Answer:
The general solution of the given differential equation
![y = ( c_{1} + c_{2} x ) cos3 x + ( c_{3} +c_{4} x) sin3 x](https://tex.z-dn.net/?f=y%20%3D%20%20%28%20c_%7B1%7D%20%2B%20c_%7B2%7D%20x%20%29%20cos3%20x%20%2B%20%28%20%20c_%7B3%7D%20%2Bc_%7B4%7D%20x%29%20sin3%20x)
Step-by-step explanation:
Step(I):-
Given differential equation
y⁴+18y"+81y=0
⇒ (D⁴+18D²+81)y =0
The auxiliary equation
![m^4+18m^2+81 =0](https://tex.z-dn.net/?f=m%5E4%2B18m%5E2%2B81%20%3D0)
![(m^2)^{2} + 2 (9) m^{2} +(9)^2 = 0](https://tex.z-dn.net/?f=%28m%5E2%29%5E%7B2%7D%20%2B%202%20%289%29%20m%5E%7B2%7D%20%2B%289%29%5E2%20%3D%200)
we will use formula ( a + b)² = a² + 2 a b + b²
⇒ ( m² + 9 ) ² = 0
⇒ ( m² + 9 ) ( m² + 9 ) = 0
![m^{2} =-9\\m= - 3i and m=3i](https://tex.z-dn.net/?f=m%5E%7B2%7D%20%3D-9%5C%5Cm%3D%20-%203i%20and%20m%3D3i)
m² + 9 = 0
![m² = -9\\m= -3i and m=3i](https://tex.z-dn.net/?f=m%C2%B2%20%3D%20-9%5C%5Cm%3D%20-3i%20and%20m%3D3i)
The complex roots are 0± 3 i ,0 ± 3 i
<em>Step(ii)</em>:-
The complementary function
![y = e^{\alpha x } ( c_{1} + c_{2} x ) cos\beta x + ( c_{3} +c_{4} x) sin\beta x](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7B%5Calpha%20x%20%7D%20%28%20c_%7B1%7D%20%2B%20c_%7B2%7D%20x%20%29%20cos%5Cbeta%20x%20%2B%20%28%20%20c_%7B3%7D%20%2Bc_%7B4%7D%20x%29%20sin%5Cbeta%20x)
The general solution of the given differential equation
![y = e^{0 x } ( c_{1} + c_{2} x ) cos3 x + ( c_{3} +c_{4} x) sin3 x](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7B0%20x%20%7D%20%28%20c_%7B1%7D%20%2B%20c_%7B2%7D%20x%20%29%20cos3%20x%20%2B%20%28%20%20c_%7B3%7D%20%2Bc_%7B4%7D%20x%29%20sin3%20x)
The general solution of the given differential equation
Answer:
26.00$
Step-by-step explanation:
add the numbers to get the answer
Answer:
- $85,000 at 6.25%
- $65,000 at 6.00%
Step-by-step explanation:
Let x represent the amount invested at 6.25%. Then the total interest earned is ...
0.0625x + 0.0600(150,000 -x) = 9212.50
0.0025x = 212.50 . . . . . . subtract 9000, collect terms
x = 212.50/0.0025 = 85,000
150,000 - 85,000 = 65,000 . . . . amount invested at the lower rate
$85,000 is invested at 6.25%; $65,000 is invested at 6%.
More info plz there is no context
Answer:
0
Step-by-step explanation:
Approximately 0.2% of the apples will be more than three standard deviations above the mean size. In a bin of 100 apples, 0.2% of 100=0.2% apples, this rounds down to zero apples that size or larger. (In a bin of 500 apples, there could be one apple of that size.)