Melody

Yep, CPhill's answer id the same as mine :)

I expect you are right rarinstraw but that is the beauty of this place.

Almost all of us see mathematics here that is new or unknown to them.  I regularly see things that Alan, Heureka, CPhill, Bertie and Geno3141 put up on the forum that are either totally beyond me or that I can learn from.

I love that.

You are getting a glimpse of what is to come.  Little bits of it you can run with and learn from if you choose to.  Plus of course we are here if you do not understand your classwork :)

Hi Guest.

cos2x - cosx = 0

\(cos2x - cosx = 0\\ cos^2x-sin^2x-cosx=0\\ cos^2x-(1-cos^2x)-cosx=0\\ cos^2x-1+cos^2x-cosx=0\\ 2cos^2x-cosx-1=0\\ let \;\;y=cosx\\ 2y^2-y-1=0\\ 2y^2-2y+y-1=0\\ 2y(y-1)+1(y-1)=0\\ (2y+1)(y-1)=0\\ 2y=-1\;\;\;\;or\;\;\;\;y=1\\ y=-\frac{1}{2}\;\;\;\;or\;\;\;\;y=1 \)

\(cosx=-\frac{1}{2} \qquad or \qquad cosx=1\\ for\;\; 0\le x<360\; degrees\\ x=180\pm 60 \;degrees \qquad or \qquad x=0\; degrees\\ General \;solutions\\ x=180\pm 60 \;+360n\;degrees \qquad or \qquad x=0+360n\; degrees\\ x=180\pm 60 \;+360n\;degrees \qquad or \qquad x=360n\; degrees\\ x=180(2n+1)\;\pm\ 60\;degrees \qquad or \qquad x=360n\; degrees\qquad n\in Z\\ \mbox{Normally this would be expressedin radians}\\ x=(2n+1)\pi\pm\frac{\pi}{3} \qquad or \qquad x=2\pi n \qquad \qquad n\in Z \)

Now that I have finished it has occurred tyo ma that maybe you wanted  the solutions to

cos^2x - cosx = 0

that is

(cosx)^2 - cosx = 0

which is a very much easier question ://

Thanks for starting that thread CaliGirl619     

There are so many great pics and slogans in there I do not know where to start!

Spawn:   That Rooster on stilts had great appeal.

The P*g and Cow best friends forever - ROF LOL

That last one from ILoveFood was funny and clever.

Thanks guys, I can (always) do with all the light entertainment that I can get.  :)

They are all great :D       

Sorry Songofflight and BruceWayne, you both got this one wrong.

Two minus only make a plus if

1)   They are so close together that you can put a circle around them and there are no numbers in the the circle.

2)   If it is a negative number multiplied by a negative number

3)   If it is a negative number divided by a negative number.

This is the question

-8-6

It does not fit the criteria above so the two negatives DO NOT make a positive.

You need to think of a number line when you do these.

This is a different question.  It is -5-3

see how I started at -5 then it is take away so you go left to the minus end.  

It is -3 so you to 3 places and you end up at -8

Now you do someting similar for your question.  start at -8 then go to the negative end 6 jumps.

-8-6 =       One of you can tell everyone the answer   :)

Thanks Alan that makes good sense.

I suppose your just run it with our own software?  

Why is it called a Monte Carlo simulation?

Here is a formalization of my answer.

This was presented by a member on another forum.

I also received help with my other answer but I understand it perfectly.

A difficult probability question.      Melody.

http://web2.0calc.com/questions/probability_882

Thanks Solveit :))

Thanks Chris