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  1. Q

    Quick question about inequality notation

    Which of the following is correct, if x = 4? n\leq3x^{2} \leq3(4)^{2} \leq48 or n\leq3x^{2} =3(4)^{2} =48 In other words, in what situations is it necessary to switch from inequality to equality, and it is always required to have only one comparison symbol per line?
  2. Q

    Proof by Induction

    This is generally a good way to think about it in my opinion.
  3. Q

    Differentiation of abs(x)

    You just go back to the definition of abs[(f(x)] abs[f(x)] = f(x) \forall f(x) \geq 0 abs[f(x)] = -f(x) \forall f(x) < 0 And differentiate separately. In other words, 'splitting the domains', as someone above said.
  4. Q

    Uniting quantum physics with the theory of relativity

    I think he's trying to ask why it's not possible?
  5. Q

    Other Should I Become an Engineer?

    I would like some advice on choosing an engineering specialisation. I have a love of mathematics so preferably I would like an engineering degree/profession with as much math as possible. I usually like a layer of abstraction - I am not one who likes physically working with technology as such...
  6. Q

    Quantifying Entropy - an analogy

    Yes I assume it'd be non-subjective shuffling
  7. Q

    Quantifying Entropy - an analogy

    Although I note Lambert looks at Entropy literally not as an analogy
  8. Q

    Heat transfer rate to heating time

    could you fix the latex?
  9. Q

    Pressure inside a sphere

    This is correct - inside hollow shell there is no gravity from the shell
  10. Q

    Need help for toboggan speed

    It is relatively simple if you assume no air resistance/friction etc. But it will depend on how much space you have and how quickly you want to reach your target speed. \frac{1}{2}m (\Delta v)^{2} = mg \Delta h (kinetic energy gained = gravitational potential energy lost) \Delta h =...
  11. Q

    What is a particle?

    Firstly mass and energy are equivalent; they are the same thing. 'Is there an accurate model that encompasses everything that we have observed about particles? - Yes, well to a sufficient accuracy anyway. Whilst there is not one 'theory of everything' that descirbes everything we know...
  12. Q

    Magnetic force vs gravity

    You require the force on the magnet to be equal to the force of gravity, as you said. F = I \Delta l B sin \theta = \frac{Gm_{1}m_{2}}{r^{2}}
  13. Q

    Gravitation qns

    1. The force of attraction is perpendicular to the velocity of the moon's orbit - ie the moon is travelling tangential to the orbit, assuming a circular orbit. Thus there is no component of the force in the direction of motion. The force remains perpendicular to the motion as it moves so it...
  14. Q

    Quantifying Entropy - an analogy

    My friend and I were playing cards, and he was shuffling the deck. He claimed that the longer he shuffled, the 'more random' the arrangement of the cards would become. I argued that at a certain point the cards would be sufficiently disorganised such that they were in a state with no pattern...
  15. Q

    News Liberal fascism

    Sounds like a crap sensationalist book that Ann Coulter would write... slipperly slope arguments, reductio ad absurdum etc...
  16. Q

    Energy to move a car

    By Newton's first law once the car is moving at 55mph you will not need to add any more energy as you will not be accelerating it any more. K=\frac{1}{2}mv^{2} \Delta{K} = \frac{1}{2}m(\Delta{v})^{2} as \frac{dm}{dt} is constant \approx\frac{1}{2}(\frac{1000}{2.2})(55*1.6)^{2} \approx\1.76 *...
  17. Q

    Ready for some LHC rap?

    hah i like it
  18. Q

    Properties of the Absolute Value

    let a = mcis(kpi) where m => 0, k is integer and b = ncis(hpi) where n => 0, h integer (clearly a,b are real) |a||b|= mn |ab|=|mcis(kpi)*ncis(hpi)| = |mncis[pi(k+h)]| = mn as required