Kyle

I think Taylor's theorem and whatever theorem introduced Fourier Series (not sure what it would be called) are pretty important.

Sine and cosine are important for almost any part of mathematics and physics. They are cyclical in at least two ways: First, as you can see they repeat. Choose any position on the graph. If you add or subtract 2pi to that x-value, you will arrive at the same place. For instance at x=0 you have sine at 0 and cosine at 1. At 2pi you have the same situation. This goes on forever. Secondly, when you differentiate sine and cosine you get repetition. The derivative of sine is cosine. The derivative of cosine is -sine. The derivative of -sine is -cosine. The derivative of -cosine is sine. And so on... A similar "end is the beginning" situation occurs with e^x The derivative of e^x is e^x, and so on...

You could mention a lot of stuff with complex numbers if you wanted. Like the roots of complex numbers circle around the complex plane, arriving back where they started: And e^(i theta) equals e^(i [theta + 2 k pi]) for k being an integer. Also anything involving sin or cos. Adding 2pi just brings you right back to where you were.

Thanks a lot. It's mostly gone by now but, since we're on the same floor as the laundry room, it'll probably happen again.

Someone spilled a jug of bleach down the hall and it's making the hallway smell really bad. Is there any chemical that can be dumped on it that will safely neutralize the smell or the chemical itself without producing another gas or a worse chemical?

[math] \int_{65}^{81} [(81-x)^{3/2}-16\sqrt{81-x}] \,dx=-4096/15 [/math] [math] \int_{0}^{4} (t^3-16t)(-2t) \,dt=4096/15 [/math] I wonder if there might be a technical problem with this question. I think I have the right answer and your equation confirms it. I'll ask a few more people around the dorms and see if anyone has figured out what my teacher was trying to ask.

[math]x=81-t^2[/math] [math]y=t^3-16t[/math] After asking about tangent lines, the question asks "The curve makes a loop which lies along the x-axis. What is the total area inside the loop?" I thought I was supposed to combine these equations so that there were no t's and then integrate it. I found that [math]y=(81-x)^{3/2}-16\sqrt{81-x}[/math] And, after looking at the curve, it looks like the answer for the Area should be [math]\int_{65}^{81} [(81-x)^{3/2}-16\sqrt{81-x}] \,dx=-4096/15[/math] I've tried this answer both negative and positive and it's been wrong. Maybe I haven't found the equation of the curve correctly or integrated correctly. Does anyone see my mistake?

I'm confused about something we learned in Calc today and thought someone could explain it a little. We're doing arc lengths and now the surface area of a solid formed by revolving a curve. Given any function [math]f(x)[/math] revolved about the x axis, We treated the surface area as a lot of circumferences stacked next to each other, with the radius equal to y. My teacher showed us the formula to be [math]\int_a^b f(x)2\pi\,ds\[/math] I understand the concept of ds I think, but I don't understand is why you have to use ds and can't use [math]\int_a^b f(x)2\pi\,dx\[/math]. I pictured this problem as finding the circumference then multiplying it by thickness dx to make a hollow cylinder. Since dx is pretty much nothing, this "cylinder" would have a height of zero and would be just a 2-D circle. We could add up all the circumferences to get a surface area. Why does arc length matter at all when your slices are infinitely thin?

If there are no interfaces then where is all the antimatter? Does the matter "zone" go on forever without any sign of antimatter?

Actually as long as both explinations/mathmatical modles have equal predictive capability the simplest explination is prefered. Also let me add that I'm not kyle I'm just posting on his account and his key board is a different configuration so please excuse any and all spelling mistakes.

I think all the aliens and their planets are made of antimatter.

Of course! I'd actually tried that before, but I had made a mistake integrating at that point. Thanks for the help! This has been bugging me.

I have this problem for my Calc class and, though I've done it manually and through my calculator, WeBWorK keeps telling me I'm wrong. I hoped someone could tell me if I'm interpreting it incorrectly or maybe just doing the wrong calculation. To me, this means that I must find [math]\int t^2 e^{-2 t} \ dt[/math] According to everything I've tried, this equals [math]e^{-2t}(-t^{2}/2-t/2-1/4)[/math] What am I doing wrong here?

Kate on Linux is a great program. It colors your tags and programming and makes it very easy to find where you've made mistakes. It's not a WYSIWYG but I find it very useful for Javascript, PHP, HTML, and CSS.

Wouldn't it be extremely unlikely for two chickens (or what we today would call chickens) to be born near each other at the same time? It's not like a bunch of nearly chickens had a bunch of chickens and from then on it was all chickens. It took a long time to stabilize into what we call the species today. One egg that has something with chicken DNA in it doesn't get you anywhere close to a whole new, stable species.

Isn't that explanation kind of obvious? From an evolutionary perspective it's always been pretty much decided as the egg - at least I thought so.

Was the Universe the size it is now at the time of the big bang?

Don't worry, it's not just you. A lot of people in this country hate the measurement system and would prefer metric be used everywhere. I remember when I visited Alfred University a tour guide who was asked how far it was to something made the estimate in meters instead of yards. I am going to try to do that - just use metric and assume everyone knows what I'm talking about.

The drive of a crackpot is the same as the drive of a scientist. They want to discover truth, they aren't happy with the truth that is offered by other sources, and they attempt to work it out and find a new possibility using the information they know. There is no problem with any of that – that's how most science starts. The problem arises when the person is misinformed and absolutely staunch in their assertion. Anyone who is too prideful to admit that their “theory” is wrong is well on the road to being a crackpot.

The feasibility of this set-up is irrelevant. I'm wondering if science allows for the system. Would more energy actually be extracted than what was put in, if we forget about all the external details like how the machine gets there, how the energy gets back? Hopefully someone can look at this hypothetically instead of being unflinchingly realistic. EDIT Thank you!

And yet, it is only for convenience and no one will ever know it was adopted from German. Really any syllable will work: zich, zig, whatever.

I think you've missed the point of the question. There are a ton of assumptions, I understand. It's not practical, this too I understand. But how do the Physics work out?

What about launching objects out of and into gravitational fields? This has bothered me for a long time and I may even have posted it here before. Suppose I take a very large mass and I use a certain amount of force to get it out of Earth's noticeable gravitational field, then aim it towards a much larger field like Jupiter (where I have previously placed a device that can harvest kinetic energy as objects fall). If you can put aside the difficulty in doing so, I get this large mass to land on my machine and I am able to contain all of its falling energy. Wouldn't I have more energy than I put in, since the weight of the object is greater in the larger field?

I can think of only one practical instance where one would run into a problem besides preference: 2B16 and the like. In this case it would be spoken "two-bee" which in every other mathematical situation I know of means "two times the variable b". I really like this solution. Adding the "zig" syllable after the first place in a two-digit number really helps. I might use a combination of this and French because I know how to pronounce A-F in French and they sound sufficiently different (unlike English, where A-E sound almost exactly the same). It just seems like there would be an adaptable system for pronouncing different based numbers. Thanks everyone for the help.

I'm trying to learn how to do mental math in base-16. I understand how it works and I can do it on paper if I think for a long time, but the biggest problem I'm encountering is what words to say in my head as I read the numbers from the page. I can't call 1716 "seventeen" when I know it equals 2310. And I have no clue what to call 1C16, 20016, 400016, etc. Usually I hear anything besides base-10 being spoken one digit at a time, so that 4D2F would be read "four-dee-two-eff." This feels very awkward and totally useless for mental math. I was wondering if anyone here has experience with this and knows of a widely accepted and intuitive spoken system for hexadecimal numbers. Thank you all in advance!