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No problem.

The problem does look intimidating at first sight. You might have gotten stuck trying to solve the whole thing at once. Once you break it down part-by-part, however, the question becomes easier.

Hmm

I need another difference between a hydrogen-3 nucleus and a helium-3 nucleus.

I've got hydrogen 3 has more binding energy per nucleus, but what else? (me thinking mass but not sure which way to go)

It's not mass. When an element as described as [element][number], then what you are talking about is an isotope. An isotope is an atom of a particular element with a particular mass, and that mass is the sum of the number of protons and neutrons in the nucleus.

For example, Carbon-14 is an isotope of carbon that has a mass of 14: it has 6 protons (because that is carbon's atomic number) and 14-6, or 8, neutrons. The most common form of carbon, C12, has 6 protons and 6 neutrons.

H3 and He3 weigh the same - because they both have that number 3 after them. Just like C14 and N14 have the same atomic weights.

So here's the main answer to your question: What is the most fundamental difference between hydrogen and helium?

I have a problem with displacement. I often can't figure out how to get the total distance from displacement.

A particle, travelling in a straight line, passes a fixed point O on the line with a speed of 0.5 m/s. The acceleration, a m/s, of the particle, t s after passing O, is given by a = 1.4 - 0.6t.

Find the total distance travelled by the particle between t=0 and t=10

We know that acceleration is the time derivative of velocity and displacement is the time derivative of velocity. The difference between displacement and distance, is that distance is a scalar; in one-dimension displacement is the velocity * time; distance is the absolute value of velocity (speed) * time.

a(t) = 1.4 -0.6t
v(t) = ∫a(t)dt = ∫(1.4 - 0.6t)dt = 1.4t - 0.3t^2 + C

Solve for C by using your knowledge that v(0) = 0.5

v(0) = 1.4*0 - 0.3*0^2 + C
0.5 = C

Thus, v(t) = 1.4t - 0.3t^2 + 0.5

Distance, we'll call it f(t) = ∫|v(t)dt| = ∫|1.4t - 0.3t^2 + 0.5 dt|. The limits of integration here are 0 and 10 (as you are concerned about the problem from t = 0 to t = 10).

Integrating an absolute value function is probably easiest by splitting it up into multiple integrals.

∫|0.3t^2 + 1.4t + 0.5 dt| =

∫0.3t^2 + 1.4t + 0.5 dt ]t=0 to t=5 + ∫-(0.3t^2 + 1.4t + 0.5)dt ]t=5 to t=10.

If the splitting or the notation is confusing, let me know.

Anyway, now it's just a matter of integrating.

[0.1t^3 + 0.7t^2 + 0.5t] t=0 to t=5 - [0.1t^3 + 0.7t^2 + 0.5t] t=5 to t=10.

0.1*5^3 + 0.7*5^2 + 0.5*5 - (0.1*5^3 + 0.7*5^2 + 0.5*5 - (0.1*10^3 + 0.7*10^2 + 0.5*10)) = 175 m

Thanks again

I have a question though, why do you put a negative symbol at the second split?

And how do you make '∫'? Alt ???? ?

I don't know the code to make an integral sign, actually, heh. I just copy and pasted from a previous post.

∫|0.3t^2 + 1.4t + 0.5 dt|

Consider the integral: ∫|f(x)|dx.

If f(x) is positive for the given limits of integration, the absolute value signs can be totally ignored. Thus for positive f(x): ∫|f(x)|dx = ∫f(x)dx.

For negative values of f(x), taking the absolute value means multiplying by -1. Thus for negative f(x): ∫|f(x)|dx = -∫f(x)dx.

Now for our original integral: ∫|0.3t^2 + 1.4t + 0.5 dt|

0.3t^2 + 1.4t + 0.5 is positive for t < 5 and negative for t > 5. Thus, we split can split the integral into two integrals.

Because the function is positive from t = 0 to t = 5, we drop the absolute value signs and integrate from 0 to 5.

Because the function is negative from t = 5 to t = 10, we multiply by -1, drop the absolute value signs, and integrate from 5 to 10.

Add the two integrals together and you have your answer.

This question is total nightmare for me.

How do you find the shortest distance between two polygons in 3D space? This is for a 3D kind of application, but I have been puzzling over it for a little while and am not sure how to go about it or start it.

If you have 2 polygons represented in 3D space by n vertices, how do you find the shortest distance between them? Assume that each vertex is represented by the three variables x,y,z and we do not know how many vertices make up a polygon.

Thanks a lot M. Bison, I realize that it actually is much easier for me to understand by finding the area under the curves, rather than the normal addition/subtraction that my teacher taught me, though integration seems a bit messier

By the way, how do you know which one is + and which one is -? Do you have to work it out or can you see it straight from the question? Or does it actually not matter whichever is + or -?

I'm currently writing my English Coursework, on, 'How realistic is 'The Cruicble'?'. We have to include a section on how it relates to the theatrical movements Realism, Naturalism, Absurdism and Melodrama.

We have to include a small description. I know what naturalism is, but my notes have really threw me...



What my notes mean leaves me seriously confused.
Basically, what was naturalism? In the text, we were told to pick up the use of poetic devices, but that's not how the characters play...

Seems confusing, but any help is appreciated.

In theater-



In literature-



Here are some websites on naturalism that might help explain it further-

http://en.wikipedia.org/wiki/Naturalism_%28theater%29

http://encarta.msn.com/encyclopedia_761 ... literature).html (copy and paste this link- I think the url tags don't like the parenthesis)

http://www.wsu.edu/~campbelld/amlit/natural.htm

Hope that helps!

Wow! Thanks Matt! That really helped alot!
Now I can carry on with my essay.

About the play, Top Girls.

"What do the chosen guests tell us about Marlene and how are men portrayed in Act 1?"

I can do the latter part, but I'm stumped on the bit about dinner guests. Help?

Need a bit of a hand with -shudders- Calculus.

Basically, I need to work out:

lim(n -> ∞) of n+1- √(n^2 – n+1)

We actually haven't done finding limits yet, so this is actually a bit of extension... I still know what a limit is though, but if you use any special theora, you'll need to explain them...

Another question from me, this one is about algorithms. (By the way, my previous question is about higher dimensional geometry, and I can't solve it yet)

I've been trying to find answers to Pell's equation (x^2 - Dy^2 = 1) for different D's, but I'm really having a problem. I've been looking in books and I simply don't understand some things such as the sqrt(D) convergents, or continued fraction expansion. If someone could explain this in layman's terms, I'd really appreciate it.