Mathematics

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,

Do you guys know of any particular strategies to use when doing when arithmetic in your head, so that you can solve your problem quickly and correctly?

:sigh: simultaniouse equasions seem to be causing me quite a lot of grief lately. basically, im relatively adept at solving simultaniouse equasions, but what do i have to be aware of when solving simultaniouse inequalities, ie 2x + y < 200 x + 2y < 500 and stuff like that. is it even possible to solve simultaniouse inequalities such as this? thanx

i had to do this reasently, and i think i may have done it a long winded way. basically, i had a list of the products of a quadratic exuasion for variouse numbers. what i did, was i terated two of them like a simultaniose equasion, ie 16a+4b+c=20 4a+2b+c=15 then jiggery-pokeried them untill there was only one equasion (times bottom by two; subtract bottom from top) 8a-c=-10 then i did the same with two different quads, to get another xa + yc = z term. then i treated both the terms as simultaniouse equasions, so that i could work out a term, and then substituted them back into the equsions to work out the other terms. it took ages. is there…

Can latex be used to make an 'arc' symbol. I want to refer to arc AB, and put a curved line above AB. Can you do that with latex? Thank you