Mathematics

It's all about the n'th root of 2, and proving its irrationality (where n > 2). Suppose [imath]\sqrt[n]{2}[/imath] is rational. Then [imath]\sqrt[n]{2} = \frac{a}{b}[/imath] for [imath]a, b \in \mathbb{Z}[/imath]. So we must have that [imath]2 = \frac{a^n}{b^n} \Rightarrow a^n = b^n + b^n[/imath]. However, this is a contradiction of Fermat's Last Theorem, so it's irrational for n > 2. Just thought it was really neat.

http://www2.hkedcity.net/sch_files/a/kst/kst-07110/photo_album/200511/204962/507977820.JPG Addition: AD=e Anyone can help me with the above question please? P.s. If it's not shown immediately, please refresh it again.

as stated, is there a none intuitive way of solving [math] cos(x)=cos(x+pi/2) [/math] I know from experience that 7pi/4 and 3pi/4 are the solutions, but is there a way to derive it?

Hi all... I have a mass flow rate of 9800Kg/h substance through a heater. If the temperature of the substance is 0deg c and the min tem to be at 15deg c. Specific Heat Capacity: 1040 J/(kg*K) 1. how much heat do i need to apply? 2. How much power do i need to generate that heat? Anyone?

Im trying to increase my level of skill in math and wanted to know if there were any good books I may want to purchase or if their were any advice anyone could give me on how to be become better in math, any help will be greatly apprciated.

If I am given 3 points I am sure (but cannot prove) that there will be only 1 porabola that can satisfy all 3 of them. What formula would allow me to solve this porabola? The same applies for 4 points and a cubic (or more generally, n points and a polynomial of n-1 degree). Of course, no two points can share a y-value and not all the points can be in a straight line. I solved this problem for a circle given 3 points, althought the porabola has proven far more difficult. Could you please help?

A man walks into a hardware store. He buys 1 for a dollar, 20 for two dollars, and 300 for three dollars. What is the man buying? What's the solution?

hi, if you are given a triangle and there is a cirlcle circumscribing it. how do you find the radius of the circle?The triangle is not special.(not a right triangle or anything) is there a formula for this? thanks

I know what inverse functions are, but how do I find an inverse of something like this: y=(e^x)/(1+e^x). What I thought of doing which I'm not sure about is: y(1+e^x) = e^x y+ye^x = e^x (y/e^x)+y = 1 1/e^x +1 = 1/y e^x = y-1 x = ln(y-1) I think what I've done is ridiculously wrong..but yeah...

Proof is proof, or is it?

i was wondering if somebody had any ideas about this: the gradient of a horizontal line = 0 the gradient of a vertical line = infinity but the product of the gradients of perpendicular lines is -1 so does that mean that 0 x infinity = -1 ??? ... or is there something in the proof for the product of the gradients equalling -1 which excludes it for these values?

can anyone help me how to derive pie the value is commonly known as 22/7 and it is circumference by diameter. but is it broughty in no.???

I am trying to write a piece of software that will plot a relation (or implicit function). Is there a know easy solution to doing this or will I have to use approximation methods? At the moment I have it trying every number from -100 to 100 for both x and for y and shading the pixel according to the absolute error, it is very slow and as you can see from these casini curves the line width varies. Please let me know if you have any suggestions or know of any tutorial that might help.

Hello! We've got the following to prove by induction: a) [math]2n+1\le{2^n}[/math] b) [math]n^2\le{2^n}[/math] (It is assumed that 0 is a natural number) a) This inequality is not valid for [math]n=1,2[/math], so to prove the inequality one has to show its validity for all [math]n\ge{3}[/math]: 1) [math]A(3):7\le{8}[/math] (true) 2) Assume that [latex]A(n)[/latex] is true. [math]A(n+1): 2(n+1)+1\le{2^{n+1}}[/math] [math]2(n+1)+1=(2n+1)+2\le{2^n+2}\le{2^{n+1}}[/math], since for [math]2^n+2\le{2^{n+1}}[/math] we have [math]n\ge{1}[/math] Is there a difference if I make the induction step this way?: 2)[math]A(n+1): 2(2n+1)\le{2^{n…

Hi. I tried these questions however i am unable to do them:embarass: Question1. There are 52 white keys on a piano.The lowest key is A. The keys are designated A,B,C,D,E,F and G in succession, and the sequence of letters repeats, ending with a C for the highest key. a) If five notes are played simultaneously, in how many ways could the notes all be i) As? ii) Gs iii) the same letter? iv) different letters? b) If the five keys are played in order, how would your answers in part a) change? Question2. A basketball team consists of five players-one centre, two forwards, and two guards. The senior squad has two centres, six forwards, and four guar…

A finite number divided by nothing (zero) is infinity. A finite number divided by infinity is nothing (zero). Therefore, nothing multiplied by infinite equals a finite number.

A light is at the top of a pole 20 m high. From a point on the ground 8m from the base of the pole a ball is thrown upwards with an inital velocity of 13 m/s. At what rate is the shadow of the ball moving along the ground 1 second later.

can soem one resolve his equation for me, find the units for k .... T is measured in seconds.... R is measured in meters . thnx

I was reading my Maths textbook for fun when I came across the chapter on combinations and permutations. The textbook states that the number of permutations of n different objects is n! = n(n-1) (n-2) x...x 3 x 2 x 1 Then how should we define 0! so that the above result would stilll hold?? I checked 0! = 1. Hmm... can somebody enlighten me how this works?

IN SUMMARY How do I best go about becoming an amateur mathematician? MORE SPECIFICALLY I've been a computer consultant for a decade now. Math has always intrigued me. My knowledge and understanding is pretty good up through integral calculus. I'm new to differential equations. I'd like very much to become a mathematician. It won't be a career, but I look forward to it becoming one heck of a hobby. My question is: How do I best go about becoming an amateur mathematician? For example, I have studied courses and text in pretty much the following order: - Arithemtic - Algebra - Geometry - Trigonometry - Differential Calculus - Integral Calculus…

Could someone help me with this question? The base of an isosceles triangle is 6 m. The other two sides are both increasing at 4m/s. Find the rate of increase of the area of the triangle when these sides are 5 m.

hey all! I currently use GraphCalc v4.0.1 It supports 3D graphing, and is a pretty interesting program, however I was wondering if there are any graphing programs that support relational graphs? I find having to create graphs as functions only a bit restrictive. an example is z^2 = x^2 + y^2 (a sphere) I can't make one with my current graphing calc because it doesnt do non-function graphing. If anyone knows of a graphing calculator that can do what I'm proposing, please post a link. BTW - It'd have to be a free one too lol Thanks in Advance!

Here's problem I need help on. It relies mainly on one's intuition and intelligence. Can anone hlep me out and give a full, good explanation? Every number can be represented in the standard form such as [math]\frac{100}{3} = 3.33 * 10^1[/math]. In this form the number [math]x = a * 10^N[/math], where [math]1<a<10[/math], while N is an integer exponent. Find the standard form for [math]x = 1234^1234[/math]. Include only three leading decimals in your answer, as in the previous example.

Look at this equation: [math] z(x,y) = (\cos(\sqrt{(x^2 + (y + .913*2\pi)^2}) + \cos(\sqrt{(x^2 + (y - .913*2\pi)^2}) + [/math] [math] (\cos(\sqrt{((x + .913*2pi)^2) + y^2}) + (\cos(sqrt{((x - .913*2pi)^2) + y^2}))*4[/math] Pretty crazy, eh? lol, It's supposed to be some kind of complex wave thing... the graph looks like this: If anyone else has any cool looking graphs, post a screenshot of it (or a link to a screenshot) on this thread, with the equation used to make it.

Í have a problem from chemistry, which translates to the following mathematical problem: Given a (non-square underdetermined) matrix A with integer elements only, find the null-space of it. I.e. determine the space of vectors x, with the property Ax = 0 The space is determined by computing all independent base vectors of the null-space. An example is given below: (1 -2 0 1) (3 -2 1 0) Here the matrix A has two rows, each having 4 elements. The null-space of this matrix A is fully specified by the following two vectors: x1 = (1 1 -1 1)T and x2 = (0 1 2 2)T With (...)T I mean a column vector (the math editor is not very cooperative to me…