CPhill

Thanks !!!!

(fg)(x)  =  f(x) * g(x) =

(2x^2 - 3) ( x + 4) =

2x^3  + 8x^2 - 3x - 12  

Let the first term = a1  and the second term = a2

Note that the 3rd term is  =  a1 + a2

And the 4th term is =    a1 + 2a2

And the 5th term is =  2a1 + 3a2 

So....the normal  Fibonacci Series is

Fib (n)            1     2     3     4    5       

Term               1     1     2    3    5        etc

Then...in the above series....it appears that the nth term (after the second one ) is given by :

Fib (n -2 )*a1 + Fib (n - 1)*a2

So....the 16th term is

Fib (16 - 2) * a1  + Fib (16 - 1) * a2  =

FIb (14) *( -3)   +  Fib (15) * 9

Note..... Fib (11) = 89       Fib (12) = 144    Fib (13) = 233   Fib (14) = 377    Fib(15) = 610

So....the 16th term is

(377)* (-3)  +  610 * 9  =

4359

Two questions, EP [ since I don't know anything about this....]

What does  uW    represent???

Also...I guess the M62  is supposed to be M^2  ????

We need the x, y coordinates of these points before we can write an equation

Thanks, EW!!!!!

First one

Avg rate of  change from 0 to 2

We have the points  at x = 0 and x = 2  of  (0, 2)  and ( 2, 1)

The average rate of change is just  the  slope between these points = 

[ 1 - 2 ] / [ 2 - 0 ]  = -1 /2

Second one

Avg rate of change on [ 3, 5 ]  

We have the points  ( 3,59)  and (5,53)

The avg rate of change is just the slope between the points  =

[ 53 - 59 ] / [ 5 - 3 ]  =  -6 / 2  =  -3

Last one

We have the points  ( 1, 484)  and ( 4,244)

Avg rate of change =  [ 244 - 484 ] / [ 4 - 1 ] =  -240 / 3   =   -80

This must pass the Triangle Inequality....thus....

6 + missing side >  9

missing side  > 3

Also

6 + 9 >  missing side

15 >  missing side

So

3 < missing side < 15

So....A, B , C and F    are possible answers

OK.....no prob.....

Second one

Avg rate of change  [2, 5 ]  =  [ 110 - 92 ] / [ 5 - 2 ]  = 18 / 3  =  6

Last one

At x = 3,  y ≈ 3.5

At x = 6, y = 9

So....the avg rate of change is   [ 9 - 3.5 ]  / [ 6 - 3 ]  =   5.5 /3  =  55 / 30  =   11 / 6