Answer:
Richard will have $60,000 in his account in 20 years.
Step-by-step explanation:
(1) Multiply $250 x 12
(2) Multiply the answer of $250 x 12 which is 3000 by 20
(3) Final answer would be $60,000
Complete Question
The complete question is shown on the first uploaded
Answer:
is not a solution of the differential equation
is not a solution of the differential equation
is not a solution of the differential equation
Step-by-step explanation:
The differential equation given is ![y'' + y' = cos2x](https://tex.z-dn.net/?f=y%27%27%20%2B%20y%27%20%3D%20cos2x)
Let consider the first equation to substitute
![y_1 = cosx +sinx](https://tex.z-dn.net/?f=y_1%20%20%3D%20cosx%20%20%2Bsinx)
![y_1' = -sinx +cosx](https://tex.z-dn.net/?f=y_1%27%20%20%3D%20-sinx%20%20%2Bcosx)
![y_1'' = -cosx -sinx](https://tex.z-dn.net/?f=y_1%27%27%20%20%3D%20-cosx%20-sinx)
So
![y_1'' - y_1' = -cosx -sinx -sinx +cosx](https://tex.z-dn.net/?f=y_1%27%27%20-%20y_1%27%20%20%3D%20-cosx%20-sinx%20-sinx%20%20%2Bcosx)
![y_1'' + y_1' = -2sinx](https://tex.z-dn.net/?f=y_1%27%27%20%2B%20y_1%27%20%20%3D%20-2sinx%20)
So
![-2sinx \ne cos2x](https://tex.z-dn.net/?f=%20%20-2sinx%20%5Cne%20%20cos2x%20)
This means that
is not a solution of the differential equation
Let consider the second equation to substitute
![y_2 = cos2x](https://tex.z-dn.net/?f=y_2%20%3D%20%20cos2x)
![y_2' = -2sin2x](https://tex.z-dn.net/?f=y_2%27%20%3D%20%20-2sin2x)
![y_2'' = -4cos2x](https://tex.z-dn.net/?f=y_2%27%27%20%3D%20%20-4cos2x)
So
![y_2'' + y_2' = -4cos2x-2sin2x](https://tex.z-dn.net/?f=y_2%27%27%20%2B%20y_2%27%20%20%3D%20-4cos2x-2sin2x%20)
So
![-4cos2x-2sin2x \ne cos2x](https://tex.z-dn.net/?f=%20-4cos2x-2sin2x%20%5Cne%20%20cos2x%20)
This means that
is not a solution of the differential equation
Let consider the third equation to substitute
![y_3 = sin 2x](https://tex.z-dn.net/?f=y_3%20%3D%20%20sin%202x)
![y_3' = 2cos 2x](https://tex.z-dn.net/?f=y_3%27%20%3D%20%202cos%202x)
![y_3'' = -4sin2x](https://tex.z-dn.net/?f=y_3%27%27%20%3D%20%20-4sin2x)
So
![y_3'' + y_3' = -4sin2x - 2cos2x](https://tex.z-dn.net/?f=y_3%27%27%20%2B%20y_3%27%20%20%3D%20-4sin2x%20%20-%202cos2x%20)
So
This means that
is not a solution of the differential equation
Answer:
2x
Step-by-step explanation:
Complete answer