This is not a homework question, per se, because I'm not a student. But it is a problem I found in a book. Actually, the problem doesn't involve what I'm going to ask, but it did present an opportunity for me to explore the subject.
I have the graph of f(x)=x^{3}+3x^{2}-9x+3. I know the x...
I'm curious as to the origin of the "1/2" in some of the basic equations in physics. For example, d=1/2at^{2}. If d=vt, and v=at, then d=at^{2}, yet in reality we need the "1/2". Why?
Thanks for the replies and the link. I'm reading that now, so the answer may be in that. But I will give a simple example. Let's say I have f(x) = x2. Now, I want to know the area under the curve from 0 to 1.
The way I understand it, I take the integral \int_{0}^{1} x^2dx. So the antiderivative...
So, the area under a curve is determined by F(b) - F(a), how does that take into account the changing area between the two extremes, a and b? I mean, since F(b) and F(a) are specific values at the ends of the graph, how is the area in between figured into it, especially if the graph is really...
If you put it like this: \pm x = \pm3 doesn't that say that x = \pm3 and -x = \pm3? That really doesn't make a lot of sense. If x = 3, then -x = -3, but it can't be both simultaneously.
A three-body problem in celestial mechanics is the one that got me thinking on this route. Apparently, a system involving two bodies is fairly simple to solve using the laws of Newton and Kepler, but add a third object to the mix, and all hell breaks loose. Well, all these bodies are doing what...
What I mean is, I have read how many equations that model physical phenomena often aren't directly solvable. Instead they are approached by successive approximations. And we get answers that are close enough.
My question is, if a physical phenomenon seems to follow a mathematical pattern, why...
I know nothing of the calculations involved in these theories, I'm not there yet. But what is the mass of the core of a collapsing star (going supernova)? What is the predicted amount of uranium and other super heavy elements on our own solar system? What I'm driving at is that the total amount...
I really don't know, for sure, because I'm not good at posing questions in such a way as to convey what I mean. So, bear with me as I try to articulate my feeling on the subject.
I don't think it is such a stretch to assume that gravity (or something else we've considered) may be flawed, in...
After re-reading this post, I think 337's question kinda boils down to this: When an atom in a transparent dielectric is struck by a photon, why does the atom feel compelled to re-radiate a photon of identical energy? Why does the atom not instead just vibrate from the absorbed energy, or...
At this point, and really, all points before, I'm just guessing. But since there is no real 100% transparent material, doesn't that suggest that at least some photons don't get re-radiated? I mean, a prism will heat up if you shine some light on it. But maybe the mechanism for re-radiation is...
So, if I empty my bank account, I am flat broke, but if I overdraw by $1, I am the richest person in the universe?
Just what does it mean to be "greater than infinity"?
I don't think it is so much that there is no cause, but that we just can never witness it in action. The very fact that the event occurs is reason enough to know that there was a cause for it. We can infer it after the fact, but never watch it in progress.
Given enough random events, they will...
Just how would you even know if such a thing was a success? You would have to be expecting and looking for the result prior to doing the experiment. And, what would happen if you got a positive result, and then decided not to do the experiment?