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3 years ago

Wrie the following equations as a product of a whole number and a fraction 3/8

Mathematics

2 answers:

densk [106]3 years ago

7 0

The answer is 1 1/8. That will be your answer. :)

Alla [95]3 years ago

4 0

What equations. I think you mean 3/8+5/8=8/8=1whole

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Find the radius of convergence, then determine the interval of convergence

galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.

First aₙ is noted and then aₙ₊₁ is noted.

For ∑ aₙ, aₙ and aₙ₊₁ is noted.

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = β

If β < 1, then the series converges

If β > 1, then the series diverges

If β = 1, then the series inconclusive

Here $a_{k}$ = $\frac{(x+2)^{k}}{\sqrt{k} }$ and $a_{k+1}$ = $\frac{(x+2)^{k+1}}{\sqrt{k+1} }$

Now limit is taken,

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|$

= $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|$

= $\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|$

= $|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}$

= $|{x+2 }|$ < 1

- 1 < ${x+2 }$ < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

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1 year ago

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Preston has a car washing business. Last year he washed 20 cars a week. This year, he washed 1,200 cars. How many more cars did

kakasveta [241]

Answer:

He washed 160 more cars this year than last year.

Step-by-step explanation:

Last year: He washed a total of 1,040 cars.

This year: He washed a total of 1,200 cars.

1,200

- 1,040

160

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3 years ago

The equation for the line of best fit is y = -3.32x + 97.05.

Tamiku [17]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

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Leon earns$14 an hour.How much does he earn in 4 weeks if he works 12 hours each week?

gavmur [86]

Let's brake this up. He earns 14 dollars per hour. Then he works 12 hours per week. So 14 times 12 is 168. 168 times 4 equals 672 dollars :P

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3 years ago

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Helpppppppppppppp plzzzzz

AnnyKZ [126]

Answer:

x = 12.75

Measure of angle YXZ = 49.75 degrees

Step-by-step explanation:

Complementary angles have a sum of 90 degrees so we add them and set them equal to 90.

3x + 2 + 5x - 14 = 90

Combine like terms

8x - 12 = 90

Add 12 to both sides

8x = 102

Divide both sides by 8 to isolate x

x = 12.75

Measure of angle YXZ = 49.75 degrees

3 0

3 years ago