
So, each student gets 5.8 ounces of clay. I hope this helps!
Step-by-step explanation:
if it's easy why don't you do it. not trying to be rude are whatever
