Answer:
120 degrees.
Step-by-step explanation:
All the angles in a triangle add up to 180. You have two of the angles given:
50 degrees and 70 degrees
To find the third angle of the triangle (BAC), use the expression:
180 - (50 + 70)
180 - 120
60
So, the third angle in the triangle is 60 degrees. Looking at angle DAB, you can see that it forms a straight line with angle BAC. A straight line is 180 degrees. Since we know BAC is 60, and BAC + DAB = 180, by doing 180 - 60, you can see that angle DAB is 120 degrees.
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
When i use " / " it's the Divider
X = -55w + 3 / 6( 165 - 4w )
