Simplify. (12c + 3d + 2) + (4c + 8d + 9)
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.
Answer:
Step-by-step explanation:
height of a triangle=4x-1
base=5x+2x-3
=7x-2
area of triangle=base*height/2
=(7x-2)(2x-3)/2
=7x*2x-7x*3-2*2x+2*3/2
=14x^2+21x-4x-6/2
=14^2+17x-6/2
area of rectangle=l*b
(7x-2)(4x+1)
7x(4x+1)-2(4x+1)
4x*7x+7x*1-2*4x-2*1
=28x^2+7x-8x-2
=28x^2-x-2
area of shaded part=area of rectangle-area of triangle
=
