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    May 2017
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  1. Hey Saloni, I chose to analyse patterns in the Arts and in Mathematics. You can center your Cs and CCs around how mathematics is the study of patterns (we seek patterns). While in the Arts artists often do not seek patterns -rejecting uniformity etc. There are tons of mathematical patterns. Obviously, choose one that you can explain clearly (I used a picture to help).. For the Arts I recommend looking at "patterns" in poetry (structure, themes between poems) etc. I guess you will be able to do a little Lang&Lit while you're at it.
  2. Calc. option question: Q: f(x) = ex - 3x = 0, prove that there are exactly two positive real numbers x. _____ My working: Since, f(x) is continuous and differentiable, I thought about how I could apply Rolle's theorem f'(x) = ex - 3 = 0 => x = ln 3 Here, f(ln 3) = 3 - 3ln 3 < 0 I reasoned: Since, there is only one stationary point (x = ln 3) and this occurs when f(x) < 0, therefore there must be exactly two roots. But how do we show that they are both positive? Thanks all!
  3. Which option are you taking?
  4. Hey Samir, I looked at Wolfram Alpha: http://mathworld.wolfram.com/ Look through the different topics (algebra, calculus and analysis etc). I did mine on pursuit curves and applied it to Star Wars (X wing fighter in pursuit of star destroyer).
  5. Q: Find the complex number z (z + 1)i = (z + 2i)*(3 + 2i) Since its linear here's another way to solve for z: Multiplying in i to both sides, iz + i = z(3 + 2i) +6i - 4 Rearrange for z 4 - 5i = z(3 + i) z = (4 - 5i)/(3 + i) Multiply 3 - i (conjugate roots technique) z = (12 - 4i - 15i - 5)/10 z = (7 - 19i)/10 A bit late to reply but at least its a quick way? Edit: Missing (-) added...
  6. Btw I think you're over complicating your IA. You should just focus on one part i.e. orbital motion of shuttle around planet. For you personal engagement how about this: In physics, the orbital motion is assumed to be circular. However this is not the case. I decided to deduce an equation that would accurately model the trajectory of a shuttle of M (mass) orbits around X planet. Lol don't forget to cite (IB will kill you if you don't).
  7. U serious?? Ok just say I'm interested in NASA and that you want to be a astronaut. The topic should genuinely interest you, if not why bother doing it?
  8. If Z~N(0,1), prove that for positive k: P(|Z|<k) = 2 - 2Φ(k). I'm pretty certain the 2 - 2Φ(k) part comes from symmetry with the distribution if Φ(k) is negative. Pretty tough question but here's my working. Hoping someone can develop this further... Thanks
  9. This link is pretty useful in explaining the trajectory of an object as it orbits around another object If you're interested in finding details about the speed at which the shuttle must be launched you can have a look here. This is physics: I'm surprised you couldn't find anything hahaha. Anyways hope you find this useful
  10. I guess you have two questions? 1. The dk/dt part is 6 ft/s because the question states that "the girl walks to the pole". This requires a rate of change of distance of the girl to the pole (dk/dt) 2. Even though k is decreasing, doesn't mean dk/dt should be negative. Note that the sign (+ or -) depends on the reference. For example, in my diagram the distance k is measured from the girl to the pole, or say, to from left to right. Thus, anything moving to the right (-->) is positive. Sorry, I think I need to change my x and k (as to avoid confusion). Let, x = dis
  11. The hard part is understanding that there are two variables. Here, I denoted k to be the distance from the pole to the girl, and from the question dk/dt (speed of girl) is 6 ft/sec. I denoted x to be the distance from pole to shadow tip. I believe the question wants us to find dx/dt (shadow tip speed). See attached:
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