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You might want to rethink that irspow. Right now we are over populating the earth, releasing CO2 into the atmosphere, over hunting, over farming, using up much of our natural resources (and not just oil). Energy is going to be a huge problem in the next 30 years. If the standard of living in countries such as China increase as it has been, the demand (and thus, price) of manufactured goods are going to skyrocket. And so on...
But then again, if we can develop new technologies, then none of these problems will exist. We'll just have to wait to see.
Yep, a lot of people say 20.
its not about transistors, its about charge in magnetic tape, there millions of seperate magnetic bits on a tape and the point either north or south, north being 0 south being 1. And its read by the computer.
You are talking about rom. The first computers didn't even have rom, all they had was ram, which was not in the form of magnetic tape.
It doesn't seem like it should work, because usually momentum is mass x velocity, but then, it doesn't seem like anything to do with light should work really.
Well said. What we are looking at is a world we can't see, so it's only intuitive that everything is counter-intuitive.
I meant that the speed of sound is variable depending on who is observing it. If you are travelling away from the sound source, then the sound will be slower for you than for someone who is stationary.
Ah, ok. I thought you meant it was the source of the sound that was moving.
But the main point of the Doppler effect has nothing to do with velocity, but frequency instead. When you move away from the source, you will hear the sound at a lower pitch or see the light at a lower frequency.
Light sometimes behaves as a particle and sometimes as a wave, does that mean that it sometimes has mass?
Light always behaves partially like a particle, and partially like a wave. A photon is a particle of light. All particles, including electrons and protons, behave as waves (although I'm not sure if the proton has to be free of the nucleus or not). But a photon is a type of particle which is always massless. But a photon does have momentum.
Some solar-powered probes are powered by light because the photons hit the probe, get reflected off and because of conservatoin of momentum, the probe gets moved by the photon. But that would mean that the photon has mass, so how is it moving at the speed of light?
Yes and no. The equation is E² = m²c^4 + p²c². If m=0 (0 mass), E² = p²c², where p is momentum. So even particles with no mass can have momentum. Weird, huh?
But this is still up to much debate and is still being explored.
Sound's speed varies depending on who is observing it, and the Doppler effect still works with that.
The speed of sound is a constant in a constant medium. It does not depend on the movement of the one who produces it, unlike, say, throwing a ball.
In fact, I'd have thought that the Doppler effect was dependent on the speed being variable.
Yes, speed is the variable in the Doppler effect. But the Doppler effect does not have to do with a change in the velocity of a sound. Instead, it is a change in pitch (frequency).
Obviously that's not true, because we can see the red-shift of all the stars that are moving away from us, but it's counter-intuitive.
You lost me here.
According to the laws of physics, nothing can reach the speed of light, so light's broken that one already!
Nothing with mass can reach the speed of light.
We can never be absolutely certain what is right, but at the moment, scientists are saying that the speed of light is constant relative to the observer.
That is a fairly well held fact in physics today. It has been tested many times. For example, we wouldn't get the Doppler effect with light if that property wasn't true.
I, for one, would think that this would be as good an investment as some of the other programs that we are currently funding.
Agreed, if not far better. The International Space Station was not a scientific project, it was a political one. And the shuttle is currently only being used to supply the international space station.
Meanwhile, Hubble telescope is losing funding.
There are so many great projects that NASA could be funding, but they are choosing all the wrong ones.
Yea... I was hoping you wouldn't catch that.
Do you know the solution?
Take 30, divide it by a half, and add 5. What's the answer?
I would imagine that processor is highly optimized for handling images and nothing else. But don't worry, processors will be getting faster very soon. Right now, manufactures are decreasing the size, power input, and heat release, while maintaining the performance, so the next step is to increase performance by increasing the size.
Now let a + b = y^3 and k = x. Then:
Plugging this back in...:
So....
Which was to be shown.
I'm going to change your scalars to k and l, since n is normally used to signify the length of a vector.
Since you don't know the dimension the vector is in, you have to use infinite sequence notation:
In R^n:
a = <a0, a1, .... an>
Then:
k(la) = k(<la0, la1, .... lan>) = <kla0, kla1, ... klan>
But
l(ka) = l(<ka0, ka1, ... kan>) = <kla0, kla1, ... klan>
And are thus, equal.
Number of keys on a phone keypad: 12
Clocks use base 10...
It's not as hard as you think it is. Just list the terms:
p=1, 10-2-1=7
p=2, 40-4-1=35
p=3, 90-6-1=83
etc
At least that's how I read it.
If you can use a graphing calculator, you can spot non-differentiable parts at a point if:
It isn't continuous (you have to lift up your pencil when drawing it)
It has a corner point
Oscillates infinitely (you only have to worry about this with cos(1/x) at 0 and the like)
You can't do this with the defintion of differentiable because the function goes from R⇒R², which means the graph of it is in R³. But you're only used to dealing with functions in R². So partial derivatives don't quite make sense yet.
f(t) = ( 4 cos(t) - 4 cos(4t) , 4 sin (t) - 4 sin(4t) )
So f : R ⇒ R²
That function is differentiable at x0 if:
where Df(x0) is the matrix of partial derivatives. In this case:
Df = ( 16sin(4t) - 4sin(t) , 4cos(t) - 16cos(4t) )
Since there is only one variable in this function, there are no partials.
Try using that definition to see if it works.
If a function is differentiable, then it is continuous.
That statement is true.
If a function is continuious, then it is differentiable.
That statement is not true. Remember that the definition of continuous at x0 means:
But consider the function f(x) = |x|. It is continuous at 0, but not differentiable.
You want differentiability, not continuity. I'm still working on this problem though.
See if what you want is on this page:
http://www.zweigmedia.com/ThirdEdSite/tccalcp.html
Something here smells a bit fishy...
You can't imagine that everything in our universe was once contained within an atom of a much larger scale?
Imagination has nothing to do with it. And besides, I don't have to imagine anything. Technically speaking, a neutron star is a huge atom about the size of chicago.
(Whoever thought up binary and applied it to computers was a genius...)
It came naturally because transistors only have two states.
But by far, the coolest base is -2:
0110 0110: 34 or 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6
My "This is the winner" theory above does just as well as the big bang theory, and I didn't even have to invent fictional forces to support it.
As for the falsificationists, they can use my third theory above, I won't charge them a dime.
I took that theory how I thought you intended, as a complete joke. But the quotes above, joke or not, are flat out wrong. Not observable, not testable, not falsifiable, and doesn't explain a single thing that the Big Bang does, come to mind.
Like I said earlier, a theory should only be used to guide future experiment, not as scientific knowledge.
What about theories like Relativity? Or the Theory of Evolution? These are treated almost universally like facts in the scientific community. Which is the same way the Big Bang is treated.