The angles are 72 degrees and 108 degrees.
Explanation:
Angle 1 : Angle 2 = 2 : 3
Angle 1 = 2k
Angle 2 = 3k
Angle 1 + Angle 2 = 180 (supplementary angles)
2k + 3k = 180
5k = 180
k = 36
Angle 1 = 2k = 2 x 36 = 72 degrees
Angle 2 = 3k = 3 x 36 = 108 degrees
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)
That would be option A as the angles and sides ( the AS) have already been stated.
well... 42+24=66 so the height of the attic is 66 feet
