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Alex_Xolod [135]
3 years ago
10

Jesse made a model of a mountain range for class. To do this, he bought a cylinder of cardboard and cut it into three cones. Eac

h cone is 5 inches tall and has a diameter of 4 inches. What was the volume of the original cylinder Jesse bought in terms of pi?
a.) 6.7pi in.^3

b.) 20pi in.^3

c.) 45pi in.^3

d.) 8pi in.^3
Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0
I think is c but i am not sure
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eimsori [14]
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3 0
3 years ago
A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol
k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

<u>Given the following data:</u>

  • Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

W = 3 + L  ......equation 1

H = 4 + L  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

Volume = length * width * height  .....equation 3.

Substituting the values into equation, we have;

224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}

Rearranging the polynomial, we have;

L^{3} + 7L^{2} +  12L - 224 = 0

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

(x - 3) = 0\\x = 3

P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9)  + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0

We would try with 4;

P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16)  + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224  - 224 = 0

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

3 0
3 years ago
Is 7 - -4 positive or negative?<br> positive<br> negative
djverab [1.8K]

Answer:

Positive.

Step-by-step explanation:

When you see two negative signs directly next to each other (as shown in the given expression), it will become a positive sign:

7 - (-4) = 7 + 4 = 11

Positive is your answer.

* To be fair, even if there is only one negative sign, the answer will still be positive, however, I am assuming you are suggesting only the sign, and not the answer.

~

7 0
3 years ago
Please solve the complex number by finding the complex conjugate.Correct answer will get brainliest!
jasenka [17]

-2 - 2i*square root of 11/483

6 0
2 years ago
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school guidelines require that there must be atleast 2 chaperones for every 25 students going on a school trip.how many chaperon
Anna007 [38]

Answer:

there must be at least 6 chaperones

Step-by-step explanation:

25 x 3= 75 so 2 chaperons x 3= 6 with a remainder of 5 students

5 0
3 years ago
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