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)
Mode is the number that most occurs in the data. From the given data set, there is no repeated number. Thus, there is no mode for the data set.
Answer:
y = -1/2x - 11/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-4 - (-5) / -3 - (-1)
1/ -2
= -1/2
y = -1/2x + b
-5 = -1/2(-1) + b
-5 = 1/2 + b
-11/2 = b
30-24=6
6/30=1/5 aka 20%
The answer is 20%
Hope this helps.
Answer:
The first point should be plotted at -4, then there should be a line that goes up 8 units and gives us a final destination of 4.
