Cap'n Refsmmat

I usually deadpan my sarcasm, or just make it unusually enthusiastic in tone.

They're not useful at all for chemistry (you can't sell a bottle of a material that lasts a few milliseconds), but for nuclear reactions they're useful, and they'll be more useful as we start smashing heavier and heavier atoms together with more and more energy. Depends on what you're using the table for, I guess.

It isn't hazmat, it's rule 2.6.

Take a peek down the index page and find the GUT forum. You can start writing there.

Interesting. I'd have to update the tutorial to explain what that means though.

That's essentially the same thing, but you changed d to r.

Chronologically: TI-BASIC, PHP, Java, a tad of C, Python. I can also work my way around JavaScript (although I never formally "learned it" -- it's just so similar to other languages).

Could you back off on the attitude some? You are no more productive when you insult your opponent than when you debate him coolly.

Last time I used BOINC I thought it allowed you to specify a maximum CPU usage. But I'm not sure if I remember that correctly.

I think I tried to convert everything to [math]\cdot[/math] at one point to be consistent, but I think I missed some.

Oh, I see. So the order of operations there isn't clear. I'll see if I can alter the post to express that in a better way. Thanks for the compliments. I'll be trying to push out the next installment of the tutorial soon, as soon as I get it revised and ready to go.

It's not three electrons being shared, it's six, and the carbon atom has a lone pair to itself as well. The electrons in the bond are fully shared between both atoms (although one may be more electronegative).

It's another incident of nerd sniping: http://xkcd.com/356/

Carbon doesn't always have four bonds. It's capable of having four bonds and remaining stable, which is helpful, but it can be stable with less as long as it still has a full outer shell of electrons.

There's no difference between [math]\cdot[/math] and [math]\times[/math]. It's just a matter of style. Sorry for being inconsistent there. Your method is correct. It's just that for more complicated problems it gets unmanageable and it becomes easier to use the product rule. As for getting from this: [math] \frac{d}{dx}u \cdot v + \frac{d}{dx}v \cdot u = \frac{d}{dx}(x-2) \cdot (x + 4) + \frac{d}{dx}(x+4) \cdot (x - 2) [/math] to this: [math] 1 \cdot (x + 4) + 1 \cdot (x - 2) = (x + 4) + (x - 2) = 2x + 2 [/math] What I did was plug in the variables. We know this: [math]u = (x - 2)[/math] [math]v= (x + 4)[/math] We can find the derivatives of each: [math]\frac{d}{dx}u = 1[/math] [math]\frac{d}{dx}v = 1[/math] using the rules that you seem to know well. It's then a matter of inserting the variables and their derivatives into the equation from before to reach our answer.

Cherenkov radiation doesn't involve anything breaking c -- only things breaking the speed of light in a particular medium. We know that nothing can travel faster than c not just because of experiments but because of the theory of relativity, which posits that it should take an infinite amount of energy to accelerate a particle to c, and that it takes more energy to accelerate a particle the faster it's going. Pretty much all aspects of relativity have been tested and shown to be true, so I wouldn't bet on faster-than-light speeds just yet. The speed of gravity has been experimentally tested and the evidence indicates that it's the speed of light, or at least close to it. That's not a certainty, of course, as the Wikipedia article notes, but at least we're not just "assuming."

The best reasoning I heard for the decision was that a rapist may be more inclined to kill his victim (thus killing the sole witness) if he knows he could face death if arrested.

I think the simplest response here would be to point out that Lamarckism has been discredited. Constant worship behavior in an adult will not genetically reprogram the brain.

Lesson 5: The Quotient Rule By now you should have a good grasp of basic differentiation. (If you don't, I suggest you try to work it out rather than plowing ahead.) However, there are still a few cases that you don't yet know how to handle. For example, what's the derivative of this? [math]f(x) = \frac{x-2}{x+4}[/math] None of the rules and shortcuts so far tells you how to do that. In steps the Quotient Rule. First, let's separate our function into two parts: [math]u = x - 2[/math] [math]v = x + 4[/math] meaning that [math]f(x) = \frac{u}{v}[/math] The quotient rule tells us that the derivative of that equation is this: [math]f'(x) = \frac{u'\cdot v - v'\cdot u}{v^2}[/math] (Remember that u' is the shorthand for the derivative of u.) So now you just need to find the derivatives of each of the parts -- the derivatives of u and v. You just apply the rules you learned before and find that they're both 1. So that means that: [math]f'(x) = \frac{1 (x + 4) - (1 (x - 2))}{(x + 4)^2}[/math] (You need to remember the parentheses after the minus sign. That negative distributes over everything in the parentheses, so remember to change the signs when you're working out the subtraction.) There's some more math you can do to simplify that out, but it's not really necessary. You get the idea. And that's all there is to the Quotient Rule. Remember, if you need help understanding any of this, you can just ask in our calculus forum.

Okay, I'm going to try to follow your diagrams exactly here. Let's suppose we build your device so that the large wheel will have a circumference of 8cm and the small a circumference of 4cm. The inner peg that the weights are wound around have a circumference of 2cm. The string the weights hang from is 40cm long, so it's wound around the inner peg 20 times. So, we start the device up. The weight is hanging 40cm down from the large pulley (pulley A) and is 0cm down from the small, ready to fall. It falls all the way down, making the small pulley (pulley B) revolve 20 times. This makes the large pulley revolve 10 times (2:1 ratio), bringing the second weight only up 20cm. Current status: pulley A has a weight hanging 20cm down, pulley B one hanging 40cm down. Switch occurs. Pulley A is now small and pulley B large. The weight falls the rest of the 20cm from pulley A, making it revolve 10 times. This makes pulley B revolve 5 times, bringing its weight up only 10cm. You're left with one weight 40cm down and one 30cm down. It'll continue to diminish until it stops.

To nitpick, that's the fallacy fallacy; his conclusion may actually be correct, even though the entire argument is bogus. But let's get back on topic, please.

The design might work if there were no friction at all. The trouble is that you will gradually lose energy to friction in the bearings and such.

Your average velocity, to be specific.

When I measure the speed of light (presumably by timing how long it takes to travel a certain distance), my measurement does depend on the standard second my atomic clock gives me.

Yeah. But I never changed the duration of a second.