Melody

Yes a great explanation Ninja,   I'd like to add just a little.

people do not like the fact that  $$-4^2=16$$   

the surface it appears that it should be thought of as    $$(-4)^2=16$$

  $$But what about $27-4^2$ ? \\
No-one would want to interpret this as $27+(-4)^2 = 27+16=43$ That would be really odd.\\
Of course not $27-4^2=27-16=11$\\\\
so here it is really obvious that -4^2=-1*4^2=-1*16=-16$$ 

Sen(2x)=½ si 0<=x=>360. ¿Qué valores de x cumplen?

I am not sure about the translation on this one ?

sine(2x)=1/2

sine is positive so 1st and 2nd quadrants       

0<=x<=360   ?

0<=2x<=720

sine 30 degrees = 1/2

2x = 30, 150, 390, 510

x = 15, 75, 195, 255 degrees

K=log(A)-2 log(B)+3 log(C)-3 log(D)

$${log}_{10}\left({\mathtt{A}}\right){\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{B}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{C}}\right){\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{D}}\right) = {\mathtt{K}}$$

$${\mathtt{K}} = {log}_{10}\left({\mathtt{A}}\right){\mathtt{\,-\,}}{log}_{10}\left({{\mathtt{B}}}^{{\mathtt{2}}}\right){\mathtt{\,\small\textbf+\,}}{log}_{10}\left({{\mathtt{C}}}^{{\mathtt{3}}}\right){\mathtt{\,-\,}}{log}_{10}\left({{\mathtt{D}}}^{{\mathtt{3}}}\right)$$

$${\mathtt{K}} = {log}_{10}\left({\frac{{{\mathtt{AC}}}^{{\mathtt{3}}}}{\left({{\mathtt{B}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{D}}}^{{\mathtt{3}}}\right)}}\right)$$

This is testing my memory 

12) Make a box- and- whisker plot for each set of values. 12 12 11 15 12 19 20 19 14 18 15 16

11 12 12 12 14 15 15 16 18 19 19 20    12 scores

Lowest = 11

Lower quartile = 12

Median=15

Upper quartile =19 

Highest=20

I think that this is it. 

$$y=x^2-3\\\\
\begin {tabular}{|c|c|c|c|c|c|c|c|}\hline
$x$&\;\;-1\;\;&\;\;0\;\;&\;\;1\;\;&\;\;2\;\;&\;\;3\;\;&\;\;4\;\;&\;\;5\;\;& \hline
$y$&(-1)^2-3=-2&0^2-3=-3&1^2-3=-2&2^2-3=1&3^2-3=6&4^2-3=13&5^2-3=22& \hline
\end{tabular}$$

Sat 23-8-14

* 1) Why is  $$-3^2=-9\;\; not\;\; +9?$$       (Great answer from Ninja)

@@ End of Day Wrap :     Fri 22/8/14          Sydney, Australia         Time 9:00pm        ♬  

Hello all,

Our great answers today were delivered by TakahiroMaeda, AzizHusain, CPhill, DragonSlayer554, Heureka, NinjaDevo and Admin.  Thank you all.  

I have definitely not looked at all the questions and answers today.  The forum is getting too popular for that to be possible on many days.  However, almost all questions have been ticked and this can only be done by moderators or the question asker.  So I am assuming most answers are satisfactory or better.  

Please if you see a great question, or answer or you write a wonderful answer yourself please let me know and I will reference it in the wrap and Ninja may reference it in one of his fabulous threads.  I want to know what is going on but I will be increasingly relying on other people to keep me informed.

Chris, you have ticked off many questions today.  I really thank you for steadily taking over this area of administration and responsibility.  

Here are some interesting posts for the day:

* 1) Bearings with Vectors (Trigonometry or vectors)

Do you mean this?  And, what is your question?

$$f(x)=7x^6-4x^4+2x-4$$

Is there a question here?

Anonymous appears to be correct except that there are 13 letters.  

(Unless I can't count which is always a possibility)

$$Number of Permutations is $\frac{13!}{2!2!2!}$$$

$${\frac{{\mathtt{13}}{!}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}} = {\mathtt{778\,377\,600}}$$

I am never overly confident about these so I used this site for reference.