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
5000 is 1/100 of the value of 500,000
Answer:
16
Step-by-step explanation:
The angle shown there is an example of a vertical angle. An opposite angle formed by intercecting lines. They are always congruent, so to solve this, you must set them equal to eachother. you can gather the equation 4x-5=59. From there, you just solve it like you would any two step equation.
Answer:
a) 60 graduates
b) Business and social science.
Step-by-step explanation:
In United States, from 2009 to 2010 the Bachelor's Degrees graduates are made up of 22% for business, 10% for social science, 8% is health related, 6% is education and 54% is others. Given that a sample of 1000 college graduates where used,
a) Number of graduates with education degree is equal to 6% of the total college graduates. Therefore:
Number of graduates with education degree = 6% × 1000 = 0.06 × 1000 = 60 graduates
b) Number of graduates with business degree = 22% × 1000 = 0.22 × 1000 = 220 graduates
Number of graduates with social science degree = 10% × 1000 = 0.1 × 1000 = 100 graduates
Number of graduates with health related degree = 8% × 1000 = 0.08 × 1000 = 80 graduates
Number of graduates with other degree = 54% × 1000 = 0.54 × 1000 = 540 graduates
Since Many graduates earn degrees in fields that result in high-paying jobs, the two fields most likely pay more than the others are that of business and social science.
