CPhill

When it hits the ground, h(t)  will = 0  .....so.....

0  =  -16t^2 + 48t + 4     divide through by -4

0 = 4t^2 -12t -1

4t^2 -12t - 1  = 0        

Using the quadratic formula....the ball hits the ground at t ≈  3.08 sec

18.  tan ( x - pi/4)

This is the graph of the tangent shifted to the right by pi/4 units

The normal tangent graph would have an asymptote at pi/2......so this graph will have an asymptote, for example, at

x = (pi/4 + pi/2)   =  3pi/4

See the graph here : https://www.desmos.com/calculator/ufvhykjqvu

19.  f(x) = 3cos(2pi *x)

The period, P, can be found as

P(2pi) = 2pi    →  P  = 1 radian

Here's the graph :   https://www.desmos.com/calculator/a4od0m3gco

1.

a.

 6x + 2 - 8x + 5   =

6x - 8x + 2 + 5  =

-2x  + 7

b.

{8x + 12 ] -  [5x - 17 ] =

8x  - 5x  + 12  - (-17)  =

3x + 29

c.  (7x) (x - 9)  =  7x * 4x  - 7x * 9    =   28x^2  - 63x

2.

2/3 (3x + 14) = 7x + 6     multiply through by 3

2(3x + 14)  = 21x + 18    simplify

6x + 28  =  21x + 18       subtract 6x, 18 from both sides

10 = 15x                         divide both sides by 15 and reduce the fraction

10/15  = x  = 2/3

Using the Law of Sines, we have

sin P / 47.6  =  sin 73 / 68     multiply both sides by 47.6

sin P  = ( 47.6 sin (73) / 68 )

Take the sine inverse to find  P

arcsin  ( 47.6 sin (73) / 68 )  = P  ≈   42.02°

Using the Law of Cosines

d =  sqrt [ 21^2 + 27^2 - 2(21)(27)cos(25) ]  ≈  11.93

The field is halved after every round......so.......after 6 rounds we have

256 / 2^6  =   256 / 64  =  4 players left

If the model is 5cm.....the real thing is 300 times as long  = 1500cm = 15m

WOW....it slipped my notice that this was your birthday.......Happy Birthday indeed.....!!!!

As an aside......Melody is one of the most caring and giving people on this site......[OK.....she may come across as a little grumpy at times, but, believe me, her bark is worse than her bite!!!]

To my good Aussie friend that I known for about 3 years now...since Omi supplied the presents......here's your cake >>>>>

P.S.........maybe  MJ can supply the ice cream......she knows a good place for that!!!!!

[3,7,15,1,292,1,1,1,2,1,3,1,…etc.].

3 + 1/1  =  4

1 + 1/4   = 5/4

2 + 4/5   =  14/5

1 + 5/14  = 19/14

1+ 14/19 = 33/19

1 + 19/33   = 52/33

292 + 33/52  = 15217/52

1 + 52/15217 = 15269/15217

15 + 15217/15269  =  244252/15269

7 + 15269/244252  = 1725033/244252

3 + 244252/1725033  =

3.14159......=   "pi"

Actually....the first "3"  should have been the tipoff....LOL!!!!

P.S. - it's accurate to 12 decimal places

2a^3   -  a    .....   a  = 4

2 (4)^3  - 4

2(64) - 4  =

128 - 4  =

124

We have that

-2  = a₁*(r)^(2-1)  →  -2 = a₁*(r)         (1)

And 

16  =  a₁* (r)^(5 -1)  →  16  = a₁*(r)^(4)     (2)

Rearrange (1)  as   -2/r   =  a₁      sub this into (2)

16  =  (-2/r) * (r)^4      simplify

16  = (-2) *(r)^3       divide both sides by  -2

-8  =  (r)^3        take the cube root of each side and   -2  = r

Using  -2/r  =   a₁     →   -2/-2   =  a₁   =  1

So....the foruteenth term is

1(-2)^(14 - 1)  =  1(-2)^13   =   - 8192