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3 years ago

How do I know is this is a proportional relationship

Mathematics

1 answer:

Irina-Kira [14]3 years ago

5 0

Answer:

They are the same

Step-by-step explanation:

Notice how both 2's, 4's, 6's, and 8's are aligned. The arrows mean this could go on forever, meaning each tic mark would be proportionate. All numbers are even, as well. If you were to find slope, or create an equation, it would be proportionte.

Hope this helps!

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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

3 years ago

If the area of a square is 100cm2, then what is its perimeter?

Vinil7 [7]

Answer:

40cm

Step-by-step explanation:

A=s*s

A=10*10

A=100 cm^2

P=4*s

P=4*10

P=40 cm

"s" represents side

6 0

3 years ago

Please help . I’ll mark you as brainliest if correct!!!

damaskus [11]

Answer:10 Seconds

Step-by-step explanation:

s=1600 ft

t=√(s) /4

t=√(1600)/4

t=40/4

t=10 seconds

8 0

3 years ago

HHHHHHHHHHHHEEEEEEEEEEEEEELLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPP

Rasek [7]

A came to C, C was supposed to go to A

8 0

3 years ago

Need some help here...

bekas [8.4K]

Cos Z = 32/40 => Z= cos-¹(32/40) =>

sin Z = sin (cos-¹(32/40)) = 3/5

4 0

3 years ago