Find all solutions to the equation in the interval [0, 2π). cos 4x - cos 2x = 0

See below in bold.

Step-by-step explanation:

cos 4x = 2cos^2 2x - 1 =  2 (2 cos^2 x - 1)^2 - 1

and cos 2x = 2 cos^2 x - 1 so we have:

2 ( 2 cos^2 x - 1)^2 - 1 - (2cos^2 x  - 1) = 0

2 ( 2 cos^2 x - 1)^2 - 2 cos^2 x = 0

(2 cos^2 x - 1)^2 -  cos^2 x = 0

Let c = cos^2 x, then:

(2c - 1)^2 - c = 0

4c^2 - 4c + 1 - c = 0

4c^2 - 5c + 1 = 0

c = 0.25, 1

cos^2 x  = 0.25 gives cos x = +/- 0.5

and cos^2 x = 1 gives cos x = +/- 1.

So for  x = +/- 1 , x = 0, π.

For cos x = +/- 0.5, x = π/3, 2π/3, 4π3,5π/3.

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

my guess would be b and d, but i didn’t actually get out the pen and paper. lol