Answer:
34/5
Step-by-step explanation:
5/5 x 6 = 30/5 + 4/5 = 34/5
1 < 34/5
Answer:
0 (I think)
Step-by-step explanation:
(1,6) (3,-6)
X1 Y1. X2 Y2
-6-6= 0
3-1=2
0/2= 0
6x^2 + x - 15 = 6x^2 - 9x + 10x - 15 = 3x(2x - 3) + 5(2x - 3) = (3x + 5)(2x - 3)
Therefore, the other factor is 3x + 5.
Answer:
![\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bu%27%3Dv%7D%20%5Catop%20%7Bv%27%3D5v-6u-5%5Csin%282t%29%7D%7D%20%5Cright.%20%5C%5Cu%280%29%3D-5%3Bu%27%280%29%3D2)
Step-by-step explanation:
The given initial value problem is;
![y''-5y'+6y=-5\sin(2t)---(1)\\y(0)=-5,y'(0)=2](https://tex.z-dn.net/?f=y%27%27-5y%27%2B6y%3D-5%5Csin%282t%29---%281%29%5C%5Cy%280%29%3D-5%2Cy%27%280%29%3D2)
Let
![u(t)=y(t)----(2)\\v(t)=y'(t)----(3)](https://tex.z-dn.net/?f=u%28t%29%3Dy%28t%29----%282%29%5C%5Cv%28t%29%3Dy%27%28t%29----%283%29)
Differentiating both sides of equation (1) with respect to
, we obtain:
![u'(t)=y'(t)---(4)\\ \\\implies u'(t)=v(t)---(5)](https://tex.z-dn.net/?f=u%27%28t%29%3Dy%27%28t%29---%284%29%5C%5C%20%5C%5C%5Cimplies%20u%27%28t%29%3Dv%28t%29---%285%29)
Differentiating both sides of equation (2) with respect to
gives:
![v'(t)=y''(t)----(6)](https://tex.z-dn.net/?f=v%27%28t%29%3Dy%27%27%28t%29----%286%29)
From equation (1),
![y''=5y'-6y-5\sin(2t)\\y''=5v(t)-6u(t)-5\sin(2t)\\\implies v'(t)=5v(t)-6u(t)-5\sin(2t)----(7)](https://tex.z-dn.net/?f=y%27%27%3D5y%27-6y-5%5Csin%282t%29%5C%5Cy%27%27%3D5v%28t%29-6u%28t%29-5%5Csin%282t%29%5C%5C%5Cimplies%20v%27%28t%29%3D5v%28t%29-6u%28t%29-5%5Csin%282t%29----%287%29)
Putting t=0 into equation (2) yields
![u(0)=y(0)\\\implies u(0)=-5](https://tex.z-dn.net/?f=u%280%29%3Dy%280%29%5C%5C%5Cimplies%20u%280%29%3D-5)
Also putting t=0 into equation (3)
![u'(0)=y'(0)\\u'(0)=2](https://tex.z-dn.net/?f=u%27%280%29%3Dy%27%280%29%5C%5Cu%27%280%29%3D2)
The system of first order equations is:
![\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bu%27%3Dv%7D%20%5Catop%20%7Bv%27%3D5v-6u-5%5Csin%282t%29%7D%7D%20%5Cright.%20%5C%5Cu%280%29%3D-5%3Bu%27%280%29%3D2)