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kompoz [17]
3 years ago
7

Is 5 a integer or a whole number or a rational number? or all?

Mathematics
2 answers:
madreJ [45]3 years ago
5 0
Integer??? Idk I'm sorry....
Strike441 [17]3 years ago
3 0
5 would be an integer
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A copy machine can print 480 copies every 4 minutes.<br> How many copies can it print in 10 minutes?
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Step-by-step explanation:

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Find the half range Fourier sine series of the function
worty [1.4K]
The full range is -\pi (length 2L=2\pi), so the half range is L=\pi. The half range sine series would then be given by

f(x)=\displaystyle\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L=\sum_{n\ge1}b_n\sin nx

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b_n=\displaystyle\frac2L\int_0^Lf(x)\sin\dfrac{n\pi x}L\,\mathrm dx=\frac2\pi\int_0^\pi(\pi-x)\sin nx\,\mathrm dx

Essentially, this is the same as finding the Fourier series for the function

\begin{cases}g(x)=\begin{cases}\pi-x&\text{for }0

Integrating by parts yields

b_n=\dfrac2\pi\left(\dfrac\pi n-\dfrac{\sin n\pi}{n^2}\right)=\dfrac2n

So the half range sine series for this function is simply

f(x)=\displaystyle\sum_{n\ge1}\frac{2\sin nx}n
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