2 years ago

22 bags of popcorn decreased by 20%

Mathematics

2 answers:

labwork [276]2 years ago

4 0

The answer is 4.4 bags

vredina [299]2 years ago

4 0

11 bags is 17.6 is the answer

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vodomira [7]

Vertex has the coordinate (1;3)

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3 years ago

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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

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

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

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3 years ago

5) HELP I don't know what I got incorrect can you please give me the answer and the step by step, THANK YOU SO MUCH TYSM!!!

MariettaO [177]

Same as moren.. sorry

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2 years ago

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two planes travel a constant speed. plane A travels 2.800 miles in 5 hours plane B travels 3.885 miles in 7 hours. which plane i

vfiekz [6]

Plane a is faster

Have a good day!!!

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