Mathematics

Hey guys, I stumbled upon these forums while looking for some help... I've registered, and hope to become a regular poster here. Anyways, How would I show that the following mathematical expressions are dimensionally equivalent? a) 1/2mv^2 and mgh b) W and 1/2mv^2 Thank you so mcuh for your help. Cya!

Could someone please explain to me this axiomisation of real numbers to me? I study further maths at A level and I have not come across this. Is it basically a set of definitions for the various sets of numbers? Cheers

Currently, I am trying to make my way through Euclid's book seven, which is on number theory. I am having trouble with his very first theorem, can anyone here help? I think the reason I am having trouble with it, is that the English translation isn't as good as it could be. Here is a link to proposition 1 of book seven: Euclid's elements, Book 7, Proposition 1 The translation that you see at the website, is not the same as is in Heath. I think Dr. Joyce tried to translate it more clearly on his own. Anyway, I was reading through a graduate text on linear algebra, and around the time they begin to discuss rings, there is a discussion on "relative p…

1 + 2 + 3 + ...+ n = n(n+1)/2 1 + 4 + 9 + ...+ n^2 = n(n+1)(2n+1)/6 1 + 8 + 27 + ...+n^3= (n^2)((n+1)^2)/4 Besides just looking at the numbers and figuring out through mathematical induction, how do you find these formulas. For the first one, there's a way that goes something like this. Sum = 1 + 2 + 3+...+(n-1)+ n Sum = n +(n-1)+...+ 2 + 1 2 Sum = (n)(n+1) Sum = (n)(n+1)/2 Can this method be applied to higher powers? If so, can you show a couple of examples? I also saw a method using dots. Like for n(n+1)/2, you can form a n(n+1) rectangle of dots by placing together 2 trianglular array of dots with one dot in the top row, 2 in the seco…

http://www.manilatimes.net/national/2005/may/05/yehey/top_stories/20050505top4.html Looks like an error was found in Wiles' solution.

I am confused of shifting a linear equation. Let f(x)=ax+b And g(x) is identical to f(x+2)+5 For example, we create a specific condition, g(x)=f(x) and (1,2) is a point on f(x) [Does this implies that (1,2) is also a point on g(x)?] Next step is to find f(x): By using the given conditions, f(x)= -5x/2+9/2 The contradiction appears: g(x)=f(x+2)+5 That's mean shifting the whole curve of f(x) to left parallel to x-axis by 2 units, then by shifting it upwards by 5 units, we get g(x). My answer to the previous question ( typed in bold ) is yes but I am not certain with my answer. If I am correct, then the point hasn't moved away. However, it's clear to know that the…

I understand everything apart from the part that is circled in red, could somebody please explain how that is obtained from the information given. Thanks.

How does the logic for the method of infinite descent work? Fermat indirectly proved that x^4 + y^4 = z^4 has no solutions through this. "In order to prove that there were no solutions, Fermat assumed that there was a hypothetical solution (A,B,C). By examining the properties of (A,B,C), he could demonstrate that if this hypothetical solution did exist, then there would have to be a smaller solution (D,E,F). Then by examining this solution, there would be an even smaller solution (G,H,I), and so on. Fermat had discovered a descending staircase of solutions, which theoretically would continue forever, generating ever small numbers. However, x,y, and z must be whole numbe…

i need to answer some of these problems, and i do not know wat a sine or cosine wave is. I need help with numbers 11, 13 and 15. I would greatly appreciate any help.

For a triangle, 3 sides are given. What's the radius of its circumcircle? Are we able to get it without using cosine law or sine law or heron formula?

you can get square of double area using given square by pythagorus theoram. no instrument of dimensioning is needed. but can you get double volume cube when cube is given to you and you can't use measuring tools. you can use diagonals, etc. which are elements of cube.

Is anyone here familiar with George Boole's work entitled "Treatise On The Difference Calculus" I was wondering if it was any good.

i hae been trying to figure out how to do the last part of the first paragraph in the below image. An equation of explanation would be great. Thx

I am looking for a quick proof that [math] 0^0=1 [/math] some kind of argument, doesnt have to be fancy Thank you e.g. let x = 0^0 therefore ln x = 0 ln 0 It's provable from the field axioms that 0*y=0, for any number y. Hence ln x = 0 therefore x=1 QED I am looking for other proofs. PS: And i know that lim x-->0+ of x = -infinity [math] \lim_{x \to 0^+} ln x = - \infty [/math] That's why I want a different proof, because the above isn't one.

You have a linear function [math]f(x)=-\frac{2}{3}x+4[/math] where [math]0\leq x\leq 6[/math] and [math]0\leq y\leq 4[/math]. What is the maximum area of a rectangle that has one side on the line of the function? I know how to optimize this, I am just having trouble finding the equation for area of such a rectangle in terms of the function. I have included an image of what I am talking about. Thanks a lot.

Gah!! I've tried and tried. Can someone please help me real quick with these two identities? [math]sin^2(x)(1 + cot^2(x)) = 1[/math] and [math]tan(x) + cot(x) = sec(x)csc(x)[/math] I keep getting places, but nowhere helpful... Edit: LaTeX. nice. ^^;

In another thread, I asked how would you locate the center of a given circle, using only a compass and straightedge, and I got absolutely wonderful answers. During that thread, many solutions involved already knowing how to construct a tangent line to one of the points on the circumference of the given circle. I must confess, I don't know how to do it. So here is a related question. Using only a compass, and a straightedge, how do you construct a line which is tangent to a given circle, at a given point on the circumference? Regards

[math] 3x^3 y^{\prime \prime \prime} + 9x y^\prime - y = 0 [/math] Where prime denotes differentiation with respect to x. i.e. y`=dy/dx Thank you Well I will just begin working on my own problem. Assume a power series solution. [math] y(x) = \sum_{n=0}^{n=\infty} C_n x^n [/math] So the first derivative with respect to x is given by: [math] y^\prime = \frac{dy}{dx} = \sum_{n=0}^{n=\infty} nC_n x^{n-1 [/math] The second derivative is given by: [math] y^{\prime \prime} = \frac{d^2y}{dx^2} = \sum_{n=0}^{n=\infty} n(n-1)C_n x^{n-2 [/math] The third derivative is given by: [math] y^{\prime \prime \prime} = \frac{d^3y}{dx^3} = \sum…

Find the last 5 digits of a number of the form 9^(9^(9^(9^.....9^(9^(9))....))) for 1001 9's. ie.powers on top of each other, if you follow

If I make an error in what follows, I would like it pointed out. The purpose has something to do with 0!, and 0^0, but I am not going to say what. Preliminary work: There is a superset [math] \mathbb{S} [/math], and any element of that superset is called a number. Axiom A [math] 0 \in \mathbb{S} [/math] Axiom B [math] \forall x \in \mathbb{S}[0+x=x] [/math] Axiom C [math] \forall x \in \mathbb{S}\forall y \in \mathbb{S} [x+y \in \mathbb{S}] [/math] Axiom D [math] \mathbb{N} \subset \mathbb{S} [/math] Undefined binary relation on S: < Definition: [math]\forall x,y \in \mathbb{S} [ x > y \Leftrightarrow y<x ] …

I give you a circle, but I don't tell you where the center is. The only tools you have, are a compass, and a straightedge. How do you locate the center of the circle?

the number 54321 is multiplied by a five digit number(*****). the product is a 10 digit number ending in 12345. what is the number we are multiplying by? find what is the astericks

Can anyone refresh my memory on the math definitions of these terms? And what the third terms is?

Can anyone give me the general formula for the number of can in a pyramidal stack? Say you have a stack of soup cans. The first row (the one on the bottom) of cans has N cans in it. The next row has N-1. This continues until you reach N rows which has 1 can in it. Thanks

Please help.Ineed something simple and in theory form.Something like maths in biology or something else interesting.Please give me some links if possible. Thank you i will appreciate. By theory i mean written stuff,