CPhill

18 + 19 + 20 + 21 + 22 =

18 + 22 + 19 + 21 + 20 =

40 + 40 + 20 =

100

So   ( a, n)  =  (18, 5)

I agree.....the result should =  pi

I do not know......maybe alan does

I can do a few

a) The velocity is positive on  0 < t  < 1

This means the ball is  rising during this time

b)  The antiderivative is     s (t) =  32t - 16t^2  + C

At  s(0)   we have    32(0) - 16(0)^2 + C = 0

So C  = 0

c)  s(1) - s(1/2)  =    [ 32(1) - 16(1)^2 ] - [ 32(1/2) - 16(1/2)^2 ]  =  [ 16] - [ 16 - 4] =  4

This represents the change in postion from t = 1/2  to t = 1

[ It rises 4 ft in this interval  = the displacement on this interval ]

d) At t = (1/2).....the height of the triangle formed is   32 - 32(1/2) =  32 - 16  = 16

So....the area =  (1/2) base * height =  (1/2) (1/2)(16) =  4 

This area also represents the displacement on t =1/2 to t =1

f) s(2) - s(0)  =  [ 32(2) - 16(2)^2] - 0   =   0

This means that the total displacement = 0 ......it falls as far as it rises

Note that the velocity at t = 0 = 32 ft/s

And at t = 2  = -32 ft/s

This makes sense.....the terminal velocity = the beginning velocity....only in the opposite direction

                 x   + 3

x^2 + 1   [ x^3 + 3x^2 - 2Ax + 3 ]

                x^3             +  1x

               ______________________

                         3x^2  - (2A + 1)x  + 3

                         3x^2                      +3

                       ____________________

                                 - (2A + 1)x

So

-(2A + 1) x = 5x

-(2A + 1)  = 5

-2A  - 1  =  5

-2A = 6

A = - 3

The  common difference is 3

So...we can solve this

11,111 = 2 + 3 (n -  1)

11,111 = 2 + 3n - 3

11,111 = 3n - 1

11,112 = 3n    

3704 = n

So.....11,111  is the 3704 term

And it appears on   page  ....  ceiling ( 3704 /100)   =  page 38

Note however.....if we drop the provision that Kylie's points be evenly divisible by 4.....at least one integer solution exists

(14, 19)

This satisfies 

3(14)  - 2(19)   =  5      which is  < 6

14  ≥  19 /4 +  9

14  ≥   13.75

And

y < 20

19 < 20

Let x = Shaniqua's points

Let y = Kylie's points

If you subtract 2 times Kylie's points from 3 times Shaniqua's points, the difference is less than 6

This translates as

3x - 2y < 6

Shaniqua scored at least as many points as nine more than 1/4 of Kylie's points

This translates as

x ≥   y/4 +  9

Kylie scored fewer then 20 points

This translates as

y < 20

Note that Kylie's number of points must be divisible by 4

And since she scoes < 20, she must have scored either 16, 12, 8 or 4    points

But....you can test for yourself.....there are no integer solutions

As close as we can be is if she scores 16

Then as few as Shaniqua could score is  16/4 + 9   =  13

But....these values make the first inequality     3(13) - 2(16)  =  7

But...the constraint is that this is < 6

So.....no integer solutions exist

1/ 90

5 +  2 x 3^2 =      

5 + 2 x 9

5 +  18  =

23

7 + 8            15

_____  =    ____  =     5

5 - 2             3

18  -  3 x 2              18   -  6                 12

_________  =        ________   =        _____    =   3

 5 -   1^2                  5 -   1                     4

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