Twerpy

but the derivative at [math]x=0[/math] is undefined?

I'm trying to numerically integrate the function [math]f(x) = |x| + |x|^3, x\in[-1,1][/math] using Simpsons rule and analyse the error. I've been trying to analyse the rate of convergence of the error but can't seem to get anywhere. Experimentally I've got that it's about [math]O(J^-2)[/math] (I think) but I can't show it mathematically. I tried using the approach of splitting up the function into subintervals, then using the formula [math]|E_2,J| = \frac{-1}{2880} (b-a)h^4 |f^{(4)} (x)|[/math] but this fails as [math]|f^{(4)}(x)|\equiv 0, \forall x\in \Re^+ [/math] Any hints?

The set of all numbers?

First simplify what you have a bit. The negative signs on each side cancel and multiply the two numbers on the right to get [math]dsin35 = (4.905)(\frac{dcos35}{25})^2[/math] then square the top and bottom of the fraction to give [math]dsin35 = (4.905)(\frac{d^2 cos^2 35}{625})[/math] cancel a d from each side: [math]sin35=(4.905)(\frac{dcos^2 35}{625})[/math] now it's just a case of rearranging and plugging it into a calculator which gives approximately 108.

It's undefined. You're assuming that infinity acts as a real number. It doesn't. It's defined by an infinite power series

Lets say that all telephone signals are made of bits. If the telephone uses a sampling rate of 40Hz lets say then it means, per conversation, it has to send 40 packages of information. Lets say each of these is 8 bits (1 byte). For one conversation the phone has to send 40 bytes of info per second. A standard optical fibre will be able to transmit thousands of bytes per second. What happens is the signal in the fibre is divided into blocks of 8, thousands of these per seconds. The system will send 1 byte of information from your conversation at a set interval, every 100 bytes per example. So for every 100 bytes going through a cable only 1 of these is yours. The switchboard or whatever at the other end then reads every hundredth byte and sends it to the right place. This way you can have lots of information at once from different conversations, each being send a byte at a time. I hope this makes at least some sense. If not let me know and I'll try and clarify.

I am doing a presentation on kevlar as a piece of AS coursework for physics. I've been told that I need to explain why the structure of Kevlar makes it a good insulator of heat (I'm saying how Kevlar is used to prevent friction burns in the Skeleton event in the winter olympics). I have googled myself half to death but I cant find anything. Can anyone help? If possible could the answers be kept relatively simple because I need to explain this to people and if I dont understand it myself I cant really impart knowledge. Thanks Anthony

I also don't see how it applies to previous posts other than maybe perhaps . If so it seems this is just a long winded way of saying 'hydrogen bonding does effect DNA in one way or another.' Forgive me if i missed something in the huge depths of that epic post but it seems to me that sunspot is just trying to redeem himself by writing long involved posts which have only the very slightest relevence to the topic. Productive. Very productive

Just out of interest, would i be right in guessing the one on the plane was slower? Also how much were they out? Off topic I know but i'm interested

There is a whole artical on it in the 24/31 december new scientist. Basically Woo Suk Hwang has retracted some of his papers on "therapeutic cloning" which were already under fire for irregularities in the data. Apparently some cells which were being worked on had died from fungal infections and other were suspected to have been swapped for other cells. Also several photos seem to have been fabricated and reused. Some of the papers which were retracted were hailed as a key step towards 'therapeutic cloning'. I'm sorry if that is vague and unorganised. My advice would just be buy the magazine or get access to it online or something. You'll get much more detail and wont have to put up with my vague mutterings.

Whilst i do not claim to be any sort of authority on the subject i believe the following to be correct. Others more in the know, please correct me if i'm wrong. 1. In theory yes but at the moment only in theory. I'm sure you are aware that stem cells have the ability to become any other type of cell in the body, e.g. heart, liver, brain etc. The problem is getting them to behave in the way you want them to. Whilst it may be possible sucess rates are low and there have recently been reports of faked results in stem cell technology (New Scientist 24/31 December). 2. This I dont know. I will guess saying that whilst very pure ethanol might do some damage in general I think it is something else (although what i dont know) that causes ulcers. Otherwise lots of people who drink alcohol, especially spirits, would have ulcers. 3. Again, i'm not too sure but I doubt ethanol is carcinogenic. Those who drink regularly do not end up with cancer of mouth, throat and esophagus which, if ethanol were a carcinogen, you would expect with the frequent exposure. Whilst these answers seem right they may well not be. They are educated guesses so dont rely on them too much. I hope this helped anyway.