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)
-1 * (-4) = 4; 3 * (-4) = -12; 6 * (-4) = -24; -3 * (-4) = 12
Of 85% of cars sold where not black then 100-85% where black = 15%
let the number of cars sold be y
then 15%*y=300
y= 300 divided by 15%
= (300*100)/15
=2000
therefore 2000 cars were sold
Answer:
Step-by-step explanation:
7x + 8y + 5z
I put the equations in parentheses, assuming that I would be adding both of the equations together. Then, I removed them and combined the like terms. I used two calculators to check my answer, and this should be correct.
2 rows of geraniums and 4rows of the other one
