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ludmilkaskok [199]
2 years ago
11

I need help with this problem please and thank you

Mathematics
2 answers:
iren2701 [21]2 years ago
5 0

Solution:

<u>Part - A:</u>

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.

  • => x⁵ - x³
  • => x⁴(x - 1)

<u>Part - B:</u>

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.

  • 3x² - 75
  • 3(x² - 25)
  • 3(x + 5)(x - 5)

<u>Part - C:</u>

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.

  • 3x⁵y + 4x⁴y - 5x²y
  • => x²y(3x³ + 4x² - 5)

<u>Part - D:</u>

Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.

MatroZZZ [7]2 years ago
3 0

a) x^5-x^3

x^3\left(x^2-1\right) ........take out x³

x^3\left(x+1\right)\left(x-1\right) ......separated (x²-1)

b) 3x^2-75

3\left(x^2-25\right) ........took out 3.

3\left(x+5\right)\left(x-5\right)  .......separated (x²-25)

c) 3x^5y+4x^4y-5x^2y

x^2y\left(3x^3+4x^2-5\right) ............takeout x²y at the front.

d) 81x^3-125

81x^3-125 ......cannot be factorised much more further.

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The ideal radius Alan must control is \frac{1}{2\pi } cm.

<h3>Define perimeter of circle.</h3>

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.

Given data -

Perimeter of circular plate = 10\pi cm

We know that perimeter of a circle is 2\pir

Therefore   10\pi = 2\pir

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The given error Alan can make is +-1 cm.

Minimum radius is given by

2\pir = 10\pi - 1

r = \frac{10\pi - 1 }{2\pi }

r = 5 - \frac{1}{2\pi }

Maximum radius is given by

2\pir = 10\pi + 1

r = \frac{10\pi + 1 }{2\pi }

r = 5 + \frac{1}{2\pi }

The ideal radius Alan must control is \frac{1}{2\pi } cm.

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Answer:

Infinite series equals 4/5

Step-by-step explanation:

Notice that the series can be written as a combination of two geometric series, that can be found independently:

\frac{3^{n-1}-1}{6^{n-1}} =\frac{3^{n-1}}{6^{n-1}} -\frac{1}{6^{n-1}} =(\frac{1}{2})^{n-1} -\frac{1}{6^{n-1}}

The first one: (\frac{1}{2})^{n-1} is a geometric sequence of first term (a_1) "1" and common ratio (r) " \frac{1}{2} ", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{2} } =\frac{1}{\frac{1}{2} } =2

The second one: \frac{1}{6^{n-1}} is a geometric sequence of first term "1", and common ratio (r) " \frac{1}{6} ". Again, since the common ratio is smaller than one, we can find its infinite sum:

Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{6} } =\frac{1}{\frac{5}{6} } =\frac{6}{5}

now we simply combine the results making sure we do the indicated difference: Infinite total sum= 2-\frac{6}{5} =\frac{10-6}{5} =\frac{4}{5}

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