Recent content by 凍鴛鴦

  1. 2u Mathematics Marathon v1.0

    Oops sorry, changed to Q38. BTW, theres a Q37(b)! Try it =D
  2. Complex Numbers in Mod-Arg form

    The Casio fx-100AU has a Complex Number Mode and is a BOS approved calculator. Note: The AU series is especially designed to meet Australian BOS requirements.
  3. 2u Mathematics Marathon v1.0

    Oops looks like I was too slow. And adgala, there's a mistake in your second answer. Anyway, make my last question on Exponential Decay 37(b) =D Answer to 37(a): Q 37, Somebody borrows $30000 with 15% interest Per Anuum. He has to pay it all off after 20 years in equal monthly repayments. He...
  4. 2u Mathematics Marathon v1.0

    Q 36: Differentiate: (a) 2 cos (3x - pi/2) (b) 5(loge x)² Answer: Q37(b): (harder 2U, or 3U question) you can apply your knowledge of 2U exp. decay in this question: dP / dt = kP(H-P) Show that the equation P = (AH) / (A + e-kHt) is a solution of the equation (A, k and H are...
  5. Trig Identity Proof

    D'oh, can't believe I didn't see that. Thanks guys!
  6. Trig Identity Proof

    Hi, How do you proof that LHS = RHS given LHS = Sqrt(3)*Cos[3t]-Sin[3t] RHS = 2Cos[3t + pi/6] ?? Thanks!
  7. Maths Induction Question

    Cheers! Thanks heaps =D
  8. Maths Induction Question

    Hi again, Can someone please help with this? Prove by induction that: (1+x)^n >= nx+1 n and x are positive integers Thanks in advance!
  9. Projectile Motion Question

    Thanks for the quick responses! I understand acmilan's answer. However, I don't understand logically why the final velocity would equal the initial velocity? Doesn't the velocity decrease by -g due to acceleration over the course of the flight? Edit Oops I get it now. It's because the...
  10. Projectile Motion Question

    Hi all, A ball is thrown from a point on a horizontal plane with an initial velocity of 25 m/s at an angle of 40 degrees to the horizontal. Taking g = 10m/s^2 calculate: (c) the speed with which it strikes the ground The answer says 25m/s, but I don't think it is. Yes, the horizontal...
  11. something new on the "pi and e" debate...

    Haha... you stole my idea!!! ><
  12. something new on the "pi and e" debate...

    Oh yeh BTW, because of the fact that the above quoted number is a closer approximation to e^6 than is pi^4 + pi^5, it proves that pi^4 + pi^5 does not equal to e^6 =)
  13. something new on the "pi and e" debate...

    How about this? =P...
  14. Interview for New Zealand Natural - any tips?

    Lol... Thanks to those who gave proper responses!
  15. Interview for New Zealand Natural - any tips?

    Hey all, I just got a call from New Zealand Natural that they're gonna have an interview with me next week. Do you guys have any tips for me? What to bring, questions to expect, etc...? Thanks a bunch!
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