Answer:
What is the question?
Step-by-step explanation:
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)
Answer:
Probability
Step-by-step explanation:
In this game, the players rely entirely on chance to win, rather than skill. Therefore, this game would be particularly useful in helping students' understanding of probability.
(Spoken from someone who played this exact game 2 years ago to learn about probability.)
Step-by-step explanation:
1.3×2×a×b
=6ab
2.c5×c
=c5+1
=c6
3.2y4×5y3
=10y4+3
=10y7
4.3gh2×4g3h3
=12g1+3h2+3
=12g4h5
Answer: 18.84cm
Step-by-step explanation: 3 x 2 x 3.14 = 18.84cm
