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Geometric series with r = 2   a1 = 1   n = 12

Sum_n =  a₁(1-r^n) / (1-r)   = 4095

1st month 1 car 

2nd month 2 car's 

3rd month 4 car's 

4th month 8 car's 

5th month 16 car's  

6th month 32 car's 

7th month 64 car's 

8th month 128 car's 

9th month  256 car's 

10th month 512 car's 

11th month 1024 car's 

12th month 2048 car's 

√2+√5

--------

√2−√5   multiply top and bottom by  √2+√5     to get   ( 7+2sqrt(10))/(-3)    or    - 7/3 - 2sqrt10/3

Thanks a lot! :)

Multiply the numerator AND the denominator by sqrt 3

to get   (5 sqrt3 - sqrt 6) / 3    

Using the same formula the first guest posted for an ordinary annuity

use  n = 12     and R = .09/12 = .0075 

FV=P{[1 + R]^N - 1}/ R

FV = 700 {(1.0075)^12 - 1}/(.0075)  = 8755.31  after the first year....

Now this amount gets compound interest monthly for the next 12 months

8755.31 (1+.0075)^12 = $ 9576.62

2013 NS 29

1.

cos-theorem:

$\begin{array}{|rcll|} \hline \mathbf{ b^2 } &\mathbf{=}& \mathbf{d^2+(a-c)^2-2d(a-c)\cos(L)} \\\\ 65^2&=& 60^2+58^2-120\cdot 58\cos(L) \\ \cos(L)&=& \dfrac{60^2+58^2-65^2 }{120\cdot 58} \\ \cos(L)&=& \dfrac{2739}{6960} \\ \cos(L)&=& 0.39353448276 \\ L &=& \arccos(0.39353448276) \\ L &=& 66.8253951955^\circ \\ \mathbf{\sin( L)} &\mathbf{=}& \mathbf{0.91930985575} \\ \hline \end{array}$

2.

cos-theorem:

$\begin{array}{|rcll|} \hline \mathbf{ d^2 } &\mathbf{=}& \mathbf{b^2+(a-c)^2-2b(a-c)\cos(K)} \\\\ 60^2&=& 65^2+58^2-130\cdot 58\cos(K) \\ \cos(K)&=& \dfrac{65^2+58^2-60^2 }{130\cdot 58} \\ \cos(K)&=& \dfrac{3989}{7540} \\ \cos(K)&=& 0.52904509284 \\ K &=& \arccos(0.52904509284 ) \\ K &=& 58.0590417221^\circ \\ \mathbf{\sin(K)} &\mathbf{=}& \mathbf{0.84859371300} \\ \hline \end{array}$

$\begin{array}{|lrcll|} \hline 1. & \sin(K) &=& \dfrac{r}{x} \qquad \text{ or } \qquad r = x\sin(K) \\\\ 2. & \sin(L) &=& \dfrac{r}{80-x} \quad | \quad r = x\sin(K) \\ & \sin(L) &=& \dfrac{x\sin(K)}{80-x} \\ & (80-x)\sin(L) &=& x\sin(K) \\ & 80\sin(L)-x\sin(L) &=& x\sin(K) \\ & x\sin(L)+x\sin(K) &=& 80\sin(L) \\ & x\Big(\sin(L)+\sin(K)\Big) &=& 80\sin(L) \\ & \mathbf{x} &\mathbf{=}& \mathbf{80\cdot \dfrac{ \sin(L)} {\sin(L)+\sin(K)} }\\\\ & x & = & 80\cdot \dfrac{0.91930985575} {0.91930985575+0.84859371300} \\ & x & = & 80 \cdot 0.52 \\ & x & = & 41.6 \\ & \mathbf{x} &\mathbf{=}& \mathbf{41 \ \dfrac{3}{5}} \\ \hline \end{array}$

The length of segment KA is $\mathbf{41 \ \dfrac{3}{5}}$

$\frac{1}{6}$ x (-3)  =   -  $\frac{3}{6}$  =  -$\frac{1}{2}$

The 'y' axis

Scaled up by factor of 2   (it has to be made larger to match DEF.....    .52 would make it smaller)

Thanx, Alan !   I see what I did incorrectly now.

Firstly,   KG is a maesure of MASS not weight, though they are used (mistakenly) interchangeably in Earth's gravity.

1 KG = 2.204622  LBs in Earths Gravity  (this IS a measure of weight).

   Given:   .    1 + 1/2 w  = w   subtract 1/2 w from both sides

         1= 1/2 w       and thus w = 2 kg.   (4.409245 pounds)

How many ways can you choose 2 digits out of 10?     10 C 2   = 45

IN 4 slots how many ways can you arrane these 2 digits?   2^4 = 16

   But two of these are without the second digit   (like 3333 and 4444) ....   so 16-2 = 14 ways

14 x 45 = 630 combos.

Teeter-totter  =  See-saw in my world growing up in the US of A.   (in the South)   ~EP

Ok you call it a see saw but the people in the video called it a Teeter Totter.

Anyway, it doesn't matter.  We all know what I was talking about  (I hope lol) 

Hi Melody.  I'm in the US.  The video you provided showed what I mean by see-saw.  I tried to find a pic/video of what I call a teeter-totter but was unable to.... everything showed a see-saw!  There is a children's ride that we called a teeter-totter, but now I'm supposing the name was local to southeast Oklahoma, where I was at the time.  I guess. 

The ride is similar to a see-saw in that it is a horizontal plank with a seat at each end where the riders face each other.  But rather than pivoting rotationally in the center, the plank swings back and forth from an overhead pivot, held by two stiff tubes that attach to the plank, making roughly a triangular shape.  I'll keep looking for a pic. 

.

ok thanks. 

Maybe when I was young you called it a Teeter totter more but now it is changing so that See Saw is more common,

Here in Australia, it has always been a See Saw.

That was just an American you tube clip which definitely called it a Teeter Totter.

anyway, this is what I am talking about.

Melody we call tettor totters see saws and vice versa. If you get what I'm saying.