1 + cosx + cos2x=0 help my math xD ty

x = π/2 + nπ or x = (2/3 π + 2nπ) or x = (4/3 π + 2nπ)

Step-by-step explanation:

1 + cosx + cos2x=0

1+cosx+(2cos²x -1) = cosx + 2cos²x = cosx (1 + 2cosx) = 0

cosx = 0    

x = 90° (π/2) or (90+180) or (90+180x2) i.e    π/2 + nπ

or 1 + 2cosx = 0

cosx = -1/2

x = 120° or 240°  (2/3 π or 4/3 π)  or (120 + 360 : 2/3 π + 2π) (120 + 2 * 360)

i.e. (2/3 π + 2nπ)

or (240 + 360 : 4/3 π + 2π) (240 + 2 * 360) i.e. (4/3 π + 2nπ)

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.