Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2pi ).

2cos^2x+cosx-1 = 0

2cos^2x + 2cosx - cosx - 1 = 0

2cosx(cosx + 1) - 1(cosx + 1) = 0

(cosx + 1)(2cosx - 1) = 0

cosx+1 = 0 gives cosx = -1, x = PI

2cosx-1 = 0 gives cosx = 1/2, x = PI/3 or x = 5PI/3

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

the answer is two. hope this !