mezarashi

Actually, a direct application of L'Hopital's rule does work, except the substitution of m->0 instead of n->infinity, where m = 1/n is much easier, and you'll be able to get the answer without any of the messy stuff. If you apply L'Hopital's rule, we see here that we have a 0/0. Taking the derivative of the top term, we have [math]\lim_{n\to\infty} \frac{-\frac{1}{n^2}}{ \frac{1}{n^2}e^{-\frac{1}{n}} }[/math] Cancelling out the [math]\frac{1}{n^2}[/math] we then have [math]\lim_{n\to\infty} \frac{-1}{ e^{-\frac{1}{n}} }[/math] which by substituting in n->infinity, will yield -1, the same result as the m substitution.

If your processor is in fact "dying" on you, the effects would most undoubtedly be more severe. Losing signals would mean your computer crashes constantly, which is the same thing that happens if you RAM or motherboard is failing. Your system slow down is completely and most definitely because of your software configuration. It is requesting resources from the CPU, and somewhere there is a resource leakage causing your CPU to use clock cycles on unnecessary or redundant tasks. From what you mentioned, I would suggest: 1. Firefox is known to be buggy when it comes to resource usage. It is known to do that 95% CPU usage, tabbed browsing is known to leak RAM memory and many discussion boards are claim that it basically hangs your system at times. 2. OS degradation - a common but slow process as you use your computer and install/uninstall programs. Because everything you've ever installed leaves some kind of trash in your configs and registry, your computer will spend more time loading. 3. Program leaking memory - you may have installed a badly programmed piece of software that is leaking memory. Any kind of windows service that runs in the background especially. This means that you have less and less fast speed memory, and your computer is constantly relying on the relatively "slow" seek and retrieval times from the hard disk. You can try tackling those problems individually, but a fresh format on your OS partition would be an easy solution too.

I guess you will be happy to know that there exists a formula in which you may calculate the sum of the Fibonacci numbers knowing only "n". This formula derivation however requires some extensive analysis using some auxilary equations and is not particularly easy, so don't give up! It may or may not be within your current mathematical level, but given that this was a problem given to you I guess it should be. This neat formula was actually credited to a French mathematician Binet in the 18th century, and it quotes: http://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html

The most simple explanation for this is that light particles have no mass! Anything with mass will not be able to achieve the speed of light. But photons along with all its zero mass cousins such as the graviton also travel at the speed of light. This means that changes or fluctuations in the gravitational or electromagnetic fields are felt at the speed of light.

As usual, it's impossible to accelerate anything to the speed of light due to the increasing mass of the object as it approaches the speed of light, and thus requiring an infinitely increasing force. Accelerating something to the speed of light however will take quite alot of time. I understand that Ion engines are not particularly "thrustful" compared to conventional rocket engines. Some calculations show here that, and I will assume up to half the speed of light, where Newtonian estimation still generally holds: Given the ion engine produces a thrust of T Newtons, and your average bulky satellite of 3 tons. acceleration = T/mass acceleration = T/3000 velocity = acceleration x time 150,000,000 meters/second =(T x days)*28.8 Days = (5208333)/Thrust Typical ion engines create a fraction of a Newton of thrust? But give it a "boost" and say it does 100 N !!! Days = 52083 days = 143 years

Personally I believe that any "bending" you see is a result of an optical illusion or some other physical phenomenon such as diffraction. Using the simple elevator thought experiment like of Einstein's, you see that in a gravitational field a horizontal ray of (such as Earth's) light will bend vertically by (delta), where delta = 1/2gt^2 = (gr^2)/(2c^2) where r is the horizontal distance travelled by that light beam, and g is the gravitational acceleration. This is of course using the elementary kinematics equations. Given this rough estimate, if you conduct your "amateur" experiment along a 1km stretch of road (r = 1000m), then you will get a displacement (delta) of delta = 9.8*(1000^2)/(2*(300000000^2)) delta = 0.0544 nanometers (So you decide that you have some equipment that can measure that, let's add in some more fun facts) - diameter of a hydrogen atom: 0.1 nanometers - curvature of Earth per kilometer: 10-15 centimeters - approximate divergence of a good laser beam: 60 millimeters at 1 kilometer

Yes, if Efnet is the network you are connected to, when you join a channel, it will be on this network. If someone joins this same channel while logged onto IRCnet, he or she will not see you. Most clients like mIRC however will allow you to join multiple servers and handle channels on multiple networks.

lol, congratulations. One best rely on one's self, or so they say.

I believe in the existence of this "spritual energy". I think the best evidence for this is when people go into a coma, and then one day they just "wake up". They say that sometimes doctors can't explain why a patient is dying. His/her bodily functions are all working, but its like they are slipping out further away. They say a person immediately after death has the chemical composition possible for life, but yet they are dead. There's something beyond that science...

I'm not sure of how Trillian handles IRC, but IRC stands for internet relay chat. Any IRC network is based on an array of servers that are linked together. Each network will have its own name. Some of the largest IRC networks are Quakenet, Undernet, Dalnet, Rizon, etc. Go to their websites (search google) to see what their server address(es) are. For example Rizon's address is: irc.rizon.net and irc.rizon.org. There is actually no point in using IRC messaging unless you have a friend network on one of those servers. For it to work, you and your friends will need to join the same network and register your user names. IRC networks are known to be generally very solid when it comes to reliability and response times. More times I have my MSN offline than I have my IRC offline. There is high level of redundancy in IRC, and the protocol is clean and fast (given text messaging is all you need). ICQ for example takes very long sometimes for a message to get to the other side. This is generally not a problem on IRC unless you are encountering server lag, which in that case you can reconnect to a server that is geographically closer to your location. IRC however, is not famous for its IM abilities but rather its chatrooms. It is an assembling place for notorious hackers and crack groups. Yes, warez and all that other underground stuff. There are a hostful of other features regarding IRC. I recommend you read a guide on the internet if you are interested and get a proper IRC client (e.g. mIRC or XChat).

I think in the end it comes down to 1. Who teaches it and 2. Whether you're capable in that subject field If you get the most horrible dumbest teacher in the world as I do my AP Physics C teacher (who now has been fired) ~.~, then life for you in that class will be hell. If you are a naturally talented mathematician, even Calculus BC will be trivial, and I remember most of the people in my class received 5. Subjects like Macro and Micro Economics maybe impossible for some but a breeze for others. I don't think you should take up subjects based on what other people say of them. Look at yourself and find what interests you (especially later in college or even as a career), and most importantly, do you like the instructor teaching that course.

From what I know, fluid dynamics is a relatively complex subject. Although not the most difficult subject the background knowledge required to do any of its analysis is vast. Normally as cars are tested in wind tunnels, you will observe how much drag or force the wind is putting on the car in test. If a car is very aerodynamic, it should experience less drag at highspeeds. The problem in your case is that the car performs at relatively highspeeds, 20 meters in a couple of seconds? I'm not sure if that qualifies for the air turning turbulent instead of laminar. Both require different equations of analysis (one bases itself on fluid viscosity-laminar while the other on particle inertia-turbulent). It is somewhat possible to model the effects using a smaller model in what mechanical engineers call Dimensional Analysis and Similitude. Kind of like how engineers predict how a river or dam will flow using a smaller scale model with different fluids. That topic is however, can be half a semesters worth of college material. I would suggest sticking to studies related to frictional forces, or do a qualitative aerodynamic study

While I agree with you that time will not be imaginary and time will be time, I think you are oversimplifying the concept of "imaginary". A number or concept is imaginary because it does not exist in a certain "real" domain. In the case of time, I think we haven't even defined the relationship between this imaginary domain and how it affects our real world domain. For example in electric circuits, imaginary current does NOT simply mean 1. no current, 2. backward current, 3. forward current. It is a more complex "tendency" of current behavior that cannot be explained if we limit ourselves to only 1 domain. Mathematics allows us to study behavior beyond simple physical observation, so I would personally not attribute those simple options to imaginary time without deeper analysis.

The equations are from the equilibrium condition. For example you know Newton's law: Fnet = ma If there is no acceleration (a), then there must be no net force. So we use this on the two axises, x and y. In the y direction, the forces are, the reaction force (Fnormal), gravitational force (mg), and the y-component of P (Psin30). In the x direction, again there is no acceleration so the force summation should be zero. The forces here are, Frictional Force (Ffriction) and the x-component of P (Pcos30). Take into consideration the directions and you will have the equations.

Sounds very interesting. The unfortunate thing is that it's not possible considering how superconductor levitation works. This is how it works basically. Understanding that you are still very young, you might need to consult some guides on the internet for the science background or ask within Because super conductors have no resistance, once you can induce a current within it, it will flow forever. Moving currents create a magnetic field. Magnetic fields in opposite directions oppose each other, and thus we have that apparent floating effect. The problems to implement this large scale? (people have actually though about applying this to hyper-speed vacuum bullet trains that float on their tracks) 1. Superconductors are relatively expensive to produce. Building something even as large as a train with superconducting tracks would be extremely costly. 2. Superconductors are "super conductors" but not "perfect conductors". Over time, you will lose some of that magnetic field generating current. 3. The superconductors we know of now only work at VERY cold temperatures. Have you seen such an experiment at school? Your physics teacher will pour in liquid nitrogen to cool down the super conductor to proper operating temperature. 4. Magnetic fields need to properly align to "float". North and North repel we know that right? But South and North, and you'll instead be stuck to each other like glue. This stability is an issue. Once your in space, which direction is the magnetic field pointing towards? There would be some limitations to where you can go. Superconductors are still so far only finding applications in small scale electronics. But I hope for the day our technology can give us all that

Pluggin in P = 40.8N doesn't seem to satisfy a zero net force condition. The question says on the verge of slipping, so in the x-direction, Force-friction and horizontal component of P are equal. Friction can only act parallel to a surface, normal forces perpendicular. Your freebody analysis should include the x and y axis. x-axis Pcos30 = Ffriction y-axis Psin30 + Fnormal = mg But we know that Ffriction = u x Fnormal, Fnormal = mg - Psin30 Try playing with those equations. Your answer shouldn't be more than 15N I'd suppose.

It's quite an honor to be picking what you will be doing for you, but okay ^^

Given that you know the x-distance travelled and that velocity in x is constant due to the absence of any force field: velocity initial X = (velocity initial) x (cos 60) distance = velocity x time 100 meters = (velocity initial X) x time In the y-component, similarly: Velocity initial Y = Velocity initial x cos 60 distance = (velocity initial) x (time) + 1/2(acceleration x time^2) : your kinematics equation 40 meters = (velocity initial Y) x (time) + 1/2( g x time^2) Two equations, two unknowns, solve simultaneously. The second problem can be solved using the component summation: velocity^2 = (velocity-X)^2 + (velocity-Y)^2

If you are referring to conventional solar cells, the main problem is not actually the current generated after the photon hits the atom, but rather, getting the photon to hit the atom in the first place !!! Solar cells work by applying a reverse bias across a p-n junction to create a depletion region. Any photon that gets absorbed in the P and N region will indeed create an electron-hole pair, but will quickly be recombined thus not contributing to the current. The objective is to get the absorption to occur at the depletion zone where it will contribute to current. The problem is that this region is created BETWEEN the P and N layers... so how exactly do we get a reasonable amount of light to pass through and make contact? Much of the research in the field focuses on this concept... getting as high a ratio as possible of photons passing through the initial surface to create hopefully current contributing electron-hole carriers. This seeks to improve quantum efficiency. You can probably see now why solar cells as we know them today are rather limited in their energy output. It's not only about getting photons to knock out electrons, but getting electrons to start "drifting" in a controlled and consequently meaningful way.

Motherboards are judged mainly by their featured chipset. A hot chipset at the moment is the nVidia nForce 4. It features an ultra compact "chip" rather than chipset, meaning there is no North and South bridge as you will usually find in most any other motherboard. It also incorporates within its chip nearly about everything you will need in a computer including ethernet, SLI, PCI express, Serial ATA, RAID if you need it. I've never seen a comparison between motherboards in terms of memory consumption. A majority of power dissipation occurs at the CPU itself rather. Choosing brands is a matter of choosing features. You can choose between Abit, Asus, MSI, Soltek, EpoX, etc. They will all have different features and different sizes. Get what you need to make it most compact. Another solid chipset is the VIA K8T890.

I understand that a "healthy" body functioning normally will maintain itself automatically by making you hungry when you are below your daily calorie intake. However, your body tends to be weird in other ways, and will make you lose your appetite when it feels that energy must be spent on other more important activities like you have the flu or some infection. Of course, in cases like these you shouldn't stop eating. As for external temperature and fuel needed to maintain body temperature, I think there is little correlation. People living in the tropics are fatter than those who live colder places? What you eat probably has a much more significant effect. In anycase, you should make sure that you aren't facing a heat related illness, namely heat exhaustion. Heat exhaustion can cause appetite loss. It's like the same kind of feeling you get after playing some intense sports and losing lots of water. You just don't feel like doing anything, including eating (although you will feel very hungry sooner or later because of the exercise). Making sure you get more water in than you are sweating is a good start.

A very common program known among anime movie editors like myself is Adobe After Effects. A trial download is available at the Adobe website. After Effects is very effective at adding effects, while its cousin Premier is better for clip compiling. Although having the software itself will not instantly create you wonders, you will need to learn how to use it (quite a learning curve). Many of these effects are achieved using pricey professional plug-ins, but for the casual artiste, you might need to churn out some extra creativity on how you will achieve certain effects using the built-in default features. Another hot program under speculation is Discreet Combustion 4. They claim that it has better effects capabilities, but I have yet to try it.

If this happens to be a more advanced calculus class, then for the distance relative to the sun, you may be required to do integration along the moon's trajectory. Given that you know its period and the integration period, this should be trivial.... numerically integrating that is

I'm sure most of you internet webbers have seen compressed files such as .zip or .rar (lossless compression). Does anybody have any opinions on what compression is best for lossless? Personally I use .rar, but I'm sure there must be better algorithms. Is there a fundamental limit to how much something can be compressed (compression ratio)? Maybe someone can help explain Shannon's theory of information and what it really means.

Another of my cruddy paints