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)
The mean is not the same thing as median
mean=78+81+85+87=331
mean=331/4=82.75
median is the middle number, but you have a par set of numbers, so your median will be the middle numbers 78,81,85,87 , which are 81+85=166, 166/2=83
83 is your median
Answer if you divide them or x them you'll get the answer!
It may be a special right triangle which would make the angles 45, 45, and 90
You can verify the zeros of the function y=x2+6x-7 by using a graph and finding where the graph C. <span>C. crosses the x-axis . Finding the zeros mean equating the equation to 0 or y =0. When y =0, this is equal to x-axis. C. is the answer to the problem given above. </span>
