Answer:
a) periodic (N = 1)
b) not periodic
c) not periodic
d) periodic (N = 8)
e) periodic (N = 16)
Explanation:
For function to be a periodic: f(n) = f(n+N)
![a) x[n]=sin(\frac{8\pi}{2}n+1)\\\\sin(\frac{8\pi}{2}n+1)=sin(4\pi n+1)](https://tex.z-dn.net/?f=a%29%20x%5Bn%5D%3Dsin%28%5Cfrac%7B8%5Cpi%7D%7B2%7Dn%2B1%29%5C%5C%5C%5Csin%28%5Cfrac%7B8%5Cpi%7D%7B2%7Dn%2B1%29%3Dsin%284%5Cpi%20n%2B1%29)
It is periodic with fundamental period N = 1
![b) x[n]=cos(\frac{n}{8} -\pi)\\\\\frac{1}{8} N=2\pi k](https://tex.z-dn.net/?f=b%29%20x%5Bn%5D%3Dcos%28%5Cfrac%7Bn%7D%7B8%7D%20-%5Cpi%29%5C%5C%5C%5C%5Cfrac%7B1%7D%7B8%7D%20N%3D2%5Cpi%20k)
N must be integer. So it is nor periodic
![c) x[n]=cos(\frac{\pi}{8} n^2)\\\\cos(\frac{\pi}{8} (n+N)^2)=cos(\frac{\pi}{8} (n^2+N^2+2nN)\\\\N^2 = 16 \:\:or\:\:2nN=16](https://tex.z-dn.net/?f=c%29%20x%5Bn%5D%3Dcos%28%5Cfrac%7B%5Cpi%7D%7B8%7D%20n%5E2%29%5C%5C%5C%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B8%7D%20%28n%2BN%29%5E2%29%3Dcos%28%5Cfrac%7B%5Cpi%7D%7B8%7D%20%28n%5E2%2BN%5E2%2B2nN%29%5C%5C%5C%5CN%5E2%20%3D%2016%20%5C%3A%5C%3Aor%5C%3A%5C%3A2nN%3D16)
Since N is dependent to n. So it is not periodic.
![d) x[n]=cos(\frac{\pi }{2} n) cos(\frac{\pi }{4} n)\\\\x[n] = \frac{1}{2} cos(\frac{3\pi }{4} n) + \frac{1}{2} cos(\frac{\pi }{4} n)\\\\N_1=8\:\:and\:\:N_2=8\\](https://tex.z-dn.net/?f=d%29%20x%5Bn%5D%3Dcos%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%20n%29%20cos%28%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%20n%29%5C%5C%5C%5Cx%5Bn%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20cos%28%5Cfrac%7B3%5Cpi%20%7D%7B4%7D%20n%29%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20cos%28%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20n%29%5C%5C%5C%5CN_1%3D8%5C%3A%5C%3Aand%5C%3A%5C%3AN_2%3D8%5C%5C)
So it is periodic with fundamental period N = 8.
![e) x[n]=2cos(\frac{\pi }{4} n)+sin(\frac{\pi }{8} n)-2cos(\frac{\pi }{2} n+\frac{\pi }{6} )\\\\N_1=8\:\:and\:\:N_2=16\:\:and\:\:N_3=4](https://tex.z-dn.net/?f=e%29%20x%5Bn%5D%3D2cos%28%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%20n%29%2Bsin%28%5Cfrac%7B%5Cpi%20%7D%7B8%7D%20n%29-2cos%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20n%2B%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%29%5C%5C%5C%5CN_1%3D8%5C%3A%5C%3Aand%5C%3A%5C%3AN_2%3D16%5C%3A%5C%3Aand%5C%3A%5C%3AN_3%3D4)
So it is periodic with N = 16.
Answer:
a) 0.76
b) 0.80
c) 1964 kW
Explanation:
GIVEN DATA:
Assume Mechanical energy at exist is negligible
A) Take lake bottom as reference, and then kinetic and potential energy are taken as zero.
change in mechanical energy is givrn as
= 0.491 kJ/kg
B) 
c) 
Answer:
A Bipolar Junction Transistor, or BJT, is a solid-state device in which the current flow between two terminals (the collector and the emitter) is controlled by the amount of current that flows through a third terminal (the base).
The main basic function of a BJT is to amplify current it will allow BJTs are used as amplifiers or switches to produce wide applicability in electronic equipment include mobile phones, industrial control, television, and radio transmitters. There are two different types of BJTs are available, they are NPN and PNP.
Answer:
The most likely cause of a double precipitin ring in a RID test is when there is an antigen-antibody reaction ratio within the equivalence zone. The precipitin line forms when the antigen (with one or more epitopes) and antibody are in optimal proportions to each other and form an insoluble precipitates.
I think the answer is the third option
