CPhill

18,600,000,000,000 = 18 trillion, six hundred billion  ....  [at least in US terms ]

sin^-1(-1/2)  = 330°  or 11pi/12

[ This could also be a 30° angle in the 3rd quadrant  = 210°  or 7pi/6 ]

 7n+17=3n+76      subtract 3n, 17 from both side

4n = 59       divide both sides by 4

n = 59/4

The "normal" surface area would be

2*pi*r (r + h)

The "new" surface area would be

2*pi*(2r) (2r + 2h)=

2*pi*(2r)(2)(r + h)=

8*pi *r (r + h) =  4 times as great

I'm assuming that this is

(2/3)S - (S - 1/3) = 1/2 - (S - 1/2) -1/3      simplify

(2/3)S - S + 1/3  = 1/2 - S + 1/2 - 1/3       add S to both sides

(2/3)S + 1/3  = 1/2 + 1/2 - 1/3          

(2/3)S + 1/3  = 1 - 1/3

(2/3)S + 1/3  = 2/3  subtract 1/3 from each side

(2/3) S  = 1/3     multiply both sides by 3/2

S  = (1/3)(3/2)  = 3/6  = 1/2

2 cos x - sec x = 1   .....note sec x = 1/cosx  so we have

2cosx - 1/cosx  = 1      multiply through by cos x

2cos^2 x  - 1  =  cos x    rearrange

2cos^2 x - cos x - 1  = 0     factor

(2 cos x + 1)(cos x - 1) = 0      so either

2 cos x + 1   = 0

2 cos x = -1

cos x = -1//2     and this occurs at  2pi/3 and 4pi/3

OR

cosx - 1  = 0   

cos x =  1    and this occurs at  0

So the solutions on the given interval are  0, 2pi/3 and 4pi/3

log(19-3x)=1

In exponential form, we have

10^1 = 19 - 3x

10 = 19 - 3x      rearrange

3x = 19 - 10

3x = 9         divide both sides by 3

x = 3

4 sin2 θ + 1 = 9 sin θ  

Angle A is given by

tan^-1( 10.7 / 44.4) = A = about 13.55°