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:
1. 4 as that is when he is closest.
2. 3 is when he is waiting as the graph is horizontal showing no movement
3. 4 would change as that is showing his pace walking home if it increased the slope would become steep but if it decreased it would level out more.
Step-by-step explanation:
Answer
In decimal form it is 1.25 and in fraction form it 1/4
Step-by-step explanation:
There might be and there are other ways but the way I did it is I converted the fractions to decimals. 1 3/4= 1.75, 1 1/2= 1.5, and 4 1/2 equals 4.5. So I added the time he practiced on Monday and Tuesday and subtracted it from the final hour of the whole entire week and the answer is 1.25 or 1/4
Answer:
d= -16
Step-by-step explanation:
To answer this question you'll have to first simplify the equation to
0.2d+-1.2=0.3d+5-3+0.1d
then combining like terms you get
0.2d-1.2=(0.3d+0.1d)+(5+-3)
0.2d-1.2=0.4d+2
then subtract 0.4d from both sides leaving you with
-0.2d-1.2=2
then add 1.2 to both sides
-0.2d=3.2
after you divide both sides by -0.2
leaving you with the answer
D= -16
