Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
A = 28.26 units^2
Step-by-step explanation:
The formula for the area of a circle is:
We can just plug in the numbers and solve.
28.26 units^2
Answer:
x=8
Step-by-step explanation:
Answer:
D) 0.1250
Step-by-step explanation:
Let P(J) = Probability of John to purchase 0 books
Let P(B) = Probability of Beth to purchase 0 books
P(J∩B) = Probability that both john and Beth will purchase 0 books .ie. a total of 0 books is purchased.
Since the decisions to purchase books are two independents events,
P(J∩B) = P(J) * P(B)
P(J) = 0.5
P(B) = 0.25
P(J∩B) = 0.5 * 0.25
P(J∩B) = 0.125
Answer: C, because it is the only one that makes sense.
