Answer:
?=4
Step-by-step explanation:
?*(3+2)=12+8
?(5)=20
20/5=4
?=4
4*(5)=20
20=20
Answer:
16.67
Step-by-step explanation:
2/12
Mean is average so you sum up all 4 numbers and divide by 4. Answer is 27.6725 or rounded 27.67
Have a nice day. Hope this helps.
Answer:
4 (a.)
Step-by-step explanation:
The x line has to be under 7 and 6 is too close to 7, therefore 4 is the answer
For any equation,
![a_ny^(n)+\dots+a_1y'+a_0y=0](https://tex.z-dn.net/?f=a_ny%5E%28n%29%2B%5Cdots%2Ba_1y%27%2Ba_0y%3D0)
assume solution of a form, ![e^{yt}](https://tex.z-dn.net/?f=e%5E%7Byt%7D)
Which leads to,
![(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0](https://tex.z-dn.net/?f=%28e%5E%7Byt%7D%29%27%27%27-%28e%5E%7Byt%7D%29%27%27%2B4%28e%5E%7Byt%7D%29%27-4e%5E%7Byt%7D%3D0)
Simplify to,
![e^{yt}(y^3-y^2+4y-4)=0](https://tex.z-dn.net/?f=e%5E%7Byt%7D%28y%5E3-y%5E2%2B4y-4%29%3D0)
Then find solutions,
![\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}](https://tex.z-dn.net/?f=%5Cunderline%7By_1%3D1%7D%2C%20%5Cunderline%7By_2%3D2i%7D%2C%20%5Cunderline%7By_3%3D-2i%7D)
For non repeated real root y, we have a form of,
![y_1=c_1e^t](https://tex.z-dn.net/?f=y_1%3Dc_1e%5Et)
Following up,
For two non repeated complex roots
where,
![y_2=a+bi](https://tex.z-dn.net/?f=y_2%3Da%2Bbi)
and,
the general solution has a form of,
![y=e^{at}(c_2\cos(bt)+c_3\sin(bt))](https://tex.z-dn.net/?f=y%3De%5E%7Bat%7D%28c_2%5Ccos%28bt%29%2Bc_3%5Csin%28bt%29%29)
Or in this case,
![y=e^0(c_2\cos(2t)+c_3\sin(2t))](https://tex.z-dn.net/?f=y%3De%5E0%28c_2%5Ccos%282t%29%2Bc_3%5Csin%282t%29%29)
Now we just refine and get,
![\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}](https://tex.z-dn.net/?f=%5Cboxed%7By%3Dc_1e%5Et%2Bc_2%5Ccos%282t%29%2Bc_3%5Csin%282t%29%7D)
Hope this helps.
r3t40