Recent content by Airman

Ok, I've spent a lot of time struggling with this one. I don't know why it's so hard for me! I understand completely how if ##x^k = y^k = e##, then the desired result that ##o(xy) = o(x)o(y)## is true. So, to prove your claim. I think this works, please let me know if it does not: ##x^k##...

So since (xy)^(o(xy)) = e, x^(o(xy)) and y^(o(xy)) are inverses of each other. We also know x^(o(xy)) = e because it's the same as x^(o(x))^(o(y), and the same goes for y^(o(xy)) = e. I feel like I'm really close but I'm still not grasping why it has to be the same.

Homework Statement Let G be an abelian group and let x, y be elements in G. Suppose that x and y are of finite order. Show that xy is of finite order and that, in fact, o(xy) divides o(x)o(y). Assume in addition that (o(x),(o(y)) = 1. Prove that o(xy) = o(x)o(y). The Attempt at a...

Vanhees, could you explain how that would work?

Thank you again! That makes perfect sense now. I realized now with your first triangle I also made a mistake and calculates arccsc instead of arcsec so it looked good. Why does Wolfram Alpha give the answer with arctan instead of arcsec? Is it preferred to do it that way? Also how do...

Thank you! I understand better now. One more thing though, why does the sign change? it was a negative inverse secant, but the arctan is positive.

Homework Statement Evaluate ∫(x^2-4)^(1/2) / x for x > 2 Homework Equations The Attempt at a Solution I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this...

When we analyze the light coming from a distant galaxy, we find a particular absorption line with a wavelength of 1118 nm. This same absorption line in light from the sun has a wavelength of 625 nm is this galaxy moving towards us or away from us? Calculate the magnitude of the velocity of...

There's so many trillions of dollars worth of infrastructure already in place around the world in combustion and fossil energy sources that any switch to cleaner energy sources will take a long time to make. Besides which, as new technologies overtake old ones the old technologies are usually...

Thank you for the detailed response! Your examples and the link were very helpful. I understand it now, and I also found this page helpful: (This was linked to from your link about the hydrostatic paradox) http://scubageek.com/articles/wwwhyd.html Thanks again my mind is now at peace...

Even if you could stop time how would you ever know? Nothing would happen. It would start again and you would never know it had stopped.

I know I must be talking about two different surfaces as I have two different surface areas. Yes but the paper is experiencing the nearly the same force on both sides. For my object the force is much greater on one of the surfaces. If the internal structure isn't strong enough in my...

Okay why? What am I thinking wrong here: I'll assume a cylinder has an inner radius of 1 and a thickness of 1. The inner surface area would be h(pi)(1)^2 or h*pi, and the outer surface area would be h(pi)(2)^2 or 4*pi. (I'm neglecting the ends, which are equal). So whatever the pressure...

Say you had a very flimsy canister. Would it be possible for it to collapse or implode even if the pressure inside it and the pressure outside of it were equal, due to the fact that it has thickness and therefor a greater outside surface area than inside surface area? If so, are there real...

I am planning to make an evolution simulator fairly soon, and am wondering just what as been done like this before. My plan is to make a simulator in that I can create a "world" with many environments, release some type of primitive "organism" and than have random mutations occur when they...