A box of 15 cloud markers cost $12. 70. A box of 42 cloud markers cost $31. 60. How much would a box of 50 cloud markers cost? W
1 answer:
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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.
ANSWER
Possible rational roots: <span><span>±1,±2,±3,±4,±6,±12</span><span>±1,±2,±3,±4,±6,±12</span></span>
Actual rational roots: <span><span>1,−1,2,−2,−3</span></span>
<span><span>see attachments for all steps.</span></span>