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
It would be 3 with be on the side and then 2/10
One pie costs 0.10
you are buying 40 pies so...
40 x 0.10 = $4
one cup of coffee costs 0.50
you are buying 20 coffee so...
20 x 0.50 = $10
$4 + $10 = $14
It costs $14 to buy 40 pieces of pie and 20 cups of coffee