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3 years ago

HELP NOW EMERGENCY PLEASE OKEASE HELP

Mathematics

2 answers:

seropon [69]3 years ago

6 0

Answer:

18.84

Step-by-step explanation:

2 $\pi$ r/2 is the circumference of half a circle. The radius is 6.

2(3.14)(6)/2 = 18.84

Yuliya22 [10]3 years ago

5 0

Answer:

18.84

Step-by-step explanation:

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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

Polygon ABCD is a rectangle. What is its area? Round your answer to the

galben [10]

9514 1404 393

Answer:

26 square units

Step-by-step explanation:

Counting grid squares on the graph, we see that segment AB is the hypotenuse of a right triangle with legs 2 and 3. Its length is ...

AB = √(2²+3²) = √13

We can also see that the adjacent longer sides are twice this length, each being the hypotenuse of a triangle that is 6 wide and 4 high.

AC = √(6² +4²) = √52 = 2√13

Then the area is ...

A = LW

A = (2√13)(√13) = 2·13 = 26 . . . square units

5 0

2 years ago

Select the scenario below that demonstrates sampling bias. Select the correct answer below:

Vsevolod [243]

Answer:

C. Elizabeth wants to estimate the mean vacation days of coworkers at her company. She collects data by selecting a random group of coworkers within her department.

Step-by-step explanation:

Sampling Bias is case, in which some section of population have higher or lower chance of being selected in sample than others.

'Elizabeth wants to estimate the mean vacation days of coworkers at her company. She collects data by selecting a random group of coworkers within her department'. This case is of Convenience Sampling, where person selects sample only as per his/ her convenience.

Elizabeth has conveniently chosen sample workers from her department, so they have higher chance of being in sample, others have lesser chance. Hence, this is Sampling Bias

7 0

3 years ago

How do i understand Vertices because i forget sometimes?

Burka [1]

the highest point; the top or apex.
"a line drawn from the vertex of the figure to the base"

GEOMETRYeach angular point of a polygon, polyhedron, or other figure.

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3 years ago

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How is everyones morning? Lets start off the day giving free points!!

Lunna [17]

Answer:

yes

Step-by-step explanation:

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3 years ago

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