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choli [55]
2 years ago
7

A geometric series that starts with 2, ends with -6250 and has a common ratio of -5

Mathematics
1 answer:
Rufina [12.5K]2 years ago
4 0
Jsjajmsmsmssmemsmjsjsnebbbhjjjskjendnud
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Prove <br><br><br><br><img src="https://tex.z-dn.net/?f=%20%5C%5C%20" id="TexFormula1" title=" \\ " alt=" \\ " align="absmiddle"
irina1246 [14]

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5 0
3 years ago
Read 2 more answers
PLS HELP ME!! STATE THE DOMAIN AND RANGE OF EACH RELATION AND WHETHER ITS A FUNCTION​
muminat
Domain is everything below 0. Range is all real numbers. It is a function as it passes the vertical line test.
5 0
2 years ago
Solve using Fourier series.
Olin [163]
With 2L=\pi, the Fourier series expansion of f(x) is

\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos\dfrac{n\pi x}L+\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L
\displaystyle f(x)\sim\frac{a_0}2+\sum_{n\ge1}a_n\cos2nx+\sum_{n\ge1}b_n\sin2nx

where the coefficients are obtained by computing

\displaystyle a_0=\frac1L\int_0^{2L}f(x)\,\mathrm dx
\displaystyle a_0=\frac2\pi\int_0^\pi f(x)\,\mathrm dx

\displaystyle a_n=\frac1L\int_0^{2L}f(x)\cos\dfrac{n\pi x}L\,\mathrm dx
\displaystyle a_n=\frac2\pi\int_0^\pi f(x)\cos2nx\,\mathrm dx

\displaystyle b_n=\frac1L\int_0^{2L}f(x)\sin\dfrac{n\pi x}L\,\mathrm dx
\displaystyle b_n=\frac2\pi\int_0^\pi f(x)\sin2nx\,\mathrm dx

You should end up with

a_0=0
a_n=0
(both due to the fact that f(x) is odd)
b_n=\dfrac1{3n}\left(2-\cos\dfrac{2n\pi}3-\cos\dfrac{4n\pi}3\right)

Now the problem is that this expansion does not match the given one. As a matter of fact, since f(x) is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.

One possibility is that you're actually supposed to use the even extension of f(x), which is to say we're actually considering the function

\varphi(x)=\begin{cases}\frac\pi3&\text{for }|x|\le\frac\pi3\\0&\text{for }\frac\pi3

and enforcing a period of 2L=2\pi. Now, you should find that

\varphi(x)\sim\dfrac2{\sqrt3}\left(\cos x-\dfrac{\cos5x}5+\dfrac{\cos7x}7-\dfrac{\cos11x}{11}+\cdots\right)

The value of the sum can then be verified by choosing x=0, which gives

\varphi(0)=\dfrac\pi3=\dfrac2{\sqrt3}\left(1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots\right)
\implies\dfrac\pi{2\sqrt3}=1-\dfrac15+\dfrac17-\dfrac1{11}+\cdots

as required.
5 0
3 years ago
There are 8 swimmers in the swimming club. The club bought c swimming caps to split among its members. Write an expression that
love history [14]

Answer:

c/8

Step-by-step explanation:

This is division. This can be figured out by reading "split". If something is to be split, it is the dividend.

5 0
2 years ago
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Write the sentence as an equation. Then solve 2 less than one-sixth of a number n is 5
lakkis [162]

Answer:

n=42

Step-by-step explanation:

n/6-2=5

n/6=7

n=42

5 0
2 years ago
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