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2 years ago

Help please will award brainliest!!

Mathematics

1 answer:

OleMash [197]2 years ago

3 0

Answer:

The answer is -x+12/ x (x-2)

Step-by-step explanation:

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Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

3 0

2 years ago

How to solve this question please helpp!!!!!! Q1. cos -1 ( - √3/2 )

Amiraneli [1.4K]

Answer:

cos( $\sqrt{\frac{3}{2} }$ ) or 0.339

Step-by-step explanation:

6 0

3 years ago

HELP I WILL MARK BRAINLIEST

Ede4ka [16]

Answer:

the answer is A.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which could be the missing data item for the given set of data if the median of the complete data set is 50?

gogolik [260]

Answer:

Find the median of this data

21+23+60+60+50+54+54+59+26+15+43+15=480/ 12 = 40

Now the median should be 50 so take 50 - 40 = 10

The missing number from the data is 10

5 0

3 years ago

Read 2 more answers

Two events, A and B, are independent of each other. P(A)=– and P(A and B)

Georgia [21]

Answer:

D: 0.75

$P(B) = \frac{6}{8} = 0.75$

Step-by-step explanation:

Explanation:-

Independent events:

If the occurrence of the event 'B' is not effected by the occurrence or non- occurrence of the event 'A' then the event 'B' is said to be independent of 'A'

The two events are independent if the incidence of one event is not affect the probability of other event.

P(A∩B) = P(A) P(B)

Given data A and B are independent events

Given data

$P(AnB) = \frac{1}{8} and P(A) =\frac{1}{6}$

we know that A and B are independent events are

P(A∩B) = P(A) P(B)

$\frac{1}{8} = \frac{1}{6} P(B)$

Now calculation we get

$P(B) = \frac{6}{8} = 0.75$

Final answer:-

$P(B) = \frac{6}{8} = 0.75$

7 0

3 years ago