Melody

Very impressive Ginger   

This needs to be added to our Puzzle thread!!      

This is not likely to be a very good 'proof' but here goes.

since f(x) and g(x) are odd funtion,

\(f(-x)=-f(x)\)            and      \(g(-x)=-g(x)\)

Let  \(x_1\)  be a point such that    

\(a=g(x_1)   \qquad     -a=g(-x_1)\)

\(f(g(x_1))=f(a) \qquad f(g(-x_1))=f(-g(x_1))=f(-a)=-f(a)\\ so\\ f(-g(x_1))=-f(g(x_1)) \\ \text{by definition this means that }f(g(x)) \text{ is an odd function.}\)

Yes we do.... need another question that is :)

I put this thread in sticky topics.

If it is used it can stay there but otherwise I will eventually take it down :)

If you are an honours student and you do not already know how to find the percentage of a number then I think you need to drop down several levels and study introductory arithmetic instead.  

15/75  *  100% = 20%

Here you go, there are  8

I think it is a nice idea and going by the scores I think other members agree that it is a nice idea. :)

So "The Question" it is quite obvious that you your assessment is given the thumbs down while "Supermanaccz" idea is give an unanimous thumbs up! 

You may Juriemagic but I certainly don't.

Guest has rearranged the numbers so that they spit out the right answer but there is no explanation given as to why he/she is doing anything. In fact there is not logical flow of the algorithm.

I suspect he/she has no understanding at all.

I did it the same way as you Juriemagic.

You have done it mathematically, BUT

I do understand what you are asking but I am not all that good at these either.

CPhill does lots of these on the forum.  He'd give you a good answer I expect.

Alan or Geno or Hectictar might give you a good answer too :)

I am not sure if the Google translation from Norwegian to English is good enough for this but lets see. 

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

There were two mathematicians who met at a conference in Nice one year, they called Nils and Magne.

They went to the same university several years ago, and they have not been met since then. After this conference, they meet in the foyer of the hotel. They talked together, and eventually Nils asked about how many children Magne had. He replied that he had three children. Nils also wanted to know how old the three were, but since both mathematicians answered Magne:

- If you add up my children's age then the number is 13

- I also noticed that if you multiply the age of my three children, then you will get the number you have in your room in this hotel. 

They each went to their own, but Nils was not yet completely satisfied. When they met again, Nils said:
- "I need information to know the age of your three kids," he said.
"Yes, that's right! My oldest child was born in New York," replied Magne.
"Ahh, I know the age of your children," replied Nils.
 
How could Nils find out the age of the three using the information given?

I do not know  

Thanks Alan,

I always think of the unit circle when I answer questions like this.

(cos(3x+1))^2=0

the cos of the angle is given by the x coordinate that it extends to on the unit circle.

x is zero on the y axis and this is when the angle is 90, 270, 450..... degrees (Alan's answer is in radians pi/2, 3pi/2, 5pi/2... radians )

so

\(3x+1 = \frac{\pi}{2} + k\pi \qquad \text{  where k is an integer}\\ 3x= \frac{\pi}{2} + k\pi -1\\ x= \frac{\pi}{6} + \frac{2k\pi}{6} -\frac{2}{6}\\ x= \frac{\pi-2+2k\pi}{6} \)