Mathematics

Hey guys, I'm about to take the USAMO. what would you suggest for me to study? -Uncool-

what does [math]\frac{\tan(\frac{\pi}{4} + a) - \tan(\frac{\pi}{4} - a)}{\tan(\frac{\pi}{4} + a) + \tan(\frac{\pi}{4} - a)}[/math] equal to?

A student comes to you, and asks you where did they get the formula y=mx+b from? How do you answer the student? Thank you

I think that any number divide by zero would equal to infinite. Here is how I think about it. Becaue of time dialation, light travels from one place to the other without taking anytime. So the speed of light would be C=x/0. Although the light speed as we know it is 300000 km/s, it is infinite due to time dialation. Therefore everything divided by zero would be zero. It sort of make sense.

I have heard of "Turing Machines", but unfortunately when I've tried to read what are, I cannot make sense of what the language and concepts are supposed to represent. At the very best, the descriptions of a Turing Machine I've come across only allow me to visualize an extremely complicated abacus as the closest thing representation of the basic function of a Turing Machine, but I suspect that such a visualization isnt terribly accurate. I have heard that the ability to build and use a Turing Machine has many scientific applications and philosophical implications, so naturally I am very interested to find out what they are, but I have yet to find a good resource that…

Can someone help me with the following: I am trying to prove that if [a,b] is a subset of a topological space X, where X is linear continuum, then everysubset of [a,b] that is bounded above has to have the least upper bound property. Can someone help me with that?

In this circle how do you find x [math]9^2+(x-3)^2=(x-3)^2[/math] right??

Basically, decided to see what people think should be done with the forum. Whilst it used to serve a purpose (for the old competition threads), I can't really see one for it anymore, and I personally think it should be merged with the General Mathematics forum. Just wanted to see what other people thought. Cheers

Howdy all. Firstly, apologies if this is in the wrong sub-forum. Now, On with the question! I've recently been reading through Marcus du Sautoys "Music Of The Primes". It's a great book, I thoroughly reccommend it to anyone wanting a book to read. I've been keeping up with what the maths ok so far (precious little that there has been), but one thing's bothered me. There's a chapter about Srinivasa Ramanujan, where it says that in his first letter to Hardy and Littlewood he wrote the line 1 + 2 + 3 + .... + n = -1/12 where n is infinity. Yes, I know it looks crazy. Apparently it took H&L an evening or two to work out that he really meant: 1 + 1/(2^-1) +…

It is 1:00 on a grandfather clock(a non-digital one), what time will it be when the minute hand and the hour hand form a 90 degree angle for the first time?

y - ln x = 8 3x + y = 11 How do you solve it algebraically?

As more maths are discovered, more applications are found. Increasingly, biology cannot be separated from math-- and hence, evolution cannot be separated from math. Everything from the way evolution of a creature is mapped (called phylogenics, see http://www.ucmp.berkeley.edu/clad/clad4.html ) to our understanding of how life and non-life might only be different in simple mathematical terms. What I'm saying here is that mathematics firmly SUPPORTS the ideas of evolution, not the other way round (refering to comments people have made that statistics show evolution is not possible). If you're not sure about this I recommend familiarizing yourself with many different maths …

If I divide a planets orbit velocity by the planets orbit radial distance from the sun, what is the resulting unit definition (frequency? or angular velocity?) and how are the actual units defined or clarified in value? Signed SpaceTime

hey guys. i need some help with this question: A man borrowed $40000 from a bank at a rate of 24% pa compounded monthly. At the end of each month, he repaid $4000. How much did he still owe the bank after the 5th payment. Can someone give me some tips or tell me the steps i should take to solve this problem. (by the way, the answer is $23347 but i can't seem to get that answer no matter what i try to do) thanx

Hi can anyone help me sketch the shape of the graph X^X . Thank you

I think this is a pretty hard question: All the whole numbers from 1 to 2002, including the both of them, are written on a chalkboard in increasing order: 1, 2, 3... 2001, 2002. Then, the first number is erased, then the fourth number, then the seventh number, then the tenth number and so forth erasing all the numbers that occupy a place in the form 3k+1. In the new list of numbers(after the first erasing) the same procedure is applied, erasing all the numbers occupying a place with the form 3k+1. This same process is repeated until all the numbers are erased from the chalkboard. What number is erased last?

I have been wondering how this is worked out without just plugging it into the calculator, is it possible to do it on paper or does it take a long time to work out? I feel i should already know this but i have never learned it in school or in my maths course. Its obviously not a ratio as: 9^1.5=27 but 9^2= 81.

Dave I don't know where to put this post, you can delete it later. I would like to know if there are any plans to implement a drawing program into this forum (you know like MSpaint only your own), so that you could draw circles and straight lines, and have the drawing incorporated neatly into your post, rather than attaching a .jpg or a .bmp. Possibly even a graph program, so that you just enter an equation, and its graph comes up. How hard would something like that be? Just a thought... Regards

Observe: 2 = 2 2² = 2² 4 = 4 Unsquare both sides, and you get either 2 = 2 or -2 = 2 And if you square both sides again, you get 4 = 4 again So, does -2 = 2? Or am I just an idiot?

the one directed by simon singh. anybody know where to find that? for an award-winning documentary, it sure doesn't like to show its face. all i've found are written transcripts and references to the book. but i actually wanna see the thing, ya know? has anybody ever seen this?

Here is a problem which was given in a Norwegian mathematical contest: Suppose [MATH]a[/MATH], [MATH]b[/MATH] and [MATH]c[/MATH] are real numbers such that [MATH]ab + bc + ca > a + b + c > 0[/MATH]. Show that [MATH]a + b + c > 3[/MATH].

So I'm writing a history paper (but I'm a math major) so I choose to write it on Gauss, CF. My basic outline for this paper is that I'm gonna write on what he accomplished in his day - which shouldn't be too hard b/c he did so much, how that changed life in his day and lastly how it is still changing out lives today. I think I'll focus a bit on the bell curve because it has so many application today (poll for election...) and on complex numbers. I'm actually getting more and more excited about his paper the more I reasearch. SO my question is do you think i'm missing any super important issues and if you have any great sources that i could get information from. an…

I'm returning to school after 18yrs of hi-tek hell / BS - so lets be honest my in that my brain is still recovering from corporate insanity at the highest levels. I'm taking bone head algebra (pre MTH95) and doing fine --- but I really freak out when it comes to factoring large numbers - esp during tests A fine example is on the last test on square roots - I ran through a word problem getting the sq root of 6400 as the answer - and that need to be simplified - I freaked and blew it - obviously the sq root of 64 is 8 so 6400 would be 80 --- but that never made it thu my panic layer What are good methods to break large numbers down beside guessing or divine…

Evaluate: [math]\sum^{49}_{k=1} (-1)^{k} \binom {99}{2k}[/math] Figure this out without using calculator at all.

Is there any way to put a dot above something. I am going to use [math] \omega [/math] to denote angular velocity, and I want to put a dot over the omega symbol, to denote the angular acceleration. The notation [math] \frac{d\omega}{dt} [/math] is too cumbersome for what I want to do. Thank you