Melody

sin-1  is     asin

I do hope that you have not passed on your CDD infection to other members of the forum Nauseated!

If any of us get CDD we will know exactly who to blame!

-------------------------------------------------------------------

On a more serious note I am going to give your 3 by 3 solution more thought. 

I have not fathomed Nauseated's answer (perhaps he can better explain)

but I did it a different way and got the same answer.

This is how I did it.

I thought of it as three ladders placed side by side.

There is the ground level - L1

the first rung                     L2

the second rung                L3

and the top rung               L4

So you have to be on each of the ladders and you can not go down a rung between ladders or you will not get to the end point in 6 units.

So here are your 'rung' possibilities as you go across the ladders.

L1    L1       L1,2,3 or 4                     4 possibilities

L1    L2       L2,3 or 4                         3 possibilities

L1    L3        L3 or 4                           2 possibilities

L1    L4        L4                                   1 possibilities

L2    L2        L2,3,or 4                         3 possibilities

L2    L3        L3,   or 4                         2 possibilities

L2     L4         L4                                 1 possibilities

L3     L3         L3 or 4                          2 possibilities

L3     L4           L4                               1 possibilities

L4     L4            L4                              1  possibilities

Total                                              = 20 possibilities

NOW Nauseated, can you explain why our 2 answers are the same.

Do you actually understand the logic behind your answer?  If so, please share  

That is not a statement. It is a question.

10f+8g=420

    F+8g=150

   Subtract

   9f.      =270

         F.  = 30

@@ End of Day Wrap    Fri 13/3/15     Sydney, Australia Time   11:35 am     ♪ ♫

Good evening everyone,

By recent standards the forum was quiet today, still there were plenty of questions, many were answered by anon people and that is fine but it is nice when people can be recognised for their efforts and today these people were Buecrab2, SamHenry, MamaLlama, Heureka, CPhill and SweatyPerson666.  Thank you.   

One year ago today CPhill (Chris) joined this forum. 

Chris's huge injection of both knowledge and humour has had a huge positive impact on our fledgling forum. 

I think that I speak for all when I say how incredibly please we are that you have spent this year with us Chris.

Thank you                 It has been a wonderful 12 months for Camelot.

Sat 14/3/15

Yes I believe you are correct annon.

I guess I need new glasses.  LOL

The second 5 appears to be irrelevent.

So you want 3 digit numbers using   4,5,6 and 7

There are 4 choices for the first digit, 3 for the second and 2 for the third - that makes

4*3*2=24

just as anon said :))

$${\mathtt{18}} = {\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\times\,}}{\mathtt{sin40}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$

$${\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{9.81}} = {\frac{{\mathtt{981}}}{{\mathtt{200}}}} = {\mathtt{4.905}}$$

$$\\-4.908t^2+40sin40-16=0\\
\\4.908t^2-40sin40+16=0\\$$$${\mathtt{4.908}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{40}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{40}}^\circ\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{16}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
{\mathtt{t}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{9}}}}\right)}{\mathtt{\,-\,}}{\mathtt{2}}}}}{{\sqrt{{\mathtt{1\,227}}}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
{\mathtt{t}} = {\mathtt{1.406\: \!665\: \!960\: \!846\: \!221\: \!3}}\\
\end{array} \right\}$$

No it doesn't       

Robin invests $1500 at 4.85% compounded quarterly

the compound interest formula is    

$$FV=PV(1+\frac{r}{t})^{nt}$$

SO

FV = future value

PV = present value

n = number of years

r is the annual interest rate (as a decimal)

t is the number of times it compounds every year.

Your problem:

Robin invests $1500 at 4.85% compounded quarterly

t=4                  (because it compounds 4 times a year)

r = 4.85/100=0.0485

$$FV = 1500(1+\frac{0.0485}{4})^{4n}$$