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Zinaida [17]
3 years ago
7

Use the graph below to answer the question that follows:

Mathematics
1 answer:
Strike441 [17]3 years ago
3 0
By graphing the given points, we will get the attached figure
which represents:
                                          f(x) = 3 sin x
but sin x = cos (x - π/2)
                                     ∴  f(x) = 3 cos ( x - π/2 )

The correct choice is option ⇒⇒⇒ <span>f(x) = 3 cos(x − pi over 2 ) </span>

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Find the Fourier series of f on the given interval. f(x) = 1, ?7 &lt; x &lt; 0 1 + x, 0 ? x &lt; 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
A blueprint of a barn is shown.The scale is 5 inches =8 feet. Find the actual length of the wall that is labeled 20 inches.
kenny6666 [7]
5=8
20/5=4
8x4=32
The answer is 32 feet
4 0
2 years ago
Find the missing angle in a triangle with the given sides.
Yuliya22 [10]

Answer:

Step-by-step explanation:

44 + 99 + x = 180

143 + x = 180

x = 37

<h2>G = 37</h2>
5 0
3 years ago
Read 2 more answers
Share successful learning strategies that you have applied in previous mathematic courses
marshall27 [118]
Sure, I have this strategy to make a sheet with questions of that chapter and do that before I study the chapter so I can see if I know a little or a lot of that chapter
5 0
2 years ago
How can you divide 58÷0.65
Orlov [11]
You can definitly use a calculator for this 
The answer would be 
<span>89.2307692308
<span><span><span><span><span>What you do is find out how many times 0.65 can go into 58 to get your answer:)

</span></span></span></span></span></span>
7 0
3 years ago
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