Solve 2sin(2x) - 2sinx +2sqrt3 cosx - sqrt3 = 0

2sin(2x)-2sinx+2sqrt3cosx-sqrt3 = 0

4sin(x)cos(x) - 2sin(x) + 2sqrt(3)cos(x) - sqrt(3) = 0

Factor:

2sin(x)[2cos(x)-1] + sqrt(3)[2cos(x)-1] = 0

[2cos(x)-1][2sin(x)+sqrt(3)] = 0

Solve:

2cos(x)-1 = 0 or 2sin(x)+sqrt(3) = 0

cos(x) = 1/2 or sin(x) = -sqrt(3)/2

x = +/-pi/3 or x = -pi/3 or (4/3)pi

hope this helps!

4.0 ft

step-by-step explanation:

4.0 ft

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: