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Leya [2.2K]
3 years ago
12

Write the function rule for the following arithmetic sequence.

Mathematics
1 answer:
irina [24]3 years ago
6 0

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=4%5E%7B2%7D" id="TexFormula1" title="4^{2}" alt="4^{2}" align="absmiddle" class="latex-formula
Komok [63]

Step-by-step explanation:

step 1. what is 4^2?

step 2. 16.

3 0
3 years ago
What is the probability of rolling a 6-sided die and getting a 2 or an odd
mars1129 [50]

Answer:

I think D

Step-by-step explanation:

4 0
3 years ago
When you calculate the number of permutations of n distinct objects taken r at a​ time, what are you​ counting?.
expeople1 [14]

Answer:

The number of ordered arrangements of n objects taken r at a time.

Step-by-step explanation:

8 0
2 years ago
Can I get help with finding the Fourier cosine series of F(x) = x - x^2
trapecia [35]
Assuming you want the cosine series expansion over an arbitrary symmetric interval [-L,L], L\neq0, the cosine series is given by

f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx

You have

a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx
a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}
a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)
a_0=-\dfrac{2L^2}3

a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}

and so

a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}

So the cosine series for f(x) periodic over an interval [-L,L] is

f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx
4 0
3 years ago
PLEASE! PLEASE HELP ME!!!!
Nataliya [291]

Answer:

c and d

Step-by-step explanation:

ok so i do not know how to explain

5 0
3 years ago
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