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I have not worked through it yet but I like the smiley face context.  :)

well, sorry, I must've forgot. I just got carried away with the fact that it was a part a and part b question

Happy, I may take a look for you but I keep telling people, one post = 1 question.

Normally I will not look at posts with more than one question.

Don't get me wrong though, it is a great answer, I just got a bit confused, and couldn't follow on. :( Thanks anyways for your time and effort, and skill!!!

a =  #adults                        revenue = 8a

c = #children = 2200-a       revenue = 4.5(2200-a)                  summed, the revenues add to 5050

8a        +      4.5(2200-a)               =    5050        solve for a, the # of adult tix   then c = 2200-a

N = 7th graders

2N = 8th graders

[.06 (2N) + .03(N) ] / 3N =  [.12 +.03]/3 = .05 =  5% of total students

Let N be the number of seventh-graders.....then, 1.5N = the number of eigth--graders....so we have

[.06(1.5)N + .03(N)] / [N + 1.5N]  =

[.09N + .03N] / [ 2.5N]  =

[.12N] / [2.5N]  =     ["cancel" the "N's" ]

.12/2.5 =  .048  =  4.8% 

1)

f(b,3) = 2b - 3(3)^2 + 7  = 2b - 20

2b - 20 = 90

2b = 110

b = 55

2)

b(3) = 2 - 3^3 = -25

a(3) = 3(3) - 7 = 2

a(b(3)) - b(a(3))

= a(-25) - b(2)

= 3(-25) - 7 - (2 - 2^3)

= -75 - 7 + 6

= -76

It's the volume of the little box plus the volume of the big box. 

Little box               7 •   5 • 5  =     175 

Big box                14 • 11 • 7  =  1,078 

Total                                           1,253  

_.

Try an example:  f(5)  =  11     f(4)  =  5     f(3)  =  3

A)  Does  f(5)  =  f(4) + f(3)?

B)  Does  f(5)  =  f(4) + 2·f(3)?

C)  Does  f(5)  =  2·f(4) + f(3)?

D)  Does  f(5)  =  2·f(4) + 2·f(3)?

26! / (13! · 13! )  +  26! / ( n! · (26 - n)! )  =  27! / ( 14! · 13! )

Rewrite as:     26! / (13! · 13! )  +  26! / (n! · (26 - n)! )  =  27 · 26! / ( 14 · 13! · 13! )

Divide by 26!:     1 / (13! · 13! )  +  1 / (n! · (26 - n)! )  =  27  / ( 14 · 13! · 13! ) 

1 / ( n! · (26 - n)! )  =  27  / ( 14 · 13! · 13! )  - 1 / (13! · 13! ) 

 Factor:                 =  1 / (13! · 13! )  ·  ( 27/14 - 1 )

 Simplify:              =  1 / (13! · 13! )  ·  ( 13/14 )

                             =  13 / ( 14! · 13! )

                             =  1 / ( 14! · 12! )

Therefore,  n! · (26 - n)!  =  14! · 12!

So,  n  is either  12  or  14 ...

If you are allowed to start with the identity:  tan( x/2 )  =  ( 1 - cos(x) ) / sin(x)  then: 

tan( x/2 )  =  ( 1 - cos(x) ) / sin(x)  =  

multiply both the numerator and denominator by  ( 1 + cos(x) )

=  ( 1 - cos(x) ) / sin(x)  ·  ( 1 + cos(x) ) / ( 1 + cos(x) )

=  [ ( 1 - cos(x) ) · ( 1 + cos(x) ) ]  / [ sin(x) · ( 1 + cos(x) ) ]

=  [ 1 - cos²(x) ] / [ sin(x) · ( 1 + cos(x) ) ]

=  sin²(x) / [ sin(x) · ( 1 + cos(x) ) ]

=  sin(x) / ( 1 + cos(x) )

To determine vertical asymptotes, you must first factor both the numerator and denominator and cancel

out those factors which are found in both the numerator and denominator.

y  =  (x - 1) / (x² + 6x - 7)  =  (x - 1) / [ (x - 1)·(x + 7) ]  =  1 / (x + 7)

Because there is a factor of (x + 7) remaining in the denominator, there is one vertical asymptote,

at x = -7.

The factor (x - 1) does not give a vertical asymptote, instead, it creates a "hole" in the graph at x = 1.

time = distance/rate

x/35  =  (169.5-x)/ 78        x is the distance by car

78x = 35(169.5-x)

78x = 5932.5   - 35x

x = 52.5 m  by car                     time by car = 52.5m / 35 m/hr = 1.5 hr    + 1.5 hr by 'copter = 3 hrs

pi/6   x   360^o/2pi  = 30⁰             pi/6  is  30⁰        sin pi/6 = sin 30 = 1/2

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten

 With a dot in beetween a whole number and the decimal part

Example:  0.0538483

We have 3/4*5/9=(3*5)/(4*9)=15/36 so we have $\dfrac{15}{36}$

Graph Here:

Actually the previously posted anserers found

z =  1 +i       1 - i      -1 +i    and   -1 - i

Or, you could check out a unit circle :)

Bisect means both angles are equal

2x+10 = 3x-18

x = 28                               2(28)+10   + 3(28) - 18 = BUL = .........

That's exactly what i said

"REALLY HARD QUESTION"   compute cos(300)  

      0.5    Actually, it was really easy: it took one tap on my scientific calculator.  

_.

I sense more AOPS