Mathematics

Can you imagine a group with infinitely many identity elements? A structure like this have discovered mathematician Algirdas Javtokas, he calls it a beta group. I have read his axioms in Beta Algebra book, but still it is hard to understand how such structure can “work”. Maybe you know something more about this?

I have this diff. equation: [math]\frac{dP}{dt}=\frac{Patm}{Volume}\sqrt{\frac{(Pin^2-P^2)}{Kv})}[/math] with Patm, Volume, Kv = constant; P = Tank Outlet Pressure; Pin = Tank Inlet Pressure I would like to have a laplace function of this so I can use it easily in simulink, this way I can put many air tanks behind each other. Isn't there a way to go to a laplace form, skipping the diff. equation problem. Matlab solved the diff. equation in a way I don't like: simplify(dsolve('DP = Patm/Volume*sqrt((Pin^2-P^2)/Kv)','P(0) = Pstart','t')) like this: F=[sin((Patm*t-atan(1/(Pstart^2-Pin^2)*(-Pstart^2+Pin^2)^(1/2)*Pstart)*Kv^(1/2)*Volum................. Matlab g…

please can someone solve 2e^5t to 3 significant figures.

on dotted paper a 3 x 3 square . . . . . . . . . you can get 8 different ways of linking 2 dots diagonally at a 45 degree angle. and 2 ways of linking 3 dots diagonally on a 3 by 4 square . . . . . . . . . . . . you can link 2 in 12 different ways and link 3 in 4 different ways on a 4 by 4 you can link 2 in 18 ways , 3 in 8 and 4 in 2. assuming the verticle hieght of the square is x and the width is y. and x is the number of dots we need to link. so can anyone formulate a formula using x y and w to give me the number of diagonal combinations on N by N sqare. the formulae for verticle and hor…

So I'm doing this science fair project & its due SOON. Its about the genotype (the gene make-up basically) of red hair. I'm trying to come up with all the possible combinations of the genes, but I can't figure out the right equation/formula. Here's the deal: There are 8 alleles for hair color. HHHHHHHH or hhhhhhhh or Hhhhhhhh or hHhhhhhhh or HHHHHHhH, etc. How do I find the # of combinations???

Fractals - any real uses? I love fractals, the question is are they useful for anything? I knowthey preduct certain shapes in nature but do they have real uses or are they just pretty patterns? Cheers, Ryan Jones

This integral Tan(x)^3+Tan(x) doing it by hang gives Tan(x)^2/2 Mathematica gives Sec(x)^2/2 so why the difference, are both correct, how to get the mathematica answer by hand?

My problem is Simplify: [use absolute value symbols if necessary] Squareroot 75a2b3c.

how to differentiate sin(x)^x for 0<x<pi/2

As a simple example. If I have a 4 balls, red, yellow, blue and green, and there are 4 places in which I could place these balls, lets say left, left middle, right middle and right. How do I figure out how many combinations of arrangements there could be? I thought it was multiplying the number of spots by how many different kinds of balls could be in one spot. However that gives me 16, and when I start doing it in my head I realize it's way more then that. If that's two hard to understand then, I want to see how many of these there are: red, yellow, blue, green yellow, blue, green, red blue, green, red, yellow etc etc After that, how bout a bigger kic…

Is there someway that I can work out mod values without a this button?

Given 3 points in 3D space as cartesian coordiantes (a triangle) I need to calculate the normal for a 3D graphing program I am making. I haven't done any calculus that might help with this and I don't know about linear algebra so Wolfram's solution is of no help: Can anybody please translate this into an algebraic solution for me? Thankyou.

I'm trying to find: [math]\int_{0}^{12}12x^{\frac{1}{2}}-x^{\frac{3}{2}}\cdot dx[/math] Which I thought was [math][12\times \frac{1}{1/2} x^{\frac{2}{3}} - \frac{1}{3/2} x^{\frac{5}{2}}]_0^{12}[/math] Which I simplified to [math][24x^{\frac{2}{3}}-\frac{2}{3}x^{\frac{5}{2}}]_0^{12}[/math] Which comes to aprox. 207. But my textbook tells me that the awnser should be around 133. Can anyone spot where I went wrong?

I have a proposition to prove FLT See attachement Fermat_Theorem1.doc

Hello, I have been away form SFN since Feb 7th. I have been busy working on things. But I am trying to do a math contest on my site. It is free and I am not selling anything. I just want to share ideas. See www.constructorscorner.com for more information. It runs from May 1st to July 30th Hope to see you there.

What is college math like? I have a few questions. 1, Why is my favorite high school olympiad math contents not here? For example, where's number theory? Where's solid geometry? Where's trigonometry? Where's.....? Do they just disappear in college? 2, this is a much more important question. I FALL FOR HIGH SCHOOL MATH OLYMPIAD PROBLEMS. I enjoy the beauty of problem solving there. Am I likely to fall for college math too? You might say "Sure!" But I've read some college math books--they really look quite different. I suppose that every problem solving fan has a BRAIN LIMIT, and she will only feel comfortable when she's solving problems within that limit. No matt…

I'm attempting to create a quiz with the first 8 answers with the possible answers of any of up, down, left, and right... From doing research, I understand this is possible for graph sketching. Is this true? I would like to make a believeable college level simple quiz/test that has these answer possibilities for the first 8 question. Please let me know, thanks.

O My God. The Golden Ratio. Its quite an interesting subject. Its defined as: [1+(Sqaure root of 5) ]/2. In words, 1 plus root 5, all over 2. In symbols, the value is represented by the greek letter, phi. Lets cut to the chase, I just recently attained a calculator that computes to 5011 digits. The value of the golden ratio is 1.618033988749894848204586834366 to 30 decimal places. Anyway, I noticed that the recipricol, or phi^(-1), is phi - 1. Yes, 0.618033988749894848204586834366. And its not a coincidence to 30 decimal places, wen computed to 5011 decimal places, same result, phi^(-1) =phi - 1. Can anyone explain why or how..or what ever.

Hi hmm...i think i have solved this problem but neither of my 2 answers look like a Laguerre polynomial..... problem: my solutions: :S Sarah

Hi all, would anyone be able to give me a bit of help with this problem: this is what i have done so far (i am now stuck ): thanks Sarah

(Dy)² = (a-y²) with y(0) = 0 How do you solve this? Matlab gives these solutions: syntax: dsolve('(Dy)^2 = (a-y^2)','y(0) = 0') y=tan(t)*(a/(tan(t)^2+1))^(1/2) and y=-tan(t)*(a/(tan(t)^2+1))^(1/2) But these solutions are periodic if you look at the diff. equation: when y²=a then y should stay constant (not periodic) can anyone help?

Has anyone studied Differential Geometry from Do Carmo's book, Riemannian Geometry? I am trying to work problem 4 page 57, but I don't even know how to start. I will scan the problem and post it laer.

There is a new theory that may end the endless debate about 1=0.999... the whole theory can be found in this link http://www.geocities.com/humood_theory here is a Quote about cracking the famouse proof: Proof (A) x=0.999... 10x= 9.999... 10x-x=9.999... - 0.999...=9 9x=9 x=1 All the theory and results can be seen in the link: http://www.geocities.com/humood_theory For comments please write it here in this forum or send it to the e-mail said_yam@yahoo.com

I'm in the middle of revision for my final GCSE maths exam. So far its been alright but today I've come across something that is not covered in any of the books I'm using. I'm assuming its an A* question (since "Introduction to modelling" comes up right at the end of one of the revision textbooks.) Here's the question - d = av + bv^2 Find the values of a and b co-ordinates on the expotential graph - (40,120) (60,240) I know the answer is (because they are provided in a separate booklet) a = 1 b= 1/20 Whats the methodology? I know that for a straight line - finding the gradient would give me the answer. I've tried rearranging the equat…

I need to express blood pressure in terms of kPa. The conversion is 1kPa - 7.5mmHg, or .133 kPa - 1mmHg, but how would this be expressed? Just kPa subsituting mmHg, ie kPa/kPa?