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)
Answer: y= 3 times 2 to the power x. Second answer
Step-by-step explanation:
if you plug in 0 for x, y= 3x 1= 3
if you plug in 1 for x y= 3 x 2 = 6
Look at the x values and y values
(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.
Answer:
its 6 I'm pretty sure about it
Answer:
The correct option is;
c. Her score was better than those of 60% of all test takers
Step-by-step explanation:
Percentile Score is the score of an exam or test candidate with regard to the relative performance of the other persons that took part in the exam or test.
The percentile score is calculated by converting candidates scores into a scale consisting of the scores of all candidates and ranging from 0 to 100
A 60th percentile score means that the student performed better than 60% of all the candidates of the test and 40% of the test takers scored the same as or better than the student.