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lbvjy [14]
3 years ago
8

Please helppppppp ASAP

Mathematics
1 answer:
pshichka [43]3 years ago
5 0

Answer:

I think it is C

Step-by-step explanation:

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Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i
serious [3.7K]

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0
2 years ago
21008 rounded to the nearest ten thousands
o-na [289]
The nearest ten thousand is 20,000
6 0
3 years ago
A trapezoid has an area of 13.5 square inches. If the bases are 3 and 6 inches what is the height?
liraira [26]
Well the formula is : b1+b2/2 (h)

so the height would be solved as : 
13.5 = 3+6/2 (h)
13.5 = 9/2 (h)
h = (13.5)/(9/2)
h = (13.5) x (2/9)  *reciprocal*
h = (27) / (9)
h = 3


5 0
3 years ago
Can sumone plzhelp..Apply the distributive property to factor out the greatest common factor of all three terms .
Nat2105 [25]

Answer:

3(3a - 6b + 7c )

Step-by-step explanation:

The greatest common factor of 9, 18 and 21 is 3

Factor out 3 from each term

9a - 18b + 21c

= 3(3a - 6b + 7c) ← in factored form

6 0
3 years ago
Read 2 more answers
HELP PLEASE WITH EXPLANATION
avanturin [10]
So hmm notice the picture below

that's the 30-60-90 rule, notice your triangle, the bottom-left-angle is a right angle, 90°, the angle atop is 30°, so the angle on the bottom-right has to be 60°, thus is a 30-60-90 triangle, and as you can see on the triangle on the left in the picture, those are the ratios for it

so 8 will be x, what is the longer leg or side in yours then? well, is \bf 8\sqrt{3}


3 0
3 years ago
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