Recent content by quark1005

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?

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

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.

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

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...

Yes I assume it'd be non-subjective shuffling

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

could you fix the latex?

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

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 =...

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...

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}}

1. The force of attraction is perpendicular to the velocity of the moon's orbit - ie the moon is traveling 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...

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...

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