Mathematics

This is fun: http://www.planarity.net/ I managed to get up to level four without too much difficulty. Edit: woo! Level six.

Two nice mathematics articles in Seed magazine http://www.seedmagazine.com/news/2006/09/putting_his_money_where_his_ma.php http://www.seedmagazine.com/news/2006/09/maths_architect_of_beauty.php

I dont know where i should put this question...please forgive me if i put this in wrong place... i have no idea how to prove this boolean algebra equation are equivalent: x'y' + xy = (xy' +x'y)' x'z + xy = x'y'z + yz + xy thank u very much for your help...

K i got this application question the other day in my introduction to calculus class and i was wondering if anyone could lend me a hand. Katie is building a wooden rectangular storage box. The box will have an open top and a volume of 1.5m cubed. For design purposes, Katie would like the length of its base to be triple its width. Thick wood for the base costs $8/m squared and thinner wood for the sides costs $5/m squared. a) Express the cost of the wood as a finction of the width of the base. b) Find all possible dimensions if Katie spends $44 for the wood. c) what dimensions would you recommend? Why? Now, i think if someone could help me with a) then i probabl…

I have this problem for my Calc class and, though I've done it manually and through my calculator, WeBWorK keeps telling me I'm wrong. I hoped someone could tell me if I'm interpreting it incorrectly or maybe just doing the wrong calculation. To me, this means that I must find [math]\int t^2 e^{-2 t} \ dt[/math] According to everything I've tried, this equals [math]e^{-2t}(-t^{2}/2-t/2-1/4)[/math] What am I doing wrong here?

Here's an incredibly simple math problem that I for the love of god cannot figure out.... help.... f(x)=(1/4)x^4 - (3/2)x^2 + 2 I need to set that to zero. I know I did this, and this is a review problem. But for the love of god I have no clue.

If (a,b)=1 , i.e. they are relatively prime to each other, b^d = 1 (mod a) where 1=< d < a-1 , how do you prove it? Also the following is my guess. IF b^h= 1 (mod a^2) Then d l h, does it make sense?

I am working on some problems on particle dynamics and I keep making errors originating from the following: [math]\int \frac{1}{x} = log_e x[/math] or [math]\int \frac{1}{x} = \int \frac{-1}{-x} = log_e -x[/math] Why is it that there are two solutions and how can I identify which is the correct one to follow?

find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3, and x=s+2, y=2s+4, z=-4s-1, and the find the plane determined by these lines. I don't know what to do...

John Baez (mathematician interested in quantum gravity, category theory and divers other stuff) has a kind of sporadic blog called This Week's Finds in Mathematical Physics. And TWF #239 just came out Baez and lady were in China for the summer and have some neat photos of life and sights you might want to look at scroll down a couple of days here http://math.ucr.edu/home/baez/diary/august_2006.html'>http://math.ucr.edu/home/baez/diary/august_2006.html to the start of the Shanghai and Suzhou pictures TWF 239 is partly about the origins of mathematics in the Mideast around 8000 BC with some clay tokens. Baez shows some photos of the tokens here http://math.u…

say, on a graphic of cubic function, there is a root at 2, a y point on 8 when x is 1, and another on 8 also when x is -1, and when x is 0, y = 8. 1) if I solve this by: (x-2)(ax^2+bx+c).... I get an answer because I can solve a, b, c by 3 different simul equations. but 2) if I solve this by: (x-2)(ax+b)(x+c), I get more answers because when I try to solve c, I get a quadratic equation for it, which means c can have 2 values...... but this cannot be possible, since c can only be one value as a root. plz help

Can anyone please explain why gcd(n,m)=gcd(n-m,m)? (n>=m) It's like everyone assumes it because, apparantly, it's so obvious, but I don't see it.

An Interesting Animation About Holy Quran http://www.simetrikkitap.com/binary/binary.html

a=3^b b^a-a^b=0 a.b=?

I need help with a maths assignment, Im having a brain block and I have a feeling that the forumula is really easy and Im just having a bad day, but this is basicly what I need to find out. (REALLY simple stuff) I have a rectangle I need to find the volume for, and I only have the length and width measurements for it. I need to find the height to calculate the volume (As Im sure you all know) volume is; width X length X height, so what have I missed, Am I having a brain block or is it something more complex? Please help, its due tomorrow. Its pretty much this, Looks simple but im stumped...

(taken from http://www.esmerel.com/circle/numeracy/tricks.html) this is news to me

Hello all, I am completely new to this stokes theorem bussiness..what i have got so far is the nabla x F part, but i am unsure of how to find N (the unit normal field i think its called). any suggestions people? i get that nabla x F or curl(F) = i + j + k cheers -sarah

Hey all, I was sent an AS Maths preparation/revision booklet for me to go over and complete questions in before i go back to school. After one of the questions, it gives a random puzzle and I am stumped. I havent been told how to do it before. It says that a cubiod has a volume of 7.5cm3, a total surface area of 26cm2 and the total lengths of all its sides is 26cm. I am told to give the dimensions of the cuboid. I have absolutely no idea on how to do this. I can find the volume etc from the dimensions easily, but i dont know how to do it in reverse. Could someone please shed some light on how i would go about doing this. Thanks

Say a scientist gave you a set of values of A from an experiment of changing the value of B. You're told that the experiment has been repeated and that the values of A are consitent (with an acceptably tiny margin of error) each try. At first glance there is nothing as simple as the value of A just going up as B increases but as there is definately a connection so the scientist has asked you, the mathematician, to describe the relationship between these to variables. How do you begin attacking this problem? Where do you start when all you have is a sheet of numbers?

Hi all, i am little puzzled by these questions, not sure if i am doing it correctly or just blundering along! what do you guys think? cheers Sarah for (a) i get: [math] I = \int_0^{2\pi}\int_{-1}^1f®rdrd\theta [/math] for (b) i get: [math] I = \int_{-\pi/4}^{\pi/4}\int_{\frac{-1}{cos\theta}}^{\frac{1}{cos\theta}}f®rdrd\theta [/math] for © i get: [math] I = \int_{0}^{2\pi}\int_{0}^{cos\theta}f(tan\theta)rdrd\theta [/math] if people want the working just shout, i just don't have quite enough time to put it up at the moment. -sarah

Hello, I am confused by what this question is asking, and i was wondering if anyone could suggest the best way to approach it? Thanks sarah

Given, [Math]S=x^{3}y^{2}z[/Math] and [Math]x+y+z=1[/Math] Determine the greatest value of S. How do we start this type of question? I started with [Math]S=xxxyyz[/Math]where there are six terms; used AM-GM and found that x=y=z, I know it's wrong, but why? Then I think it occurs because there's no limits of them. Therefore, I sub [Math]z=1-x-y[/Math] So [Math]S=(1-x-y)(x^{3}y^{2})[/Math] But there's no clear solution for me. What should I do next?

I got a notes but have difficulty in interpreting all the material there. Later give you. It's about using Vieta's formula and Newton-Girard Formula to prove/find the general solution of sequence? I'v read some other material but most didn't give me a clear concept as they don't have relevant detail. The closer one is telling that the general solution for one linear equation and two equations. How can I find that of three?

Given, [Math]S=x^{3}y^{2}z[/Math] and [Math]x+y+z=1[/Math] Determine the greatest value of S. How do we start this type of question? I started with [Math]S=xxxyyz[/Math] where there are six terms; used AM-GM and found that x=y=z, I know it's wrong, but why? Then I think it occurs because there's no limits of them. Therefore, I sub [Math]z=1-x-y[/Math] So [Math]S=(1-x-y)(x^{3}y^{2})[/Math] But there's no clear solution for me. What should I do next?

Here is a rather tough problem for me. I appreciate any suggestion for the solution from any of you cause I really don't have any idea.