3 7/12 = 43/12
2 7/9 = 25/9
both denominators must be the same to add together.
(25/9)x 12
(43/12) x 9
300/108 + 387/108 =
687/108
which in its simplest form is 229/36
and in a mixed number is 6 13/36
cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
The greatest number of sets would be 20 with one girl and one boy in each.
