Solve the initial value problem: 9y′′−6y′+8y=0, y(π/2)=−2, y′(π/2)=−1. Give your answer as y=... . Use x as the independent vari
able.
1 answer:
Answer:
y = e^(x/3)[0.0016cos(x√7/3) - 1.2056sin(x√7/3)]
Step-by-step explanation:
The problem is solved by first writing an auxiliary equation
9m² - 6m + 8 = 0
of the differential equation
9y'' - 6y' + 8y = 0.
The auxiliary equation is the solved to obtain the values (1/3 ± i√7/3) of m. These values are then used to obtain the complementary equation
y = e^(x/3)[Acos(x√7/3) + Bsin(x√7/3)]
of the differential equation.
The conditions given are then applied.
1. y(π/2) = -2
Put y = -2 and x = π/2.
This gives an equation in terms of A and B.
2. y'(π/2) = -1
Differentiate y to obtain y', and put y' = -1 and x = π/2.
This gives another equation in terms of A and B.
The two equations obtained here are then solved simultaneously to obtain values for A (0.0016), and B (-1.2056).
These values of A and B are substituted into the complimentary solution obtained earlier to have the desired particular solution.
The step-by-step explanation is shown in the attachment.
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Answer:
The change to the face 3 affects the value of P(Odd Number)
Step-by-step explanation:
Analysing the question one statement at a time.
Before the face with 3 is loaded to be twice likely to come up.
The sample space is:
And the probability of each is:
P(Odd Number) is then calculated as:
Take LCM
After the face with 3 is loaded to be twice likely to come up.
The sample space becomes:
The probability of each is:
Take LCM
Comparing P(Odd Number) before and after
--- Before
--- After
<em>We can conclude that the change to the face 3 affects the value of P(Odd Number)</em>
Answer:
Start
A2
B2
B1
C1
C2
D2
D3
D4
C4
END
Step-by-step explanation:
Start (A3)
x is equal to 141 because they are alternate interior angles.
A2. x is equal to 39 because they are corresponding angles.
B2. x would be supplementary to 41 because the angle that x supplements is corresponding to 41.
41 + x = 180 due to the linear pair postulate. Therefore, x = 139.
B1. x would be supplementary to 82 because they are consecutive exterior angles.
82 + x = 180 due to the linear pair postulate. Therefore, x = 98.
C1. x = 102 due to the vertical angles theorem.
C2. x would be supplementary to 130 because the angle that x supplements is equal to 130 (Alternate Exterior Angles).
130 + x = 180, x = 50.
D2. x = 74, corresponding angles.
D3. x = 83, corresponding angles.
D4. x = 95, corresponding
C4. x is supplementary to 18 because of the consecutive interior angles theorem.
x = 162
END
