# Search results

1. ### 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. ### Proof by Induction

This is generally a good way to think about it in my opinion.
3. ### 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. ### Uniting quantum physics with the theory of relativity

I think he's trying to ask why it's not possible?
5. ### 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. ### Quantifying Entropy - an analogy

Yes I assume it'd be non-subjective shuffling
7. ### Quantifying Entropy - an analogy

Although I note Lambert looks at Entropy literally not as an analogy
8. ### Heat transfer rate to heating time

could you fix the latex?
9. ### Pressure inside a sphere

This is correct - inside hollow shell there is no gravity from the shell
10. ### 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. ### 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. ### 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. ### 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. ### 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. ### News Liberal fascism

Sounds like a crap sensationalist book that Ann Coulter would write... slipperly slope arguments, reductio ad absurdum etc...
16. ### 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. ### Ready for some LHC rap?

hah i like it
18. ### 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