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Mathematics

1 answer:

lianna [129]2 years ago

5 0

Answer:

30625

Step-by-step explanation:

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Please help me I just want to finish this so I can go to sleep.

nikdorinn [45]

The third and last options are the answers.
The graph is shifted to the right by some number. The coordinates aren't numbered, so it could be literally anything. To shift to the right, the equation will be |x-y| where y is any number.

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3 years ago

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Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|$

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

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3 years ago

A rotating sprinkler waters the lawn outside the lodge at Oak Tree State Park. The sprinkler rotates in a full circular path and

ki77a [65]

Answer:

it is 7squere meters

Step-by-step explanation:

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3 years ago

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olchik [2.2K]

Answer: D. (x-6)(x-6)