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3241004551 [841]
3 years ago
8

What is volume of a cylinder with base area 64πcm2 and a height equal to twice the radius? Give your answer in terms of π

Mathematics
1 answer:
bagirrra123 [75]3 years ago
3 0

Answer:

1024π

Step-by-step explanation:

<em>Took a quiz, got this answer right.</em>

<u>Here are the steps anyways:</u>

64π cm² is the base area

The height is equal to twice the radius

<h3>Volume of a Cylinder: V=B×h/V=πr²×h</h3>

1. Find radius: √64 (Which is 8)

2. Double the radius, 8×2=16

3. Multiply 16 and 64π, 16×64π=1024π

hopefully this was understandable, first time answering a question

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Using the Factor Theorem, the polynomials are given as follows:

1. P(x) = x^5 + 2x^4 - 7x^3 + x^2

2. P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots x_1, x_2, \codts, x_n is given by:

f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)

In which a is the leading coefficient.

Item a:

The parameters are:

a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

P(x) = x^5 + 2x^4 - 7x^3 + x^2

Item b:

The roots are:

x_1 = x_2 = 4, x_3 = 0, x_4 = -4

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)

Item 3:

The roots are:

x_1 = x_2 = 3, x_3 = -2

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

5 0
2 years ago
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