Yes]]>

The coefficient of restitution is taken to be a positive number between 0 and 1 (inclusive). For an object that bounces off a fixed surface, clearly it will change direction after the impact. For a pair of objects colliding and bouncing apart it is necessary to consider the relative velocities. The law, usually attributed to Newton, incorporates a negative sign in order to cover this point:

Note that, in the question, positivity is implied:

the coefficient of restitution for the collision is 1/k (k greater or equal to 1

I have successfully done all parts of this question. I started with initial velocities for each as two components in the direction made by the centres (x) and perpendicular (y). Similarly two components after the collision.

I constructed four equations: (1) conservation of momentum in the x direction; (2) same in the y direction; (3) restitution law in the x direction; (4) no change in relative velocity in the y direction.

I don't think you will succeed with less.

Bob

]]>Let n be a whole number,n>=2.Real numbers

with the sum s have the property that

Prove that

.

I have been trying to prove it for days but I had no luck.Please help me !

EDIT:Thanks,Bob!It was the first time I have ever tried to write sums in Latex]]>

Agreed!

Please don't misunderstand me. I found your earlier post very helpful. I couldn't see where 3/5 came from until then. The difficulty lies with the wording of the question. If it said " A class is chosen at random, and then a student within that class is chosen at random", then I would be happy with 3/5 as an answer.

But the question only says a student is chosen at random, so that makes each of the 45 students equally likely to be picked. Knowing a girl has been picked further reduces us to 22 of the students. The number of boys becomes irrelevant.

When exam questions are made in the UK, the paper is then checked by someone else independently, in order to try to avoid this sort of thing. I wonder which book this came from?

Bob

]]>I have to read this a couple of times and reading a few texts should help me .

Its so nice to finally have a grasp of all the necessary fundamentals before i can delve a bit more deep into this subject

All these information should be very helpful in the future

Thanks

]]>Welcome to the forum.

This is a long thread and there's at least one other on this question. The answer to your question is in there somewhere; you just need to go back to the early posts. I recommend you use my labelling rather than using M and N. Then you'll find the answer.

Bob

]]>OK. I need to put more detail to the story.

A catalogue is a special book; it consists of a list of books of a certain type. For example, if you are interested in Einstein's theory of relativity you might have a look at 'the catalogue of all books about Einstein's theory'. Saves time and allows you to make a good choice about which to read first.

But catalogues can be lists of any type of book. I'm not saying it's such a useful catalogue, but the one that lists all the red books can exist in my imaginary library if I say so. They are part of the library.

So when we look inside 'the catalogue of all books written in English', one of the entries is this catalogue itself. It is an example of a catalogue that contains itself.

'The catalogue of all the books in the library' is another self containing catalogue as it is a book and it is in the library.

'The catalogue of all catalogues that contain themselves' is another example. This catalogue actually lists itself, which means it qualifies as a catalogue that contains itself .............. but, that's ok because it does contain itself. No contradiction there.

The tricky one is 'the catalogue of all catalogues that don't list themselves'. Let's take a guess and say it doesn't have itself in the lists. In that case it satisfies the criterion for inclusion so it should contain itself. But if it does contain itself then it is one of the ones that don't contain itself. This is the paradox.

Here's another way of looking at it.

Fred is a barber and he shaves every man who doesn't shave themselves. So does he shave himself?

More importantly, how do you know the librarian is a female?

A good question. In the UK, it used to be the case that one would say 'he' in giving examples. But we have had an equality revolution and so I thought I should make an effort not to do this. So my librarian is a lady. Fred is a man, so there's a balance here. You might have spotted a flaw in the barber example. If so, keep it to yourself; it's only a story anyway.

Bob

]]>I have an answer:

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