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
Answer:
Step-by-step explanation:
Given that in the weekly ad 5 pound bag of organic apples will cost 13.95 dollars
To find unit rate
Unit rate can be found in two ways either cost of 1 apple or no of apples for 1 dollars
I part:
5 apples = 13.95 dollars
1 apple = 13.95/5 (since direct variation)
Unit rate for one apple= 2.79 dollars
Part II:
13.95 dollars = 1 apple
1 dollar = 1/13.95 = 0.071
=0.07
But normally since apples are countable as 1,2 ... we use the first type of rate only unit rate per apple
Answer:
-3.06
Step-by-step explanation:
3-6=-3
-3/5=-0.6
Answer:
the answer that I got is 867 3/7
Step-by-step explanation:
the formula to find the volume of a sphere is 4/3 pi r³. just find the volume of both the spheres separately and minus them.
