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Everything posted by Dapthar

  1. Same here. Good to hear that the problem's not immediately life-threatening.
  2. Yeah, that's a pretty big problem. <rant>I've never really understood why a rather large portion of people who have a fair amount of money are so eager to dodge taxes. I mean, at that point in time, one is living rather comfortably, and assuming that one doesn't ramp up their spending proportionately, there's no danger of themselves or their family not satisfying their basic needs (food, shelter, health care), or having the necessary funds to pursue a collegiate education if they so wish. Thus, any 'extra' money that one is able to reclaim by opting out of social security would be spent on luxuries, which by definition are unnecessary. However, I guess I'm one of the few people that realizes even though those in power tend to misuse tax dollars, there are some programs and organizations (such as public schools, higher education, the NSF, social security, and medicaid) that are being funded, and that still makes them worth paying.</rant> The exact thought would most likely occur to business owners across the US, and I'd be willing to wager that the more unscrupulous ones wouldn't be as considerate as yourself, i.e., they wouldn't consider paying out an equivalent amount into a retirement plan of any sort.
  3. If you're imposing the relative topology (also known as the subspace topology) on [math][a,b][/math], then, by definition, if [math]U[/math] is open in [math]X[/math], then [math]U \cap [a,b][/math] is open in [math][a,b][/math].
  4. I found a link that may be of some use to you, one that describes parrot and crow behavioral patterns in a very easy-to-read manner: http://www.pbs.org/lifeofbirds/brain/ Also, a few more interesting links came up on the first page of the Google search that I ran. Link: http://www.google.com/search?hl=en&lr=&client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&q=parrot+crow+brain+&btnG=Search Just in case the link doesn't work for you, my search terms were: "parrot crow brain", without the quotation marks.
  5. Yup, you're right. When I was going back through and changing all the signs I missed a few. I went back and edited my previous post, and fixed the signs again.
  6. I cancel out the [math]-1[/math] from the numerator and the denominator in this step: [math]\frac{-4x-1}{-x - \sqrt{x^2+4x+1}}[/math][math]\cdot \frac{\frac{1}{x}}{\frac{1}{x}}[/math] [math]=\frac{4+1/x}{1+\frac{1}{x} \sqrt{x^2+4x+1}}[/math] If that's the error you're referring to.
  7. Ok, I fixed my earlier calculation. (See above post.)
  8. Thus, we eventually end up looking like the stereotypical Roswell alien. Then, just to satisfy causality, future 'humans' end up going back to 1947 and crashing their time machine in New Mexico.
  9. You need the [ math] [/ math] tags wrapped around it to get it to work (without the spaces, of course), like: [math]\ce{H2 + O2 -> H2O + Energy}[/math] Also, you had some syntax errors. The code for the above was: \ce{H2 + O2 -> H2O + Energy}
  10. Just a placeholder to let you know that I am looking at this problem, and will reply soon (1-2 days). If you need a hint more quickly than that, just mention so, and I'll try to speed up a bit.
  11. Derivation: Consider [math]0 \cdot x + 0 \cdot x[/math] By the distributive axiom, [math]x(y+z)=xy+xz, \forall x,y,z \in \mathbb{R}[/math]. Therefore, [math]0 \cdot x + 0 \cdot x = (0+0)\cdot x = 0 \cdot x[/math]. One of the consequences of the axioms is that [math]x+y=x \implies y = 0[/math], therefore [math]0 \cdot x = 0[/math] Yes, as long as whomever is grading your assignment has access to the list as well, otherwise they won't know which axiom you are referring to.
  12. Contradiction seems to be the most straigthforward approach. One can easily prove that [math]\lim_{x\to \infty}{g(x)}[/math] cannot be [math]\infty[/math] or [math]-\infty[/math]' date=' and similarly that it cannot be any finite, non-zero value. Thus, the only case that is left is that if the [math']\lim_{x\to \infty}{g(x)}[/math] does not exist. Thus, assume that [math]\lim_{x\to \infty}{xg(x)}=L[/math], but that [math]\lim_{x\to \infty}{g(x)}[/math] does not exist, and find a contradiction, and then you're done. (You should be able to do this part on your own, just go back to the definition of the existence of a limit.)
  13. The approximate relationship between air temperature and the speed of sound is: [math]v_{sound} \approx 331.4 + 0.6 \cdot T_C[/math] [math]\frac{m}{s}[/math] Where [math]T_C[/math] is the temperature in Celsius. Source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe.html
  14. This is one of the axioms of the real numbers. Nope. I can provide a list of the axioms for the real numbers if you care to know what they are.
  15. Yup. However, this is only possible if there are more than 3 vectors that we are dealing with. I made a minor simplification since the question only deals with 3 vectors.
  16. The columns of [math]A[/math] span [math]\mathbb{R} ^3[/math] if and only if they are linearly independent. The columns of [math]A[/math] are linearly independent if and only if, when you create a matrix, call it [math]B[/math], whose rows are the columns of [math]A[/math], and compute the reduced row echelon form of [math]B[/math], you get that the reduced row echelon form of [math]B[/math] is the 3 x 3 identity matrix. Using the above information, you should be able to determine whether or not part d.) is true.
  17. Zero is a rational number, since it can be written as a quotient of two integers. Namely, we can write [math]0=\frac{0}{a}[/math], where [math]a[/math] is any non-zero integer.
  18. One possible project is modeling bacterial growth. Materials You'll Need: Basically any type of bacteria (You should be able to get a suitable specimen from your Biology instructor. If not, he/she should have access to a catalog from which they can order bacteria specially cultivated for school experiments, or at the very least, refer you to someone/somewhere you can order bacteria from.) A petri dish (with agar) (Your Biology instructor should definitely have these, and be able to lend them to you.) A light microscope (Again, your Biology instructor should definitely have these, and be able to lend them to you.) Basic Idea: Given sufficient food (such as agar), and favorable temperatures (like room temperature), a bacterium will divide into two separate bacteria at fairly regular time intervals (somewhere between 1 - 2 hours). So, if you begin with one bacterium, at the end of first hour there will be two bacteria, at the end of the second hour there will be four bacteria, at the end of the third hour there will be eight bacteria, and so on. The equation that describes this relationship is [math]y=2^x[/math], where [math]x[/math] is the number of hours since you have started the experiment, and [math]y[/math] is the number of bacteria. As we see, [math]2^0 = 1[/math], [math]2^1 = 2[/math], [math]2^2 = 4[/math], and [math]2^3 = 8[/math]. The bacteria grow exponentially, i.e. the number of them that exist at any given hour is proportional the number of them that existed in the previous hour. As we see, the number of bacteria at any given hour is twice the number of bacteria in the previous hour. Your Experiment: Now, what you can do for your project is verify that bacteria grow exponentially. Put a single bacterium in the petri dish with the agar, and watch it through the light microscope for a few hours. Count the bacteria every hour, and plot your data afterwards. Check to make sure it matches with the above predictions. This material should give you plenty to write about for your report, and the experiment only takes a few hours of your time. Six hours of watching the bacteria should give you more than enough data points, however, you can cut it down to four hours if you're pressed for time. If you have any questions about the above experiment, feel free to ask me. Reference: http://www.science.org.au/nova/020/020box03.htm
  19. I'll write up something soon (in next 1-2 days), as I'm bit busy at the moment.
  20. I ended up getting [math]v_p\approx1.737228848 \cdot 10^7[/math][math]m/s[/math] [math]v_\alpha\approx-4.34307212 \cdot 10^6[/math][math]m/s[/math]. Where [math]v_p[/math] is the velocity of the proton, and [math]v_\alpha[/math] is the velocity of the alpha particle. Of course, [math]v_p\approx-1.737228848 \cdot 10^7[/math][math]m/s[/math] [math]v_\alpha\approx4.34307212 \cdot 10^6[/math][math]m/s[/math] is correct as well.
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