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3 years ago

Help please thank youuu

Mathematics

1 answer:

adelina 88 [10]3 years ago

8 0

Answer:

Step-by-step explanation:

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Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

On Monday morning,there were 30 tickets available for a concert if 1/3 of the tickets were sold on Monday and 1/5 of those left

lianna [129]

I think the answer would be 16, Hope this helps

8 0

3 years ago

A rectangle measures 2 4/ 5 inches by 1 1/ 5 inches. What is its area?

AlexFokin [52]

[ Answer ]

$\boxed{3\frac{9}{25} }$

[ Explanation ]

Area Of Rectangle: Length * Width

2 4/5 * 1 1/5

=======================

Convert Fractions Into Mixed Numbers:

2 4/5 = 14/5

1 1/5 = 6/5

Multiply Across:

14 * 6

5 * 5

= 84/ 25

Simplify:

3 9/25

$\boxed{[ \ Eclipsed \ ]}$

4 0

3 years ago

Martinez' General Store is having a 45% off sale on men's clothing. John paid $70.95 for a jacket that was on sale. What was the

Butoxors [25]

Answer:

$129

Step-by-step explanation:

We can use this equation:

x - 0.45x = 70.95

0.55x = 70.95

x = $129

8 0

3 years ago

Douglas said he can find 240÷10 by taking the 0 off 240 to get 24.

julia-pushkina [17]

Answer:

a. incorrect
A. equal to
59.20 ÷ 10 = 5.920

Step-by-step explanation:

What Douglas doesn't seem to realize is that it is not the act of removing the trailing zero that gives division by 10. It is the act of moving the decimal point left one place that divides the number by 10.

8 0

3 years ago