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2 years ago

Last year the chess club had 40 members.this year the club has 30 members.find the percent of decrease in the number of members

Mathematics

1 answer:

lisabon 2012 [21]2 years ago

8 0

There is a 25% decrease

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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

I need help ASAP! It's urgent.. PLISSSSS

Soloha48 [4]

Answer:

hope this helps you

7 0

3 years ago

Help on $3.70÷2=no clue

Daniel [21]

3.7/2 = 1.85
2 goes into 3 1 time.
you have a remainder of 1
That one gets a 7 after it
now you have 17
2 goes into 17 8 times
remainder of 1
bring down the 0 that's there, but is not shown because it's not important in standard form or decimals.
You get 10 and that's 5
so you have 1.85
1.85$

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2 years ago

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What is the cost of four $4.50 small drinks with a sales tax of 4%?

Andreyy89

It would be 18.72$. Hope dis helps :)

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3 years ago

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What is the value of the expression 2x2 3xy – 4y2when x = 2 and y = –4? a. –80 b. –32 c. 32 d. 80

FinnZ [79.3K]

2x^2 + 3xy - 4y^2 when x = 2 and y = -4
= 2(2)^2 + 3(2)(-4) - 4(-4)^2 = 2(4) + (-24) - 4(16) = 8 - 24 - 64 = -80

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3 years ago