CPhill

(-3, 4, -12)

tan θ= y/x = 4/-3

tan Φ = √ [ x^2 + y^2 ] / z = 5 / -12

And their sum is 

  -4/3 + - 5/12  =  

-16/12 - 5/ 12 =

-21 / 12 =

-7 / 4

I think this correct, NSS..

We either get a sports car,  a utility vehicle or a luxury car

So.....3 possible ooutcomes

Just count the odds between 1 - 25 inclusive...

I'm digging deep here, Rekt...!!!....LOL!!!!

First....let's convert these to cylindrical coordinates  (r, θ, z)

r = p sin Φ   =   12 sin 3pi/4  =  6√2

θ = θ = 2pi/3

z = p cos Φ =  12 cos 3pi/ 4 =    -6√2

Then....convert these to rectangular (Cartesian) coordinates (x, y, z)

x = r cos  θ =  6√2 * cos 2pi/ 3 =  6√2 (-1/2) = -3√2

y = r sin θ =   6√2 * sin 2pi/ 3 =  6√2 * √3/2 =  3√6

z =   -6√2

So   (x, y , z)  =   ( -3√2 ,  3√6,  -6√2 )

So.... x + z =  -9√2

If the circle is inscribed in the square....let the side of the square = S...so...its area = S^2

The radius of the circle is S/2

So....the area of the circle is pi (S/2)^2 =  (pi/4)S^2

And the black area is (1/2) of this =  (pi/8)S^2

So....P(hitting the black area)  =   Black Area / Total Area of Square =

(pi/ 8)S^2              pi / 8   ≈   .3927 =   39.27%  

________  = 

      S^2

P(1 on the die) = 1/6

P (1 on the spinner) = 1/4

P (both happening) =  1/6 * 1/4 =    1/24

f(0)  =   a/2

Find the inverse.....get x by itself

y = a / (x + 2)

yx + 2y = a

yx  =  a - 2y     divide both sides by y

x = [ a - 2y] / y           "swap" x and y

y = [ a - 2x] / x     

f^-1(x) = [ a - 2x ] / x           this is the inverse

f^-1 (3a)  = [ a - 2(3a) ]/ (3a) =       - 5a / 3a   =   -5/3

And this equals f(0).....so

a/2 = -5/3     multiply both sides by 2

a =  -10/3

We have a 1/2 chance for any  coin to come up tails...so...

(1/2) (1/2)(1/2) (1/2)  =   1/16

Which one do you think, NSS ???

[ Remember that we had one like this a few days ago...]

[8 possible outcomes for  president] * [6 outcomes for vice-president] =

8* 6 =

48