Recent content by jdavel

the voltage in the other two branches also have to be 12.46. So, 24 + 3*i1 = 12.46 E + 2*i2 = 12.46 i1+i2 = 1.78 That's 3 equations and 3 unknowns

No, that's not right. Do what macro_84 said. let t = cos(x) Now substitute t everywhere you see a cos(x) in the integrand that macro gave you (the one with nothing but cosines). it's staring you in the face.

Say what? The acceleration due to gravity near the Earth's surface is g. How is that quadratic?

the pebble will move. remember, while the engine is on, the pebble isn't floating weightlessly in the middle of the spaceship. it's jammed up against the back wall. so when the engine cuts off, the wall will act like a compressed spring and push the pebble forward. only if both the pebble and...

What if you think about it like this. Imagine a large mass suspended from a string made up of a single chain of atoms. The string is in tension with each pair of adjacent atoms held together by the electrostatic attraction between them. Then instead of cutting the string, just gradually...

a field whose magnitude decays exponentially (either in 1-D or radially from some central point) has a non-zero divergence everywhere. so if by "free space" you mean no charge density, then I don't think such a field could exist anywhere in free space.

you're missing a pair of parenetheses in your 3rd equation that's leading to an error in the last term of your 4th equation. what should that last term be?

the last term in your sum (where i = n) is going to be 1/n(n+1). if you take the sum one further (to i = n+1) what will the last term be now?

JesseM, "The twin at the center won't see the traveling twin's clock rate affected by the doppler effect..." I didn't explain clearly enough. The star is at the center of the big circle; the Earth is on the circle. So neither twin sits at the center of the circle. In the interem an even...

I haven't seen the twin problem configured this way before. But it seems to me it should lay to rest the argument that SR can't account for the age difference. Instead of going from the Earth to the star and back, the traveler goes from the Earth in a big circle around the star and back. The...

Gib Z, Very nice! Let me ask you something. If you were teaching integration, how would you explain to your students what went through your head to come up with the idea of multiplying the integrand by cos(x)/cos(x)? Is there an insight that could be used when they hit another integral...

I've been wondering how all those indefinite integrals in a comprehensive table were figured out. Can they all be done with one (or some combination) of the standard methods, (substitution, parts etc.)? Or did somebody just poke around until they figured them out? For example, how do you find...

"Since the light changed its direction it had to slow down..." Not true. Even a massive object can follow a curved path without changing its speed. So can light.

Another way is to use the fact that the inverse of A is the transpose of the matrix of cofactors of A divided by the determinant of A. Probably more calculations than row reduction, but I find it easier to remember. And for a given size matrix, it's pretty easy to program in Excel.

DoDo, That works. Nice! P.S. Ben Niehoff, this really wasn't from a homework assignment. I ran across this problem years ago, could never solve it, and just happen to think of it a few days ago.