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Sladkaya [172]
3 years ago
5

Ayliah is 7 years more than 1/2 of Deb's age use x for the variable

Mathematics
1 answer:
irina [24]3 years ago
7 0

Answer:

The expression \frac{1}{2}x+7 can be used to find Ayliah's age.

Step-by-step explanation:

Given statement is:

Ayliah is 7 years more than 1/2 of Deb's age.

Let,

x represent Deb's age.

The expression for Ayliah's age would be;

7 more means addition.

Ayliah's age = \frac{1}{2}x+7

Hence,

The expression \frac{1}{2}x+7 can be used to find Ayliah's age.

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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

#SPJ1

5 0
1 year ago
Read 2 more answers
Can someone help me.
Alex
I’m sorry I don’t know
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3 years ago
The ordered pairs in the table below represent a linear function.
sdas [7]

Slope = Change in Y / change in X

Slope = (8 - 2) / (9-6)

Slope = 6 / 3

Slope = 2

4 0
4 years ago
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3-7 Please Help BRAINLEST
9966 [12]

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------

<h2>Answer: r = 7.</h2><h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2>

17 = r + 10

Swap sides so that all variable terms are on the left hand side.

r + 10 = 17

Subtract 10 from both sides.

r = 17 - 10

<h2>Subtract 10 from 17 to get, you guessed it, 7!</h2>
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3 years ago
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