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3 years ago

What number makes the the number sentence true 420,008 - 9,569 =n

Mathematics

2 answers:

kupik [55]3 years ago

8 0

Answer: its 410439

(all u need to do is subtract!)

LekaFEV [45]3 years ago

4 0

N=410,439
You can just type your problem into a calculator-- you're just finding out what 420,008-9,569 is. :)

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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

3 years ago

Find the value of y if the value of x is 2 for each equation and match it with the appropriate result.

Xelga [282]

9514 1404 393

Answer:

3, 0, 2, -2

Step-by-step explanation:

Put x=2 into each equation and solve for y.

2 + y = 5

y = 5 -2

y = 3

3x +2y = 6

3·2 +2y = 6

2y = 6 -6 = 0

y = 0

2x +y = 6

2·2 +y = 6

y = 6 -4

y = 2

5x +3y = 4

5·2 +3y = 4

3y = 4 -10 = -6

y = -2

4 0

3 years ago

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

salantis [7]

Answer:

b =15

Step-by-step explanation:

We can use Pythagoras theorem to find b:

$a^{2}+b^{2} = c^{2}$

$8^{2} + b^{2} = 17^{2}$

64 + $b^{2}$ = 289

64 + 225 = 289

64 + $15^{2}$ = 289

b = 15

hope this helps :) and sorry if not right

7 0

3 years ago

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Are the two triangles similar? Explain your answer.

Sveta_85 [38]

Answer:

Step-by-step explanation:

Two triangles are similar if their corresponding angles are congruent and the corresponding sides are in proportion They are the same shape, but not necessarily the same size

Triangle ABC 54 +68 + 58 = 180

Triangle EFG 68 +63 +49 = 180

In this case their corresponding angles are nor congruent

8 0

3 years ago

What's 65-70 days in weeks

dusya [7]

Answer:

About 9-10 weeks

Step-by-step explanation:

70/7= 10

4 0

3 years ago

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