The first thing we must do in this case is find the derivatives:
 y = a sin (x) + b cos (x)
 y '= a cos (x) - b sin (x)
 y '' = -a sin (x) - b cos (x)
 Substituting the values:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 We rewrite:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
 sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
 From here we get the system:
 -b-8a = 1
 a-8b = 0
 Whose solution is:
 a = -8 / 65
 b = -1 / 65
 Answer:
 constants a and b are:
 a = -8 / 65
 b = -1 / 65
        
             
        
        
        
The probability will be :
C(12,2) / C(40,2) = 11/130, which is around 8.46%
        
             
        
        
        
Answer:
65 degrees because tangent chord angles are half the size of the arc
 
        
             
        
        
        
3/2x - 4 = 16
Add 4 to both sides.
3/2x = 20
Multiply by 2/3.
x = 13 1/3