Bignose

Why not break up the integral into two parts? The integral from -1 to 0 of -x-x^3, and the integral from 0 to 1 of x+x^3, and the benefit is that both of those function do have a derivative at x=0.

netlib.org is one that I use a lot. Have you looked around there?

is this for homework, or is this just for your own personal improvement? Because it seems awfully homework-like (just like the other thread you started), and if so, your text or your class notes should have the equations you need. You shouldn't have to look online.

Look through the Table of Contents on that Geometry for Dummies book. If you know all the stuff in the TOC, then you should find a good algebra, or trigonometry or pre-calculus book. Geometry isn't really just an isolated field, and many of the concepts from geometry are introduced in algebra, trig, and calculus. Otherwise, there are some advanced geometry-specific books. E.g. http://www.amazon.com/College-Geometry-Introduction-Triangle-Mathematics/dp/0486458059/ref=sr_1_14?ie=UTF8&s=books&qid=1236533997&sr=8-14 But, I don't think that geometry alone will get you in a place to read about null lines and metrics and such. You will have to go through calculus and differential equations, too.

throng, there are ways to describe what you are saying in mathematics -- you just need a metric space that has a null line or null space in it. That is, a space wherein you define the distance measure so that that distance measure = 0 for points along the null line. See Tensor Calculus by Synge and Schild page 46 for more. (Note that you better have a very strong math background to read this book, it isn't for beginners in any way.) (And please don't take that last comment as being mean, because I'm not trying to be mean, just telling you that unless you have a strong background in calculus and differential equations and geometry, you will not be able to read more than 1 or 2 pages without being completely lost. It is a very advanced text.) Finally, I think that it is also important so say that just because there are mathematics to describe spaces with null lines and the like, doesn't mean that that translates into reality. That is, reality as we know it cannot have two non-equal points that don't have a distance between them. But, we can write the mathematics of such a situation.

Have you drawn a free body diagram so you can figure what the situation looks like and what force or forces could be acting in this situation? If you haven't, it is probably a very good habit to get into because 1) it always helps to have a picture to see exactly what is and isn't happening and 2) if you drawn out the diagram, most teachers give at least some partial credit even if you don't do anything else from that point. Not necessarily a lot, but something like 20% is better than 0%.

In very short, it is the mathematics of change. For example, if a particle's position changes, the rate at which the position changes is called the acceleration. Calculus describes particle's velocity, the rate of change of it's position. Similarly, is that particle changes velocity, the rate of that change of velocity is it's acceleration. Put slightly more mathematically, when you have an algebraic equation like x+7 = 10, the value of x isn't directly known, but can be solved for. x=3 in this case. 3 is the only solution to this equation, and in this regard x is going to be a constant because it can only equal 3. In calculus, we are interested in what happens when the value of x changes. In calculus, x isn't necessarily going to be equal to a constant. It may have a value that changes, and how it's value changes depends on the equation it needs to solve. Wikipedia's intro article isn't too bad at all: http://en.wikipedia.org/wiki/Calculus

There is a dark matter map that has been presented in Nature. http://www.nature.com/nature/journal/v445/n7125/abs/nature05497.html I don't know if it is going to qualify as "direct observance", but they used gravitational lensing to generate a map of it. If you don't have access to Nature, there are articles that present some of the images: e.g. http://news.nationalgeographic.com/news/2007/01/070108-dark-matter.html To Tango, are you prepared to scientifically bust that article in Nature? Because you have a pretty huge hill to climb, if that is the case, so let's start to see some good evidence. Because right now the good evidence is on the side of dark matter, at the very least.

I've moved this post to Homework, since it sure seems like a Homework problem. And, as such, the forum doesn't do people's homework for them. We will help you with concepts, we will help point out mistakes when we see them, we will help guide in the right direction and give suggestions. But, we don't just post answers and do the work for others. So, in that vein. What ideas do you have to solve this? What equations do you think are pertinent? What work have you done so far?

Any chance you can provide a quantitative prediction? You've made a qualitative one: "more plate than bowl shaped", so let's start getting more scientific by generating some numbers. Let's see some calculations based on your idea, let's see it applied to some of the data that is out there now, and also proposals about what kind of experiments would either confirm or disprove your idea.

But this isn't true. Photons have been shown to be the force carrier for the electromagnetic force. That is physics not being silent on how dislike charges cause attraction. Perhaps you should read a little more in depth before criticizing things you don't know that much about. E.g. read up on the Standard Model of particle physics. It certainly isn't complete, and there are actual questions that merit discussion. But the point I quoted above is pretty much settled -- the evidence to support it it very conclusive. You would do well to read up on that evidence and learn why the standard model is the standard model -- that is specifically what evidence supports the model and why.

I think we should extend this to everything, then. Do you understand every part of your car? Because if not, we probably shouldn't use them either, or believe in them either. How about your computer? Do you understand the design of the chip? If not, you probably shouldn't use your computer or believe in it. How about television, and radio? Do you understand how pictures and sounds are transmitted through the air to arrive to your house? If not, you probably shouldn't believe in them, too. Heck, for that matter, do you understand all the details of how your body functions? What about your brain? Can you explain it to anybody (i.e. your barmaid)? Because, if not, you probably shouldn't believe in it, either. Come on... there is a reason we have experts in every field. There is too much information for everyone to be able to consume it all. You take your car to a mechanic and let Ford and GM design them for you, you let Intel and AMD design your computer chips for you, you let Sony and Panasonic design and build your TVs for you. That's why you go to a doctor when you are sick. We don't do all of these other exceptionally complex things ourselves, why should the study of black holes and other complex scientific things be different? Just like it takes time to understand how to design a car, a computer chip, a TV or radio, or understand parts of the human body, it takes time and study to learn the scientific cosmological theories and the evidence that strongly supports the current theories.

I.e. it doesn't matter if you pushed you car 100 m to the North, or 100 m to the East, or 100 m to the West, (of course, assuming a perfectly flat, uniform piece of land), you have done the same amount of work. Similarly, if you calculated how much work you did by pushing your car 100 m to the North. Then, the next day, everyone in the world agreed to start calling "North", "East", it doesn't change the amount of work performed. I know that that example is pretty farcical, but the idea is to show that if you choose one direction as the x coordinate, and then rotated the coordinates 90 degrees so that what was x is now y, it doesn't change the amount of work that was performed. I.e., the specific direction doesn't matter.

(emphasis added because that's the particular phrase I want to focus my reply on) How can you say that conclusively? I.e. can you back that up with some math? And, if things happen more frequently than it "should" mathematically, then in all likelihood the model used was probably wrong and needs modified.

RC, The rules of this forum don't allow members to post solutions to your problems directly. What members of this forum will do is help guide you along the way, will point out mistakes where they seem them, etc. Basically, what I am getting at, is please post what work you and your group has done so far, and the forum may be able to help nudge you on the correct path, and correct mistakes where we see them.

Well, Firstly, as this is in your own words a project for school, I'm going to move this thread to homework help. Secondly, the rules of this forum don't permit the member from directly doing your work for you. We will however, give you suggestions and critique work. So, in that vein, why don't you post what you have found and what you think is important and what isn't important. Post some of the sources you have used to look up info. Basically, post what work you have done, and the forum will guide you on your way.

If you calculate both components [math]x_1[/math] and [math]x_2[/math] of the vector, you have everything. The angle, the orientation (which maybe I am missing something, aren't these the two words pretty much synonymous?), whatever you want calculated. The angle comes from converting the components of the angle from Cartesian to cylindrical or spherical or whatever specific angle you want. I am saying that in 2-D, you can find the bisecting angle, by calculating [math]\cos\theta[/math] and the using that [math]\theta[/math] to calculate [math]\cos\frac{1}{2}\theta[/math] for use in those two equations for the two unknown components of the bisecting vector.

No, the equation he posted is fine. It is the formula to find the angle between given vectors. And, I can see how that would be useful to find the bisecting angle because if you knew that the angle was [math]\theta[/math] then obviously the bisecting vector makes the angle [math]\frac{1}{2}\theta[/math] with both of the original angles. In fact, I think that in 2-D just that knowledge would be enough to solve for the bisecting vector: Given vectors a and b: and [math]\cos{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}||\mathbf{b}|} [/math] there is a unique bisecting vector, call it x from which we can make 2 equations: [math]\cos{\frac{\theta}{2}} = \frac{\mathbf{a}\cdot\mathbf{x}}{|\mathbf{a}||\mathbf{x}|} [/math] and [math]\cos{\frac{\theta}{2}} = \frac{\mathbf{x}\cdot\mathbf{b}}{|\mathbf{x}||\mathbf{b}|} [/math] If the vector is restricted to 2-D, there are only two unknowns in this case, the two vector components [math]x_1[/math] and [math]x_2[/math]. Which are going to be part of [math]\mathbf{a}\cdot\mathbf{x}[/math] and [math]\mathbf{x}\cdot\mathbf{b}[/math]. Two equations, two unknowns should be solvable. The bisecting vector would, of course, only be known to a constant as was mentioned. I.e. if vector x bisects a and b, then so does 0.5x and 158.9x and so on.

Just crack open a university-level calculus-based physics text, assuming you've had the calculus (if not, start there). I guarantee that no one wants someone who can just memorize the equations -- the best people know the equations inside and out. How to derive them, what all the terms mean, all the assumptions that went into them, etc. The best professor I ever had never brought any notes to class. He just asked a person in the front row what was the last line or two of what we did last time, and he just went from there. He re-derived the day's lecture every time -- really all because he knew the fundamentals and knew where we wanted to go with the analysis. So, on that note, I'd just study the fundamentals like physics, like calculus, and know that inside and out. No one here can tell you an equation for "how much fuel it takes to accelerate to x" anyway, because there are way too many varibles in such an equation. What kind of fuel? What kind of propulsion system? What is the mass of the vehicle? What is the efficiency of the engine? I know that there are more, but these 4 instantly popped into my head. edited to add: D H and I wrote pretty much the same thing here (he must have been posting while I was writing) -- and if it wasn't obvious, I couldn't agree more. Really and truly, as simple as it sounds, everything comes back to conservation of mass, momentum, and energy. Using that to solve the problem isn't always going to be easy, but that is all engineering really is: the bookkeepers of nature. Conservation of mass, momentum, and energy.

uh huh.... [math]\mathbf{F} = m\mathbf{a}[/math] pretty much disagrees with that. A force is an acceleration multiplied by a factor of the object's mass. If an object undergoes an acceleration -- it experiences a force that is directly proportional to that acceleration. There is no separating the two. If something causes an acceleration, then it is also a force, and if something is a force it causes an acceleration.

I concur completely. This is the main reason I've haven't participated much in these threads. Because it is obvious to me as well that you aren't really learning anything either. So, I'm with D H: do it yourself, or at the very least go and have a long sit-down with your TA and/or professor.

So, 1) I moved a bunch more of these threads from Math to Homework, since you seem to be constantly posting on how to do these problems, may I suggest you continue to post in Homework when you need help. 2) I am hoping that this doesn't come off too snide or rude or anything, because I really don't mean it to sound that way: But, is there not a TA or professor's office hours you can visit to get the help you seem to need with these? Because you've asked a lot of questions that are pretty similar, and if you continuously struggle with these, I think that talking with your instructor would be much, much more fruitful than asking a forum.

Not that your other claims don't need citations, but this one is quite a whopper. Any chance at all you can provide a peer-reviewed journal article from a physics or math journal to back this up? The amount of evidence supporting GR is pretty overwhelming, that's why it is the current theory. It's not like GR just won "Physics Idol" one year and hence became the theory du jour. It is backed up by a lot of evidence. Please see: Clifford M. Will, “The Confrontation between General Relativity and Experiment”, http://www.livingreviews.org/lrr-2006-3 which is an incredible review of the many experimental results that support general relativity. Saying that "every experimental result disagrees" means you need to provide evidence how every single experiment in the cited article above actually disagrees with GR. If you cannot do this, then you must drop your claim. (or, I guess you could just be a troll, though I sincerely hope not)

Faraday cages (EM shielding) aren't all that expensive. People buy them routines to protect valuable computer and other electronic equipment. Why don't those computers inside the Faraday cages float?

Please be a little clearer: What exactly do you mean by "abused"? Because while words can be incredibly descriptive -- I'm sure we've all read some very wonderful novel ans stories -- words are incredibly inexact. What each of us thinks of as a "large number" is different, based on our history and experiences. Just as a simple example, say I hit a golf ball with a certain speed, launched at a certain angle, and with a given spin rate. With math, I can predict exactly where that ball will hit the ground. With words, the best you can do is "over there" or "near that sign" or "on top that hill" or something similar. With math, I can be very exact, saying "134 yards" or "255 yards". If you limit yourself to only words, how can you conduct any kind of experiment with any kind of accuracy? How can you make a prediction with any kind of specificity?