Recent content by QuanticEnigma

\frac{dv_{x}}{dt} = 2\omega (v_{y}\sin{\varphi} - v_{z}\cos{\varphi}) \frac{dv_{y}}{dt} = 2\omega (-v_{x}\sin{\varphi}) \frac{dv_{z}}{dt} = 2\omega (v_{x}\cos{\varphi}) Ok, so I suppose this will give me a velocity vector dependent on time t ... is this correct? Also, when I...

Homework Statement An object is dropped from rest at height H = 40m above the ground at latitude 31.3^{o}S. Calculate the final displacement, in magnitude and direction, due to the Coriolis effect. Homework Equations \Omega = \omega \left( \begin{array}{cc} 0\\ \cos{\varphi}\\...

Homework Statement 1. Establish the vector identity \nabla . (B x A) = (\nabla x A).B - A.(\nabla x B) 2. Calculate the partial derivative with respect to x_{k} of the quadratic form A_{rs}x_{r}x_{s} with the A_{rs} all constant, i.e. calculate A_{rs}x_{r}x_{s,k} Homework Equations The...

Ok with that in mind, does MWI imply that if you are killed in, for example, a car accident, would your consciousness be "shifted" to an alternate reality where you survive? Or would it only apply to situations where there are only 2 possible outcomes (because if you die in a car accident, there...

So it just seems that the results of your experiment always have the same outcome...I suppose you would start to question that after a while, why you keep surviving when there is an equal chance of dying.

Hey guys, I'm having a bit of trouble getting my head around the quantum suicide and immortality thought experiment, http://en.wikipedia.org/wiki/Quantum_suicide_and_immortality" (Sorry to quote Wikipedia, lol) IF the Many Worlds interpretation of QM is true, would this imply that the...

-1 = 1 ?? -1 = -1 \Rightarrow \frac{-1}{1}=\frac{1}{-1} \Rightarrow \sqrt{\frac{-1}{1}}=\sqrt{\frac{1}{-1}} \Rightarrow \frac{\sqrt{-1}}{\sqrt{1}}=\frac{\sqrt{1}}{\sqrt{-1}} \Rightarrow \frac{i}{1}=\frac{1}{i} \Rightarrow i^2=1 \Rightarrow -1 = 1 As you can see, -1 clearly...

Sweet, thanks for the help :smile:

Would sin\theta and cos\theta being \leq 1 mean that the expression inside the bracket is between -1 and 1?

Sorry, it's supposed to be f(r,\theta) not f(x,y)

Ok, I have f(x,y)=\frac{r^3\cos^3(\theta)r\sin(\theta)-3r^3\sin^3(\theta)}{r^2\cos^2(\theta)+r^2\sin^2(\theta)} = \frac{r^3(r\cos^3(\theta)\sin(\theta)-3\sin^3(\theta)}{r^2}=r(r\cos^3(\theta)\sin(\theta)-3\sin^3(\theta)) Since I have an r out the front of everything, i didn't worry about...

Yeah it is, my bad (hope I don't make that mistake in the exam :-p) I don't really know what you mean by theta, I've already worked out the limit of f (in polar coordinates) as r tends to 0 to be zero, and I thought this implied that any line approaching (0,0) would have limit zero...I'm not...

Ok, I've decided to cheat and use Mathematica to plot the function, and I can see that the function is continuous everywhere :-p I think there must be some problem in my working, as the limits as f tends to (0,0) along the x and y axes is not the same as the limit along the line y=x...I'm confused

Someone help!

Homework Statement Is the function f(x,y) defined by f(x,y) = (yx^3 - 3y^3)/(x^2 + y^2), (x,y)!=(0,0) =0, (x,y)=(0,0) continuous everywhere in R^2? Give reasons for your answer. Homework Equations The Attempt at a Solution I changed f(x,y) into polar coordinates and found the limit as...