Recent content by Trepidation

Hey, I have a general question about summations. Is there any steadfast rule for calculating, or obtaining a sometimes-calculatable function for, the derivative of x, where x is the upper bound of summation in a simple summation expression (the summation of f(n), from n = 1 to x)? If not...

I comprehend the idea, but the important thing is that I apparently don't comprehend simple Newtonian physics. Forgive me for the incorrect formula and the idiotic post... I just saw something that sort-of corresponded and then decided to post it, and consequently wound up with a bunch of...

EK = mv^2 energy kinetic = mass times velocity squared So... Isn't one way to interpret time dilation that everything moves through time and space with a sum velocity of c (somehow), and that as velocity in space increases velocity in time therefore decreases? I've read this in several...

That's actually really helpful... Thank you. However, couldn't you apply the same argument to space; or to the balls themselves? If the balls do not exist, obviously nothing can interact and hence nothing exists. However, it is possible for the balls to not exist and for something ELSE to...

Right, which is why it (obviously) couldn't be a temporally emergent property. However, that does not mean that time couldn't be a by-product of some more fundamental entity that does NOT change; there could be some entity that logically necessitates some method for "change", but not...

What are your thoughts, in general terms, on the notion of time as an emergent property? In what ways could time be a product and side effect of some other, move fundamental process or entity? I've been thinking on it, and I thought some other people's thoughts would be useful. Thanks!

Thank you, TD... Mm... Why not, and how would you get a numerical approximation?

\int^{6}_{0} \sqrt{1-n^2x^2}dx=\pi+e I need to solve this for n. I believe there should only be one possible function of the form y=x^n that gives an arclength of \pi+e over the interval x=0 to x=6, and wish to find the value of n that such a function must have. Does anyone know how to do...

x and y (and z, if you care to answer the other parts) are arbitrary variables; they have nothing to do with any coordinates.

arccos(x) + arccos(y) = ? How are these added? I can't find it anywhere, and I'm sure there has to be a way... Actually, what would be more helpful would be arccos(x) + arccos(y) + arccos(z) Or even cos(x) + cos(y) + cox(z) Well... Thanks for your help.

Thank you very much...

I know... The first part of my question was what the mathematical expression would be, and the second part was whether it would or would not be physically useful.

Acceleration is motion at a velocity that is in a consistent state of change, right? So... v is in terms of m/s a is in terms of m/s^2 So what is motion at an acceleration that is in a consistent change? a^2 is in terms of m/s^3 or a^2 is in terms of m/s^4 ? Is this...

Oh, I didn't think of wikipedia... Thank you!

1) Yes, I've tried looking them up. All I've found, however, are conceptual explanations of what they are and, occasionally, vague and dubious references to limits. 2) Of course not. If my school assigned interesting problems like this, I'd get more out of doing them than hanging around...