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2 years ago

X-4/y+2=5 solve for x I NEED THIS

Mathematics

1 answer:

zhannawk [14.2K]2 years ago

7 0

Answer:

x - ----- = 3

Step-by-step explanation:

I'm assuming that you mean:

x - ----- + 2 = 5

Subtracting 2 from both sides, we get

x - ----- = 3

adding 4/y to both sides yields:

x = 3 + -----

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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

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

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2 years ago

When Mohammed was born, the baby was 21 inches tall. at his last check up, he was 38 inches tall. what is the percent increase i

denis23 [38]

Answer:

80.95

Step-by-step explanation:

Percentage increase = $\frac{New Value - Old Value}{Old Value}$ *100

=> (38-21)* 100/21 = 80.9523%

The answer round it to the nearest 100th = 80.95%

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2 years ago

Functions can be defined using graphs, tables, and ordered pairs. Define the domain and range of a function.

Harrizon [31]

The domain is the input and the ramge is the output.

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3 years ago

Read 2 more answers

8x = 2y + 5 3x = y + 7 Solve the system of equations by substitution.

jasenka [17]

3x = y + 7
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8x = 2y + 5
8x = 2(3x-7) + 5
8x=6x-14+5
8x-6x=-9
2x=-9
x=-4.5

8x = 2y + 5
8(4.5)=2y+5
36=2y+5
2y=31
y=15.5

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3 years ago