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)
Act like it's a rectangle. The height is 10 because 7+3=10 and the length it 27. Multiply them for the are and you get 270 in. Then multiply 6x7=42 because that's the are of the space that is missing from the imaginary rectangle. Multiply by 2 (84 in.) because there are 2 missing spaces and subtract from 270= 186 inches is your answer.
Answer:
-4
Step-by-step explanation:
Answer:
y = 140, x = 159
Step-by-step explanation:
Angle y:
we can find this angle by subtracting 40 from 180, 180-40 = 140 = y
Angle x:
Some measure of an angle plus angle b is equal to 180 degrees: 180-61 = 119
We can now find the measure of the third angle of the triangle: 180-(119+40) = 21
The third angle plus angle x is equal to 180: 180-21 = 159 = x
Answer:
ALL CAN BE MADE IN SOLID FIGURES
