Mathematics

Hi there. I'm having problems integrating [math]y=x^x[/math] Any help would be appreciated.

Make L the subject of the equation for [math]\frac{1}{3}pK^{\frac{1}{3}L^{-\frac{2}{3}}}=w[/math]. My friend told me that the answer is [math]L=\left(\frac{p}{3w}\right)^\frac{3}{2}K^2[/math], but I got [math]L=\left(\frac{p}{3w}\right)^\frac{3}{2}K^\frac{1}{2}[/math]. Am I right or is my friend wrong? _____________________ Kettheya Uong

Please solve the problem in detail The height of the cone is 30cm.A small cone is cut off at the top by a plane parallel to base.If its volume be 1/27 of the volume of the given cone, at what height above the surface the section made? Thanks

having some trouble with proving identities, problem is: sec2x = sec^2(x) / 2-sec^2(x) and the second one is tany = sin2y / 1+cos2y much help is appreciated

I just created a script that writes any number up to 303 digits long in English: http://www.random.abrahamjoffe.com.au/public/JavaScripts/number_pronunciator.htm Tell me what you think, is it flawed in any way? Like for example: 1001 outputs: "One thousand, and one.", is the comma supposed to be there, and the "and" ?

Hi, I am trying to write a program that will take a number and output the numerator and the denominator of the number as a ratio. I know one way of doing this mathematically: [math]x = 5.142857142857142857 (given)[/math] [math]1,000,000x = 5,142,857.142857142857[/math] [math]1,000,000x - x = 999,999x = 5,142,852[/math] [math]x = \frac{5,142,852}{999,999}[/math] [math]x = \tfrac{36}{7}[/math] I could write a code that does this but this piece of code will be executed very often in my code so I want it to be optimised to be very efficient. Does anybody know any other ways of doing this? - Oh if it is any help, the input number has a maxim…

I've been thinking about this for a while and I just wanted somebody to show me where my proof becomes faulty. This was my attempt to find an asymptotic formula for Mertens' function (the sum of the Mobius function). Oh, and if you aren't clear of my reasoning behind something, just ask...and in case it isn't obvious, I used pn to denote the nth prime number. Sorry about the cheap scan...I don't know how to use Latex... Asymptotic formula for Mertens' Function

Right Well ive screen shotted them and they do fit exactly over one another, and we prosume the writing along with the triangles is true. So im stuck, but im sure theres a really simple explanation which you can all see and im jus being dumb. The only thing i have noted is that when placed over the top of each other the lower triangle's hypotonuse does seem to bulge slightly.

What is the best way to manually find the square root of a positive rational number? I understand that it will be an approximation, what what is the way to get the closest possible answer rounded to 2-3 decimal places.

Does it make sense to write: [math] y = \prod_{n=-\infty^2}^{\infty^2}\frac{x+{\tfrac{n}{\infty}}}{x+{\tfrac{n}{\infty}}} [/math] Would this create a line with infinity gaps in it? Or does it not make sense to write [math]\infty^2[/math] ? I also was curios about the curve created by this psuedo-exponential: [math]y = (-2)^x[/math] It seems to create a regular exponential above and below the axis, both with infinity gaps, and both with infinity points, this interested me, is there a name for this type of graph? Are these two equations I have posted related in any way? Thanks. - BigMoosie

What would decimal fractions be like if we didn't count in Base 10? I'm guessing 1.5 in decimal would be equal to 1.8 in hexadecimal, but what about with numbers that have more than one digit after the decimal point? 0.125 decimal would be about 0.2 hex I think? Also, how do you say "five and a quater" in binary; 101.01?

what is the difference between an open interval (i.e. (a,b) ) and a closed interval (i.e. [a,b] )?? does the open interval not contain the endpoints (i.e. a & b) or something like that? :S Cheers Sarah

Hi everyone. My name is Hans, and I'm new here. I'm an undergraduate student at the University of Michigan studying electrical engineering and performing arts technology. Throughout high school I was very interested in mathematics, but now that I'm in college and studying other things I don't have the time to take more advanced, formal mathematics courses. The last courses I took were in multivariable calculus and linear algebra. I'm still interested in continuing my study of math, though. So here's my question to the community: Where do I go from here? I'd like to get some books and continue to learn, but I'm not sure which areas of mathematics I'd be r…

Here is an inline synopsis without using latex. and with lots of deletions to save space. the original is post 13 in the thread on manual evaluaiton of exponents. johnny asked me to point out where I thought it was wrong so here it is. no, you are presuming that 0! is writable as a product (it is - the empty product, but I suspect you don't get that) you have rewritten the taylor series and introduced a mistake. The next bit is you attempting to correct this self introduced mistake. yes, why tell us? note this product is indexed from 1 to 0. This isn't allowed. no, it was caused by you thinking 0! was a product from 0 to 1. at be…

hey is this right? i thought only the sum of just i = n(n+1)/2 ??

I read that when IBM were building deep blue they had to find innovative ways to get around the fact that chess can produce more combinations of moves than all the atoms in the universe, this is obviously beyond what any computer can currently cope with. How did they work out the total number of moves? And, i dont know if this is a viable question but say i wanted to work out how many connections could be made between every atom in the universe ie every atom is connected to every other atom regardless of distancs etc. How would this be calculated and would the number be of any significance?

For example, I know sine is: x - x^3/3! + x^5/5! - x^7/7! + x^9/9! ... But how would one express 4! without saying 1x2x3x4 so that I can solve such questions as 5.6! I heard that gamma(n-1) = n! , only problem is I dont know anything about gamma, can somebody offer some insight?

While trying to learn about rotation matrices I came across this: Quaternion Tutorial If you go to page 15, you will see this: Definition of a Quaternion A quaternion is the geometrical quotient of two vectors. Let A denote a vector, and let B denote a vector. Q = quaternion = A/B Tom Mattson said that vector division isn't defined. Apparently it is.

A quick question about Bachman's A Geometric Approach to Differential Forms. I've read: 1. [imath]T_{p}\mathbb{R}^n[/imath] to mean "the tangent space of some path/surface in [imath]\mathbb{R}^n[/imath]" and, 2. [imath]T_{p}\mathbb{R}^n \times \mathbb{R}^m[/imath] to mean "some (n-1)*m dimensional space of real numbers." I haven't run into any problems using this definition but I think it would make the text easier to read if I actually understood what was going on (especially in the second example. Rev Prez

tommarrow, i am going to order some books and i need some information: i already have a background in differentiation and integration. what do i need to know before topology? is differential geometry before or after or the same as topology? any reccomendations on books would be nice as well.

Does it make sense to say that two points is a zero-sphere? I read that an n-spehere is the structure made from all the points being exactly the same radius from a single point in (n+1) dimensions (thats of the top of my head). But also shouldnt the resulting structure be of n-dimensions itself? I'm not sure whether two points would be called 0 dimensional would it? Also, could one visualise a 3-sphere (picturing it with 3 spatial dimensions and the fourth as time) as a point that grows to a sphere and then shrinks back down?

Suppose i have the following function of the variable z: [math] f(z) = \frac{z^2-1}{z-1} [/math] Is it true or false that f(1) = 2 ?

Hello, Suppose we have a truncated taylor series for exp(x), truncated at the term, just beyond the N-th power. Let's call these truncated series trunc(N, x). Some examples: trunc(0, x) = 1 trunc(1, x) = 1 + x trunc(2, x) = 1 + x + x^2/2 ... trunc(N, x) = 1 + x + x^2/2! + .... x^N/N! Here N! means the factorial of the integer N. Here, trunc(N, x) is an N-th degree polynomial over the complex numbers with variable x. The zeros of trunc(N, x) are on a very regularly shaped curve. The shape of the curve hardly depends on N. As an example I'll show the zeros for trunc(400, x) as a gif image, computed by means of my polynomial so…

how do you find the integral of x^x from some given negative number to 0? I can't even see the graph of x^x from -something to 0

Hi guys I'm on my vectors again. Last time you really helped me understand what i was doing! Refered to a fixed origin A=(5i-j-k) B=(i-5j+7k) Find the position vector of the point D, where Dis not A on AB such that |OD|=|OA| i did OD= xi+yj+zk from r=a+t(B-A) x=5-4t y=-1-4t z=-1+8t |AD|^2=(x-5)^2+(y+1)^2+(z+1)^2 |AD|^2=(5-4t-5)^2+(-1-4t+1)^2+(-1+8t+1)^2 d(|AD|^2)/dt=(32+32+128)t am i using the right method? i also did Cos(OAOD) but got silly decimals. for the vector eq. Thanks in advance!