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Everything posted by Petanquell

  1. I thing Big Nose said it perfect. [math] 8^{x^2 - 2x} = \frac{1}{2} [/math] the first step is: [math] 8^{x^2 - 2x} = 8^{-\frac{1}{3}}[/math] using fact that [math]\frac{1}{2}=8^{-\frac{1}{3}}[/math] Than using the old rule "when bases are equal than exponents must be equal too" or with "more official" way, use logarithm with base 8 on both sides we get: [math]\mathrm{log_{8}}(8^{x^2 - 2x})=\mathrm{log_{8}}(8^{-\frac{1}{3}}) [/math] [math](x^2 - 2x) \cdot \mathrm{log_{8}}(8)=-\frac{1}{3} \cdot \mathrm{log_{8}(8)} [/math] and we get to easy equation [math] x^2 - 2x= -\frac{1}{3} [/math] or in the first step use that [math](\frac{1}{2})^{-3}=8[/math] and do the same again only with some small changes: [math] ((\frac{1}{2})^{-3})^{x^2 - 2x} = \frac{1}{2}[/math] [math]\mathrm{log_{\frac{1}{2}}}((\frac{1}{2})^{-3})^{x^2 - 2x}=\mathrm{log_{\frac{1}{2}}}\frac{1}{2} [/math] [math]\mathrm{log_{\frac{1}{2}}}(\frac{1}{2})^{-3x^2 + 6x}=\mathrm{log_{\frac{1}{2}}}\frac{1}{2} [/math] [math](-3x^2 + 6x) \cdot \mathrm{log_{\frac{1}{2}}}\frac{1}{2}=\mathrm{log_{\frac{1}{2}}}\frac{1}{2} [/math] [math] -3x^2 + 6x= 1 [/math] (dividing with [math]-3[/math] you get the same equation as before..) I hope it helps. Pq
  2. I've found only this but it's barely useful... http://www.newsobserver.com/news/story/1591089.html Pq
  3. Hey guys, I've never got problem with solving quadratic, logarithmic or goniometric equations, but I don't know how to solve them when they are all together. The most simple example is: [math] \textup{log}(x)+\textup{sin}(x)+x^2+x+1=0 [/math] Is there any way to solve them without "computer help"? Thanks, pq
  4. Page 40 contains this exercise: [math](x+1)^2=-25[/math] [math]x+1=\pm-25[/math] [math]x=-1\pm-25[/math] [math]x=-1-25 \textrm{ or } x=-1+25[/math] [math]x=-26,24[/math] and note probably about complex solution..(?) What tells you that it hasn't got real solutions? Pq
  5. Well, I hate people doing this but it's well known trick: 1) go to the shop 2) buy the most expensive calculator 3) do an exam 4) complain and return your calculator to the shop Pq
  6. Of course there are some things we can't understand on the first sight, but like Feynmann said: "It's like a park with huge number of ways. If you can't find one, there are some other reaching the same place." Or other point of view, everything must be proved so folowing the prove must lead to understanding. Could this be a way to avoid incomprehension? Pq
  7. It will be grievous to have a limit on high school....
  8. Hey guys, I talked with a guy who studies mathematics and he told me that his friends from collage found their "limits" (mostly in third grade) and now the don't have a clue what's going on, and just learn mechanically like medival scholars did. He also told me that only some chosen ones still understand it. Does anyone you know of feel a similar effect? And now something completly diffrent, will you press (softly, of course) on your child to do math?
  9. I'll try it explain with my words despite my level of english. I have three very related reasons: The first reason should be clear, I'm bored and curious. In a curious-period I wonder how things work and how they were invented. In a bored-period I just sit and read, or work on a book I'm writing for my schoolmates, because they complain about the speed of our math teacher (she's really fast, I guess it's about 180 words per minute ). The second reason is a little related to the book I write. I want to motivate others to do mathematics because I consider mathematics as a basic knowledge which builds you among others a useful logic."I believe everyone has some measure of talent for mathematics in them, it's just that many don't know about that, which is what I try to change. I'm also convinced that while I'm not inteligent enough to invent something great, I might be "inteligent" enough to find someone who can. The third reason is that mathematics is something like meassure of intelligence for others (I really don't know why). And it gives you the respect needed to be listened to by others. In a nutshell, I study to relax and to motivate others to be better then me. All those things I very enjoy. When I'm writing that book or teaching my schoolmate (sometimes more then 6 hour a day) it gives me feel, that I'm useful for others. Sometimes I regret that my father forbid me to study mathematics at the university Pq Google dofinition of toy: "An artifact designed to be played with." Richard P. Feynman's did exactly what i want to do . His quotation express it nicely: "Physics is like sex: sure, it may give some practical results, but that's not why we do it."
  10. Well , we haven't learned trigonimetric functions yet so I can't see it there. But I'll take a look sometime... And that conversation, I don't remember why I did it. Maybe because Maple doesn't take degrees, really don't know. pq
  11. Ok, i'll try First of all, I coversed degrees to radians [math]T*\sin(37\pi/180)+\frac{4}{3}*T*\sin(53\pi/180)-100N = 0[/math] [math]T*\sin(37\pi/180)+\frac{4}{3}*T*\sin(53\pi/180)=100N[/math] [math]T(\sin(37\pi/180)+\frac{4}{3}*\sin(53\pi/180))=100N[/math] [math]T=\frac{100}{\sin(37\pi/180)+\frac{4}{3}*\sin(53\pi/180)}N[/math] And aproximate... pq
  12. is it [math] T*\sin{37}+1.33*T*\sin{53}-100N=0[/math] ? Eventually, can I use 4/3 exept 1,33 ?
  13. Much better jetpack have Yves Rossy here.. That's impressive... Does someone here fly with hang*glider? It must be possible to fly with something like it even if it will be grafted on your back...
  14. No, I won't click it! it was a hard day today
  15. What is it? If it has something to do mathematics, then it could be a destiny...
  16. My knowledge in ornithology is very limited so are there any difrences between gliding birds and the others in anatomy and muscles activity during flight?
  17. My nick is lucky double-keyboard hit with some leteers added
  18. If you mean inverse function to sin() so it is arcsin() (or [math]\sin^{-1} [/math] but i hate this notation...]. For others it's the same: cos() - arccos(); tg() - arctg(),....).... I don't understand your last formula so I show my you way: [math] e=\sqrt{a^2+b^2} [/math] [math] f=\sqrt{b^2+c^2} [/math] [math] g=\sqrt{a^2+c^2} [/math] We want to find angle [math] x [/math] between [math] f [/math] and [math] g [/math]. for illustration... I'll try it with cosine rule [math] c^2 = a^2 + b^2 - 2ab\cos(\gamma) [/math] ...we want an angle so... [math] \cos(\gamma) = \frac{a^2 + b^2 - c^2}{2ab} [/math] and now it's seems easy [math] a=g,b=f,c=e [/math] [math]\cos(x) = \frac{(a^2+c^2) + (b^2+c^2)- (a^2+b^2)}{2\sqrt{(a^2+c^2)}\sqrt{(b^2+c^2)}} [/math] [math]\cos(x) = \frac{2c^2}{2\sqrt{(a^2+c^2)}\sqrt{(b^2+c^2)}}[/math] [math]\cos(x) = \frac{c^2}{\sqrt{(a^2+c^2)}\sqrt{(b^2+c^2)}}[/math] and finally [math] x=\arccos(\frac{c^2}{\sqrt{(a^2+c^2)}\sqrt{(b^2+c^2)}}) [/math] I hope, everything's correct... Pq
  19. in math, always [math] 1+1=2 [/math] in nature, sometimes [math]\mbox{male} \bigcap \mbox{female} = \begin{cases} \mbox{boy} & \mbox{if } \mathbb{R^+} \\ \mbox{girl} & \mbox{if } \mathbb{R^-} \\ 0 & \mbox{if } \varnothing \\ \mbox{something else}&\mbox{if something else} \end{cases}[/math] Do you see it??
  20. I asked google on "the largest flying bird" and the answer is...hopeful for you, Demosthenes. Argentavis magnificens. The nature is just marvellous. Despite their 7-meter wingspan, their weight was only 70 Kilograms(try rack and diet ). Read through this, there are some interesting things especially their taking off problems and expert ability of riding on thermals and updrafts. Some pages about this: National Geographic Wiki: Argentavis Takes off problems (freerepublic.com) By the way, a few years ago a read an article about Angles and there was quotated one aviation engineer that the "classic angels" (i.e. wing on back) couldn't be able to fly. They have to have wings instead of arms.. Pq edit: I forgot, o really don't know how ia get used to 3,5-metre long things on my back....
  21. Officially, or at least according to wiki, it's 440, but i see in the United States and United Kingdom it's 442 (wiki:"19th and 20th century standards"). It surprised me.. Back to frequencies, I've never played on trumpet but violin, vibraphone and bass have the same frequencies. I'll ask our conductor, in our orchestra we tune all instruments (including tumpets and flutes) by one "A", but i really don't know, which button are trumpetists pressing...
  22. I'm just very often bored and I chosed mathematics to fill my long days because it seems much more logical and easier than nature...
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