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2 years ago

Need answer fast as possible

Mathematics

2 answers:

k0ka [10]2 years ago

7 0

Answer:15

Step-by-step explanation:

The box on the left is square in a square all side are equal

Luden [163]2 years ago

6 0

Answer:

Step-by-step explanation:

That's a square, so all lengths are the same

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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

Simplify the expression: Show your work. Write the answer in standard form (15 +6d - d²) + (-5d² - 18 + 6d) PLEASE HELP

mezya [45]

Answer:

-6d^2 + 12d - 3

Step-by-step explanation:

use PEMDAS

parentheses

exponents

multiplication

division

addition

subtraction

use that order to solve problems like that.

6 0

3 years ago

Is the following argument valid?

cestrela7 [59]

I believe the answer is A! I hope that's correct! :)

3 0

3 years ago

Read 2 more answers

Solve each equation

Darya [45]

Answer:

r= 0

r= 1

b= -3

x= -3

Step-by-step explanation:

4r-8r=0

-4r=0

r=0

-15=-8r-7r

-15= -15r

r=1

3b+7-1=-3

3b= -3-7+1

3b= -9

b= -9/3

b=-3

3x+1-6x=7

-3x= 7-1

-3x= 6

x= -6/3

x= -3

7 0

3 years ago

If 14 g of a radioactive substance are present initially and 3 yr later only 7 g remain, how much of the substance will be pres

marishachu [46]

It would be 48 bc if you add it all up and subtract it and add again and multiply and divide and multiply within a and the substance of present after 6 yr you will see that i have wasted your time and that is not the answer

5 0

2 years ago