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2 years ago

Will mark brainiest if right Is this function linear or nonlinear? y=3x−5

Mathematics

1 answer:

qwelly [4]2 years ago

6 0

Answer: This function is linear because it forms a straight line when graphed.

Would appreciate brainly <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

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

3 0

3 years ago

3. Se le ha encargado a usted la provisión de muestras para vender en el lanzamiento de la nueva bebida de aguapanela con limón

tamaranim1 [39]

I- I would help but- o meh lord

7 0

3 years ago

If Aditya can travel 80 km in 2 hours how many kilometres can he travel in 3 and half hours

ivann1987 [24]

Answer:

distance covered in 2 hours = 80 km

distance covered in 1 hour = 80÷2 = 40 km

distance covered in 7/2 hours = 40 × 7/2

= 140 km

(3 1/2hours = 7/2 hours)

8 0

3 years ago

Find the remainder of (x4 – 2) ÷ (x + 1).

prisoha [69]

Please write (x4 – 2) ÷ (x + 1) as (x^4 – 2) ÷ (x + 1).

We can find the remainder using synth. div. as follows:

_________________
-1 / 1 0 0 0 -2
-1 1 -1 1
------------------------------
1 -1 1 -1 -1

The remainder is -1.

5 0

3 years ago

The length of a rectangular garden is 8m greater than twice the width the area of the garden is 280m^2 what is the width of the

yarga [219]

Step-by-step explanation:

Given :-

The length of the garden 8m greater than 2 times the width.

Area of the garden is 280 m²

Let us consider the length as x and width as y.

Sp, we can day length as :-

x = 8 + 2y ---(1)

Now, we know that:-

Area of Rectangle = Length × Breadth

280 = x * y

We can replace the value of x now,

280 = y × ( 8 + 2y)

280 = 8y + 2y²

2y² + 8y - 280 = 0

y² + 4y - 140 = 0

Factorise it.

(y -10)(y + 14)

Cancelling -ve value, we get the width as 10 metres.

Hope it helps :)

5 0

3 years ago

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