Answer:
The answer is .
Step-by-step explanation:
Given:
Multiply by 14 on both the side, it gives
.
Now we add 3 on both sides.
Therefore, the answer is .
Bart has these quiz scores: 78, 76, 74, 80, 82, 78, 82, 75, 77, 82. Bart tells his parents that his typical score is an 82. Whic
2 answers:
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Answer:
− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped
− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped
1 y ' ' + 7 y ' + 5 y = 0: over-damped
Step-by-step explanation:
Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:
This differential equation will have a characteristic equation of the form:
Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.
- If the discriminant is greater than zero, the solution is over-damped
- If the discriminant is less than zero, the solution is under-damped
- If the discriminant is equal to zero, the solution is critically damped
So, given the differential equation:
Which has characteristic equation of the form:
The quadratic polynomial of the form:
Has discriminant:
In this case:
So:
In this case:
Therefore the solution is over-damped.
Now, given the differential equation:
Which has characteristic equation of the form:
The quadratic polynomial of the form:
Has discriminant:
In this case:
So:
In this case:
Therefore the solution is over-damped.
Finally, given the differential equation:
Which has characteristic equation of the form:
The quadratic polynomial of the form:
Has discriminant:
In this case:
So:
In this case:
Therefore the solution is over-damped.
Therefore the answer is D. (x + 1)(x2 + 2)
