Recent content by haroldholt

When you say that the Einstein argument is rather dated, do you mean that the idea of treating the traveling twin's frame of reference as an inertial one is dated in general?

Which explanation, from the point of view of the traveling twin, is the most widely accepted?

If the equivalence principle only applies locally, how do we conclude that the non-traveling twin has a higher gravitational potential energy?

I could probably simplify my question by asking the following: if the traveling observer has a lower gravitational potential energy and is therefore further down the "gravitational well", then where is the bottom of the well? Taking the gravitational field of the earth, for example, the...

I'm having a little trouble understanding the equivalence principle explanation of the twin paradox. I understand that the resolution to the paradox according to the equivalence principle is that the non-traveling twin has a higher gravitational potential energy in the pseudo-gravitational...

Oh yes of course. Stupid mistake on my behalf. But if the integral of the top surface is \pi I still don't get the correct answer. I found the unit normal using \frac{\partial{\mathbf{r}}}{\partial{t}}\times\frac{\partial{\mathbf{r}}}{\partial{z}} then dividing the result by the magnitude...

The question I was given asks to verify the divergence theorem by showing that both sides of the theorem show the same result. With the divergence theorem obviously being \iint_S\mathbf{F}\cdot\mathbf{n}\,dS = \iiint_V \nabla\cdot\mathbf{F}\,dV . The vector field is...

Those photons still took 5 years to leave the star and travel to us so we're still seeing the star as it was 5 years ago.

Cheers mate. Can't say I've ever heard of the rational zero theorem.

What method did you use to find those roots?

I'm having some trouble with this particular question. ∫∫x dA bound by y = 4x^3 - x^4 and y = 3 - 4x + 4x^2. All I can think to do is equate the two equations to find where they intercept to give the bounds for the double integral giving 0 = x^4 - 4x^3 + 4x^2 - 4x + 3. But I don't know...

Thanks for that. I now realize that y can be set to zero in the equation 8x(e^y - 1). And then if you sub y = 0 into the other equation you get 1 and -1 which yields the points (-1,0) and (1,0) (which is the answer in the back of the book :smile:). And if x = 0 then the other equation doesn't...

0 = 8x(e^y - 1). But I still don't know what to do with the exponential.

Thanks Well it's 0 = 8xe^y - 8x and 0 = (4x^2)(e^y) - 4e^4y. But I'm not sure where to go from there. I'm not sure what to do with the exponentials, I know they can never equal zero, but I'm not sure what that means for my equations.

Hi I'm studying for a calculus exam and I'm a little stuck on finding the extrema for multivariable functions. For the particular question I'm trying to do now I need to find and classify the extrema for the function f(x,y) = (4x^2)(e^y) - 2x^4 - e^4y. I can find the first derivatives...