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2 years ago

Been working on this for too long. thank u :)

Mathematics

1 answer:

Ket [755]2 years ago

8 0

Answer:

Im not a 100% sure but my best guess would be the 3rd equation:

f(x) = (x - 1) (x + 3)

Please let me know if I was wrong, but i hope this helped you!

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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 $-1\le x$ .

6 0

3 years ago

An object moves in simple harmonic motion with period 8 seconds and amplitude 6cm. At time = t 0 seconds, its displacement d fro

Murrr4er [49]

Answer:

123456789012345678901234567890

6 0

2 years ago

Kendra is participating in a fundraiser walk-a-thon she walks 4 miles in 60 minutes how many minutes will it take to walk 7 mile

Lemur [1.5K]

Answer:

105 min

Step-by-step explanation:

60 minutes ÷ 4 miles= 15 minutes per mile

15min per mile x 7 miles = 105 minutes

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3 years ago

Which of the following are true about regression with one predictor variable (often called "simple regression")? Check all that

AfilCa [17]

Answer:

<h3>A. The slope describes the amount of change in Y for a one-unit increase in X .</h3><h3>B. The regression equation is the line that best fits a set of data as determined by having the least squared error.</h3>

Step-by-step explanation:

In statistics, linear regression is a analysis we do to describe the relationship between two variables. With this study, we pretend to know if there's a positive or negative correlation between those variables, if that correlation is strong or weak.

In a linear regression analysis, we modeled the data set using a regression equation, which is basically the line that best fits to the data set, this line is like the average where the majority of data falls. That means choice A is right.

When we use linear equations, we need to know its characteristics, and the most important one is the slope, which is the ratio between the dependent variable and the independent variable. Basically, the slope states the unit rate between Y and X, in other words, it states the amount of Y per unit of X. That means choice B is correct.

Therefore, the correct answers are A and B.

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3 years ago

Find a16 of the sequence 1,6,11,16

babymother [125]

$\bf 1~~,~~\stackrel{1+5}{6}~~,~~\stackrel{6+5}{11}~~,~~\stackrel{11+5}{16}...\qquad \qquad \stackrel{\textit{common difference}}{d=5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=1\\ d=5\\ n=16 \end{cases} \\\\\\ a_{16}=1+(16-1)5\implies a_{16}=1+(15)5\implies a_{16}=76$

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3 years ago