m4rc

The derivative of [math]x^2-2x-15[/math] is [math]2x-2[/math] (because the derivative of a sum of functions is equal to the sum of the derivatives of each function). The slope of any function will be zero at its maximum/minimums, therefore the derivative of the function will be zero. So [math]2x-2=0[/math] leading to [math]x=1[/math] We can conclude that [math]x^2-2x-15[/math] is horizontal at [math]x=1[/math]. This still does not indicate it is a maximum, minimum or neither. To be certain you should calculate the second derivative of y. The second derivative of [math]x^2-2x-15[/math] is the derivative of [math]2x-2 [/math]which is 2. If the second derivative is positive then you have a minimum, if the second derivative is negative then you have a maximum.

The measurement of the mass of an ion before and after emitting a photon has been done by David Pritchard at MIT. "The mass difference was measured by comparing the cyclotron orbit frequencies of two single molecules trapped in a strong magnetic field for several weeks"( http://web.mit.edu/newsoffice/2005/emc2.html ) . In the case of you affecting your weight by jumping on your bathroom scales, you will not get an accurate measurement while you are accelerating. So for the ion, you need to measure the mass of the ion before and after it emits the photon, but not during the short time in which it is emitting the photon (a few nanoseconds). I am certain that the researcher took the recoil of the ion into consideration when doing their experiment.

Actually atoms do lose mass when they emit a photon http://www.newscientist.com/channel/fundamentals/mg18925411.300.html . If something absorbes a photon, it will gain a small amount of mass. Mass and energy always go together. If something has energy it has mass, if something has mass then it has energy. The two are related by E=mc^2. When people say that photons have no mass, they are refering to its rest mass. You can measure a photon's relativistic mass by measuring the difference in mass of an atom after it emits a photon, but "that's not a huge change: detecting the difference is equivalent to detecting a hair's breadth change in the distance from New York to Los Angeles. Weighing an ion to that accuracy requires more than your standard set of kitchen scales. In fact, it requires quantum scales. David Pritchard started building his quantum scales at the Massachusetts Institute of Technology in 1985. Back then he wasn't interested in verifying Einstein's equation."

I assume that you can differentiate Y with respect to L and get a dY/DL as a function of L and K. Then the tricky part is getting rid of the term in the square bracket. Express the term in the square bracket as a function of Y and alpha. Then substitute the expression you get for the term in the sqare bracket into your solution for DY/DL.

The website that you refer to mentions that there are 4 contributions to the perihelion advance and that "the advance δ4 which to this day remains unknown can be calculated..." Why didn't you calculate δ4? It may have added credibility to your website. You are in fact asking us to doubt the accepted explanation which gives exactly the right answer for an explanation that is simple to calculate, but that you don't know if it comes even close to the correct answer. Without this calculation, or at least the result, your explanation is not very convincing.

To get an interference pattern, you must have a constant phase difference between the two sources. This can be accomplished in two ways. One way is to use two coherent sources of light (two lasers). If you use two incoherent sources of light, the phase difference between the two sources is not constant so no pattern is made. So your headlights do not make an interference pattern. Another way to get interference is to use a single source of light and have it interfere with itself. You can make a single source look like two sources by using mirrors and/or slits. In this case, if the phase of the source changes (as it will in an incoherent source), it will change by the same amount for each path.

From The New Encyclopedia of Birds and http://www.aad.gov.au/default.asp?casid=3524 , "Emperor penguins endure the coldest conditions encountered by any bird...where the average temperature is -20C." They also breed in the middle of winter when "wind chill temperatures reaching down to minus 60ºC", they do not reveal what the actual temperature is. These penguins have adapted to live in the coldest place on earth. I believe that it is possible for life to adapt itself to even colder temperatures, however so far it has had no reason to do so because there is no place that is that cold.

Yes, according to Maxwell's equations on electromagnetism, the speed of light should be constant. This result is not compatible with the concepts of Newtonian mechanics and the concept of an ether. The discrepency between Maxwell's equations and Newtons' mechanics is what compelled Einstein to propose his theory of relativity.

The experiment consist of sending signal from one plane A to plane B then from plane B to plane A and seeing if there is any significant difference in the time for light to travel the same distance but in different directions. As mentioned by insan_alien "michelson morely experiment does it quite nicely" as well. Although I am not familiar with any experiment done with planes, this has been done with satelites. The delays in the incoming timing signal of GPS satelites are used to calculate position. According to all published material on GPS systems, no correction for the movement of the ether is done. Despite this accurate results can still be obtained. So we can conclude that either there is no ether or the GPS sytems makes a correction for the movement of the ether and there's a huge conspiracy to hide the presence of ether from us.

When electrons(or anything else) travel at velocities, their interactions between each other and other particles slow down. Chemical reaction using these electrons will also slow down. Any biochemical reaction will slow down as well so while travelling near the speed of light we will move slower, think slower and age slower. However we will not notice unless we observe the outside world aound us because the rate of everything travelling with us is slowed down by the same amount. Even our clock will run slower (both our internal body clock and any mechanical clock we bring with us). When we return to earth, and meet with people who didn't have their internal body clocks slowed down they will have aged more than we did.

The returning pilot would be able to interact with others without any problem. He would simply be a few miliseconds younger than expected. Lets look at a situation where the difference is larger. If an astronaught leave earth. If he travels near the speed of light his clock might show that his return trip lasted 1 year while a clock left on earth shows that he has been gone for 10 years. As before it is the moving clock that shows a shorter time interval. The astronaught will have aged one year (the same amount of time indicated by the clock that travelled with him) while everybody on earth will have aged 10 years. Once he is back, he will be able to hold conversations with the people that stayed. All of his friends that he grew up with however will be 10 years older while he will be only 1 year older than when he left. All that has happened is that the astronaught has slowed down his aging while travelling.

Sounds right.

I believe that I have thought of a possible olfactory illusion. Consider the following situation: In a circular room, you set up some fans to create a strong wind going around the room. You then place a source of odor to the left of you (downwind). The wind will carry the smell around the room then back to you. If you smell while moving, trying to locate the source of the smell, it will seem that it is to your right when it is in fact to your left.

I agree with the previous comment but not the following comment: It is the moving clocks that run slow.

In order to use special relativity to calculate the time spent in another reference frame, you must stay in the same reference frame. So in the case of a plane that takes off, accelerates and then returns, you can apply special relativity from the earth's frame of reference to calculate the time elapsed by a clock on the plane. You can't start from the frame of reference of the plane and use special relativity to determine the time spent on earth because the plane accelerated. You will need to apply general relativity which is much more complicated. In the case of twins that take off in separate space ships, I believe (although not certain of this) that you can solve for the difference in the age of the two twins if you know their acceleration profile. You will need to assume an observer in a un-accelerated frame of reference and make all calculations from that frame of reference. It should not matter which un-accelerated frame of reference you chose.

Why don't you use the spring from the pen? You can use a retractible pen (the type with a spring in them. All you need to do is push it down compressing the spring, then let go, and it will jump. If you want it to jump higher all you have to do is replace the spring with a stronger spring. Another option is to do something like the Mario toy shown in http://www.nintendoland.com/funfacts/merchs/mcmario.htm .

forgot 22116 and its permutations. That should bring the total to 40.

There are 34 different numbers that match. 11114 22228 51118,15118,11518,11158 31116,13116,11316,11136 42118 and permutations of the first four digits make 12 more 32218 and permutations of the first four digits make 12 more

With just the ratio of the function to its derivative you almost have enough info to find the function. You need to solve a first order differential equation. See http://mathworld.wolfram.com/First-OrderOrdinaryDifferentialEquation.html . Your solution will have integration constants that you will not be able to determine unless you have values for the function at particular points. It may be possible to determine the function in a simpler way if the ratio of the function to its derivative is a simple function (like a constant).

Although theoretically, you can transfer energy with radio waves, in practice it would be difficult and it will depend on what you are trying to heat. For example, microwaves heat foods fast because they are emitted at a particular wavelength that is easily absorbed by water, but microwaves are not as good for heating anything that doesn't contain water. It might be easier to make suggestions if you would tell us what you are trying to heat, and how much of it.

I have used a rapid thermal annealer to process silicon. This particular furnace used hallogen lamps to heat a small volume very quickly. The fastest and most intense heat treatments I put my samples through is going from room temperature to 1000C in 5 seconds. The sample can remain at that temperature for anything from a few seconds to a few minutes. The system the cools down to about 200C in about 1 minute or two, where it is safe to open again. I know that the system is capable of reaching 1410C (the melting point of silicon) because on a bad run, the thermocouple (temperature sensor) broke resulting in a melted sample, although the highest temperature you can program in this particular furnace is 1100C. If you want more information on different furnaces like this try a search for "rapid thermal annealer" in google.

Global warming is melting as much ice in the south as in the north. The reason there are more news reports about the arctic ice is that more people live near the north pole. I do remember reading several articles about the ice shelf in antarctica melting as well. For example http://www.newscientist.com/channel/earth/dn8173 states that "The edges of the Antarctic ice sheets are slipping into the ocean at an unprecedented rate" (oct 2005). I also remember news stories about extreamly large sections of the antarctic ice shelf collapsing. So it is the news reporting that is biased to repporting events in the northern hemisphere.

One example where relativity affects radioactivity is the decay of muons. Muons are created in the high atmosphere in a reaction between cosmic rays and the atmosphere. They have very short lifetime and if we assume newtonian mechanics, even if they travel at c they don't have enough time to reach the surface before decaying. However some do reach the surface of the earth because the lifetime of the muon undergoes time dilation. For more information see http://nobelprize.org/physics/educational/relativity/transformations-4.html or do a google search on muon and relativity.

I see Moore's law more as a self fufilling prophesy. After Moore noticed the trend and published it, the computer chip manufacturers had something to compare to their progress. If they could not keep up with Moore's law then they were not at the cutting edge. So they would all spend enough on reseach until they either reached the level predicted by Moore's law or went bankrupt. So the existance of Moore's law (along with the fear of not keeping up with it) is the reason that it is true.

Quantasm's answer is wrong. You can tell by expanding his expression. I could not factor your expression (either on paper or using mathcad) therefore I think that it can't be done. By the way is this homework? Why else would you need to factor that expression?