Recent content by codec9

3. if a body is only floating on the surface, it is not displacing anything. it might as well not be there. if the body sinks down into the fluid, then the fluid basically has a big hole in it filled by this body and the fluid is 'displaced.'

I don't think I saw an explanation for KE apart from those of the form "since KE = 1/2mv^2, ..." From the very basics, we know matter has inertia. This can proved (informally I guess) by considering a ball going up and down a V shape and one side gets progressively flatter. I won't explain...

There is no certain rate. Read the thread, or at least the post above yours!

With respect to the center of the ball, point 1 is moving at the same speed as point 2. All parts are from the center. I don't see how the velocities you mention have relevance. The directions are the only things that matter to understand why it dives. Air at the top of the ball pushes against...

Why is point 1 moving faster than point 2?

The slope of x^2 is 2x. Therefore, as x goes to infinity so does the slope.

stewart, regarding post 19 the rate of change of a line is not automatically 0. I don't know where you got that from. A vertical line has an infinite rate of change; y = x has a rate of change of 1. Skhandelwal, was there something wrong with my explanations on posts 9 and 11? MaWM's first...

OK, but the d(denominator) with respect to S1 which is a variable is 1, right?

infinity has to do with height, not angle. y = x goes to infinity in either direction, but it is a clear 45 degrees with respect to the x-axis no matter where you are.

I forgot how to take these derivatives. Could someone tell me the rule/work it out. P = (doS1 + d1So) / (d1 + S1) dP/dS1 = ? I think it should be (denominator*d(numerator) - d(denom.)num.) / denom^2 but that gets the wrong answer.

I don't know what you mean by theory of multiplication. I realized, though, that it does not matter where the different systems start but what they are capable of. Off the top of my head you can multiply x and y by copying y to the left then adding the left y to the right x times. You delete x...

Oh, we weren't really disagreeing. Sorry. I never learned about beta in PA, but in Turing Machines and Abacuses one can work out exp in terms of addition and multiplication, and further multiplication in terms of addition. In PA, assuming beta works exp is not explicitly needed, but in Turing...

You need exponentiation for the Proof function.

I explained it spinning on the side, counterclockwise if you look from the top. So if you hit the ball I am talking about, and you are right handed, you would hit it on the right side most likely or else move the paddle from the left side of your body across to the right side and beyond.

I see the problem. It is right to say that the angle of the section you are looking at will keep increasing with respect to the x-axis. If I understand this correctly, the angle will approach 90 degrees. 180 degrees would mean it is parallel to the x-axis if you are measuring with respect to it...