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pshichka [43]
3 years ago
10

Julia is hanging birdhouses on her fence. The first birdhouse is 21 inches to the right of a red fence post. The second birdhous

e is 29 inches and o the left of the first birdhouse. Use a number line below to represent this scenario. Let 0 on the number line represent the red fence

Mathematics
1 answer:
emmasim [6.3K]3 years ago
5 0

Answer: The number line is attached.

Step-by-step explanation:

Observe the number line attached.

You know that 0 represents the red fence post.

Since Julia is hanging the first birdhouse 21 inches to the right of the red fence post, then the location on this birdhouse on the number line is at:

21

Then you must plot it on the number line.

According to the exercise, the second birdhouse is to the left of the first birdhouse.

When you move 29 units to the left of the point 21, you get that the location of the second birdhouse is at:

-8

(Notice that: 21-29=-8)

So you can plot it on the number line.

Therefore, the number line that represents this scenario is attached.

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For given power series \sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n} the radius of convergence is 2.

For given question,

We have been given a power series \sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}

We need to find the radius of convergence of the power series.

We use ratio test to find the radius of convergence of the power series.

Let a_n=\frac{(-1)^nx^n}{2^n}

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\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}

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So, the radius of convergence is 2.

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