TheLivingMartyr
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Integrating factorised quadratics
TheLivingMartyr replied to TheLivingMartyr's topic in Analysis and Calculus
Hah, thanks! Anyway, it was nice to end the night having resolved my problem -
Integrating factorised quadratics
TheLivingMartyr replied to TheLivingMartyr's topic in Analysis and Calculus
oh..... fiddlesticks -.-" Simple syntax mistake on my calculator caused this whole mishap. I put "3*32" as equalling "92" instead of "3*9" I haven't made many posts here, but I'm pretty sure I've made myself look like an utter fool :') -
I will soon be starting my first year in sixth form college, studying Maths, Further Maths, Physics and Chemistry.
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Integrating factorised quadratics
TheLivingMartyr replied to TheLivingMartyr's topic in Analysis and Calculus
so it does.... hmmm, now i just have to work out why I was getting the wrong answer when working out the area under it. Thankyou the thing is if I evaluate the integral: "-1/3x3 + 3/2x2" with the values x=0 and x=3 then i get a different area to if I evaluate the integral: "-((2x3 - 9x2)/6)" with the same values. I realise that the fractions are equal, but why then do i get different areas? I'm at a loss -
I'm not fantastic at integration, but I can integrate any number of polynomials pretty easily. I was given the equation "y=x(3-x)" to integrate. so I naturally treated it as a factorised quadratic, expanded it, and did: Int.(-x2 + 3x)dx = -1/3x3 + 3/2x2 I therefore assumed that: Int.(-x2 + 3x)dx = Int.(x(3 - x))dx It turns out i was wrong, and that I can't just expand these brackets, as the actual answer is (according to an integral calculator): -((2x3 - 9x2)/6) I need to know why I can't just expand these brackets and integrate, and how to integrate a factorised quadratic like this one. Please help me I also don't think a "u" substitution would work any differently, although i'm not particularly knowledgeable when it comes to those, soooo...
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MgBr+ -- Where is the charge at? What is the name of it?
TheLivingMartyr replied to Genecks's topic in Inorganic Chemistry
all wrong sorry, didnt look properly -
and anyway, there must be some type of way of extracting sodium from compounds, or how would we get hold of any of it? oh wait, couldn't you reduce sodium compound with carbon monoxide? ahh yes thanks, i thought there must be some way of doing it
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Could you not electrolysise molten sodium chloride? i know it would be a hugely high temperature, but could you not theoretically do it?
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I know that the area of an ellipse is: Pi x Semimajor x Semiminor But after quite a long time of figuring, i thought, why can't we just treat the ellipse as a circle by hypothetically shortening the semimajor and lengthening the semiminor to the same length (averaging them) and then using Pi x Radius2 I know they give different answers, but i don't see why my way is wrong. I know that it is, but i would like someone to prove to me that it isn't, and prove to me that Pi x ab is thanks once again
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i'm sorry, i didn't know which specific subcatergory to put this in, there was no geometry section. According to mathematics you can draw a line. this is 1 dimensional. you can then draw another line at 90o to this; this occupies 2 dimensions: a square. you can then draw a third line which obviously cannot be at 90o to both of these, but represents it. this is 3 dimensional space: a cube. so far, this can all be realised in a physcial situation, as you can take for example 12 pieces of uncooked spaghetti and put them into a cube. all the intersections will be at 90o. now once again, according to modern mathematics, you can draw a fourth line, which connects 2 cubes, and this is supposed to be in 4 dimensions: a tesseract. this is where my logical, physics orientated brain, stops and says "hang on, surely, this 4th dimension thing is all void if i can't be physically realised". I am sure you all know what a tesseract looks like, so i wont explain it, but i would argue that it does not occupy 4 dimensions! the 4th set of lines are diagonal: that is not at 90o to the others. i try to accept this fourth mathematical dimension and move on, but then realise, "oh dear, if you can just draw another line, then you can have infinite dimensions". so what i am saying is, what is achieved by "making up" more dimensions when they do not exist physically? There are 3 spacial dimensions that we exist in, and they are all at 90o to each other. in our universe, for a fourth dimension to be achieved, it would have to be drawn at a non-right angle to the others, therefore making it not another dimension at all, just a line occupying 2 dimensions. i would like to hear people's views on this, and maybe someone more understanding of maths can explain my fault
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so basically, an antiparticle travelling forward in time will be drawn as though it were travelling back in time?
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I was looking at a feynman diagram to show the decay of a neutron into a proton (by a down quark decaying into an up quark by emitting a W- boson which then decays into an electron and an electron antineutrino). In a nutshell, Beta- decay. Here is the said diagram this article is not questioning beta- decay, but asking about the directions of the arrows on the diagram. As you can see, the electron antineutrino is pointing towards the vertex, whereas the electron is pointing away from it. now this would seem to mean that that the antineutrino is going back in time. this is not the only diagram i've seen that does this. http://images-mediawiki-sites.thefullwiki.org/10/1/1/4/4483182193902691.png same affair here, the positron goes back in time, and so does the antiquark. please could someone explain what this is suggesting, whether it is just a standard procedure in feynman diagrams, or if i've just found dud diagrams. thank you
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okay thanx Merged post follows: Consecutive posts mergedi'm assuming that it's an electron neutrino? not for some random reason a muon or tauon neutrino Merged post follows: Consecutive posts mergedoooo, i found a good feynmann diagram that explains Beta- decay http://upload.wikimedia.org/wikipedia/commons/8/89/Beta_Negative_Decay.svg the down quark of the neutrons decays into an up quark, by emitting a W- boson, which then decays into an electron and an electron neutrino
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doesn't it emit a neutrino by converting one of it's neutrons into a proton by emitting an electron and a neutrino?
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What happens to the atom of a radioisotope (an element with a different number of neutrons, making it unstable) is that it emits radiation. the types of radiation are: Alpha: the nucleus emits a helium nucleus (2 protons, 2 neutrons, with no electrons) this obviously means that the atomic mass of the element decreases by 4 Beta: the atom emits an e- particle (an electron) Gamma: the atom emits gamma rays (photons, and this form of radiation occurs along side alpha radiation) if you would like me to explain what these certain types of radiation can do, then i will be happy to:-)
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I am acquainted with Standard Model, but thankyou for the explanation anyway:D Merged post follows: Consecutive posts merged you may call me LM. And the name was not specifically in relation to my views towards life, I just thought it sounded cool.
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Energy-Momentum Relation: Am I the only one whose noticed?
TheLivingMartyr replied to TheLivingMartyr's topic in Relativity
well, thanks for explaining it to me and the reason I often say things like "I'm such an idiot" is because i'm quite a self-concious/anxious person, but i learnt something, so i'm not complaining! -
can someone tell me what all these "lepton" or "meson" or "mr.wizard" or "molecule" next to peoples' names mean?
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Energy-Momentum Relation: Am I the only one whose noticed?
TheLivingMartyr replied to TheLivingMartyr's topic in Relativity
oh dear, i have made a fool of myself. *slaps face* so the actual momentum of the object cannot be converted into pure energy (by this i mean photons)? -
The Official "Introduce Yourself" Thread
TheLivingMartyr replied to Radical Edward's topic in The Lounge
hello, i'm new. my name's, i'm 15 and i'm interested in physics and theoretical science/maths -
this whole thread assumes that momentum is the same as movement through space-time, please tell me if i am wrong. I was browsing around some articles on particle physics and relativity and the like, and I stumbled across a short article on Energy-Momentum Relation. It stated that mass and energy are proportional (which I already knew), but then that Energy, Mass and Momentum are also proportional. i found this intruiging, but didn't expect to discover anything exceptional. the equations stated that: (i can't use superscript characters in this, so ^ indicates superscript) E^2=m^2c^4+p^2c^2 where E is the total energy, m is the mass, p is the momentum and c is the speed of light then we have the good old Mass-Energy Relation equation that is used in nuclear physics E=mc^2 and then there was the E-p relation for massless particles (eg. photons) E=pc i looked at this and thought, "hang on a minute, this means that if you give a massive body momentum, then the energy produced from it will be greater than the energy produced from a still body" so i did some quick calculations with this and here is an example we'll say that: m=10 p=5 c=300000000 for a body with no mass, but with momentum: E=1.5x10^9 for a body with mass, but no momentum: E=9x10^17 and for a body with both mass and momentum: E=8.1x10^35 what i am thinking from this is, "why don't they just move nuclear fuel around in generators?" because this obviously shows that a body with momentum produces more energy than a body without momentum. could anyone who is knowledgable on this subject please reply to this and tell me whether or not i am right or have made a "discovery"