Mathematics

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

I am studying Maths at varsity and I'm doing ok in it academically but I would like to do better, I find that I lose motivation a lot because I fail to see how what I am doing relates to real life, sometimes, like how is this applied in the modern world. Applications we do in class are far and few in between so I often loose interest. I think that if I had more motivation I would do better, and I would like to know if anyone knows of any good (not too technical)books about maths specifically its development and the people involved in coming up with importnat discoveries(I find that very interesting) as well as modern applications of Maths (I'm not looking for a textbook t…

Hi i am doing my dissertattion and have run a GLM repeated measures ANOVA on my data - I know need to perform a Tukey HSD, but cant do it on SPSS so doing it by hand. The problem that I have is that I cant seem to find where the significant difference is. Stats is not my strong suit i am really bad at it. I have a significant difference between condition and between condition*Time Name: Blood Lactate (Cond*Time) Significance = 0.01 K= 12 dfe= 24 (K,dfe) = 6.105 MSE = 0.74 N= 5 HSD = 2.348640394 Works = YES but when i do it for condition it wont work Name: Blood Lactate (Cond) S…

I have a general question on properties of intervals from a topological point of view( intervals in any ordered , linear continuum space, not only reals), so if we have a non-empty open set A in [a,b], and let b be in A for example, and let x < b , x in A. I need to prove that there exists an interval (y,x] in A. I believe that the fact that A is open and the betweenness of A has to do something with that proof. Again, A is any subset of [a,b], not necessary a convex subset. Will someone help me with this, please? Thanks in advance.

OK boys, this one has been a wonderment to me for years. They tell me that the ancient Greeks came up with the formula for the sine tables. Now, since these constants are expressed in numbers carried out to 7 or 8 decimal places, how did these old boys figure that shit out in the first place? How did they come up with Pi? They didn't have all the stuff to take measurements that we do today. So my question is, is there some sort of natural law that they were able to apply to get the sines, cosines, tangents, etc?

Hi, i'm new, and i wanted to share a very simple algebra problem i like. [math]x^{2x}=2x[/math] It's very simple, but not as easy as it looks, if you know the answer right away, give others a chance.

You are given two right triangles, one with a larger area than the other. Each of the triangles has the angle [math] \theta [/math] in it. The legs of the smaller right triangle are a, b; with a>b. The legs of the larger right triangle are A,B; with A>B. I am trying to prove that: [math] \frac{a}{b} = \frac{A}{B} [/math] I just can't find a simple way to prove it. Anyone know how? Thanks

Does anybody know how to number matrices in Latex, it should follow the equation numbering, so I can effectively refere them. Many thanks