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:
The volume of the larger rectangular prism is 
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x-----> the volume of the larger rectangular prism
y-----> the volume of the smaller rectangular prism
In this problem we have
---> the scale factor is equal to the ratio of its corresponding sides
substitute and solve for x
Answer:
2700.
Step-by-step explanation:
The total distance would be 2700.
Distance traveled between in 6th second and 12th second is 2430-2160=270 meter. That means Superman covered 270 meter in 6 seconds.
So, now if he is moving at the same speed, he should cover the same distance in first 6 seconds which is 270 meter.
Suppose the whole distance is X when time is 0, and after flying for 6 seconds he now is 2430 meter away. It means that he must have covered the distance of X-2430=270.
Finding for X, we gets the full initial distance, when time was 0.
The simple trick is, once we get the distance he has covered in 6 seconds, we can form the equation like subtracting the whole distance- remaining distance equals to covered distance.
Answer:
The first one is a line because a line extends infinitely in both directions which the arrows indicate.
The second one is a plane since it is a 2-dimensional shape.
The last one depicts 2 rays because rays have one endpoint, but extend infinitely in the other direction.
