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2 years ago

Image down below thx:)

Mathematics

1 answer:

user100 [1]2 years ago

5 0

Answer:

(1,2)

Step-by-step explanation:

You go over 1 and then up 2 and that is where Q is.

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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

2 years ago

Plz help quickly!!!! You will get 36 POINTS!!!

liq [111]

If clearer picture i may help for it is far to dark and clouded to read

4 0

2 years ago

Read 2 more answers

Chris is 6 feet tall. To find the height of a tree, he measures his shadow and the tree's

Ket [755]

Answer:

click the the photo to see better

Step-by-step explanation:

6 0

1 year ago

Help me find p.....

asambeis [7]

Answer: p = 120 degrees

Step-by-step explanation:

Figure a shows a pentagon. The sum of interior angles in a pentagon is equal to 540 degrees.

1. Subtract the known numerical angle

540 - 60 = 480

All of the remaining angles (represented by the variable p) are equal to one another. Therefore, we can use the expression 4p = 480 to find the value of p.

2. Evaluate the equation to find the value of p.

4p = 480

p = 120

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2 years ago

Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone

timofeeve [1]

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2 years ago