Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0
=> For general solution of equation,
Solve D4 - 5D3 + 5D2 + 5D - 6 = 0
=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0
=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0
=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)
Now
D2 - 1 = (D - 1)(D + 1) and
Factors of D2 - 5D + 6
D2 - 5D + 6 = D2 - 2D - 3D + 6
= D(D - 2) - 3(D - 2)
= (D - 3)(D - 2)
Therefore, equation (1) implies
(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0
=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3
=> General solution of differential equation is,<span>
=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
Hope it helps
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The given parabola will open; Down
<h3>How to interpret a parabola curve?</h3>
In parabolic curves, if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
Now, we are given the equation of the parabola s;
-36y = x²
divide both sides by -36 to get;
y = -x²/36
From the above it is clear that the leading coefficient is less than zero and as such the parabola will open in the downward direction.
Read more about parabola curve at; brainly.com/question/1480401
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Answer:
D hope this helps
Step-by-step explanation:
-y •2=-2
-2+2=0
4x+x=5x
6+3=9
5x=9
9 divided by 5
x=1.9
So there for I think the answer is 2 it’s closest to 1.9
Answer:
Step-by-step explanation:
Hello!
Maria and John want to adopt a pet. The animals available for adoption are:
7 Siamese cats
9 common cats
4 German Shepherds
2 Labrador Retrievers
6 mixed-breed dogs
Total pets available: 28
To reach the probability of each pet category you have to divide the number of observed pets for the said category by the total of pets available for adoption:
P(Siam)= 7/28= 0.25
P(Comm)= 9/28= 0.32
P(Ger)= 4/28= 0.14
P(Lab)= 2/28=0.07
P(Mix)= 6/28=0.21
a.
You need to calculate the probability that the selected pet is a cat, this situation includes the categories "Siamese" and "common cat"
P(Cat)= P(Siam) + P(Comm)= 0.25+0.32= 0.57
b.
You have a total of 16 cats out of 28 pets. If you express it in the ratio: 16:28 → using 4 as a common denominator the odds of selecting a cat is: 4:7
c.
P(Cat∪Mix)
The events "cat" and "mixed-breed dog" are mutually exclusive, so you can calculate the probability of the union of both events as:
P(Cat∪Mix)= P(Cat)+P(Mix)= 0.57+0.21= 0.78
d.
Now you are in the situation that they select a dog that is not a labrador, this situation includes the categories " German shepherd" and "mixed-breed"
P(NotLab)= P(Ger)+P(Mix)= 0.14 + 0.21= 0.35
I hope this helps!
Answer:
D
Step-by-step explanation:
Its the only one that makes sense.
