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    Hi guys ok I wonder if you can help me...Im currently revising for D1 edexcel maths....im trying to check my past paper and have got the mark scheme but it hasn't helped as I need to actually see a diagram...its Q8d in the paper I have attached...mark scheme just says see overlay.....would be great if someone could help me by drawing a diagram or something to check to see if i have it right or even tell me!!!!! Thanks any help appreciated!!
    Attached Files
  2. File Type: pdf d1_qp_jan_2004.pdf (188.1 KB, 60 views)
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    (Original post by am05317z)
    Hi guys ok I wonder if you can help me...Im currently revising for D1 edexcel maths....im trying to check my past paper and have got the mark scheme but it hasn't helped as I need to actually see a diagram...its Q8d in the paper I have attached...mark scheme just says see overlay.....would be great if someone could help me by drawing a diagram or something to check to see if i have it right or even tell me!!!!! Thanks any help appreciated!!
    you need to post this in a new thread in the main maths help section.
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    What is everybody's philosophy of maths?
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    (Original post by DeanK22)
    What is everybody's philosophy of maths?
    Provides better understanding of the environment around you, not always relating to maths......critical thinking and as a result, copious amounts of opinions in all affairs......
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    (Original post by DeanK22)
    What is everybody's philosophy of maths?
    Probably a Platonist if pushed, but the amount I care varies with how long it has been since I've read a philosophy book.
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    (Original post by DeanK22)
    What is everybody's philosophy of maths?
    i like playing games
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    (Original post by DeanK22)
    What is everybody's philosophy of maths?
    Probably some kind of Platonist. Maybe. But also relativist, so maybe not. I need to read more about the philosophy of mathematics.
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    I like to think that CH is either true or false. I suppose that makes me a Platonist.
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    (Original post by DeanK22)
    What is everybody's philosophy of maths?
    http://www.timecube.com/
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    Fun fact: Every continuous real-valued function on [a, b] \subset (0, 1) can be uniformly approximated by polynomials with integer coefficients.

    Exercise: Start by showing that the constant \frac{1}{2} function may be so approximated. Then show that every real number may be so approximated.
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    Some useful inequalities: http://www.lkozma.net/inequalities_cheat_sheet/
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    (Original post by The Muon)
    A little one which isn't massively mathematical but it quite nice.

    You travel from A to B at a speed of 30m/s and then back at a different speed. What speed should you travel back if you wish the average speed of the whole journey to be 60m/s?

    I heard it in the pub the other night and so I hope that I got the numbers right :tongue:
    Would it not depend on the distance between A and B?
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    (Original post by ZeedoZee)
    Would it not depend on the distance between A and B?
    No.
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    (Original post by Slumpy)
    No.
    Ok I'm stumped. Give me a hint, how to approach the question and I'll try from there.
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    (Original post by ZeedoZee)
    Ok I'm stumped. Give me a hint, how to approach the question and I'll try from there.
    Let the distance A to B be d. Work out the time it would take to get an average speed of the speed you want in terms of d. Then compare that to how much time you've already taken in the case given, and you'll spot something.
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    Did you lot see that the Collatz conjecture may have been proved?

    Related:
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    I hope it's that guy from the nrich forums, he used to post every day about his progress and then get taken apart by all the clever regulars. Poor guy I hope it's him.
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    (Original post by ziedj)
    I hope it's that guy from the nrich forums, he used to post every day about his progress and then get taken apart by all the clever regulars. Poor guy I hope it's him.
    But isn't that better? I mean if he did resolve the conjecture, I would think it would be better to get it right when published rather than rush publication and get it horribly wrong.
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    Here's a tricky one:
    Does:
    \displaystyle\sum_{k=1}^{\infty}  \frac{sink}{k}
    converge and, if so, to what?
    When I first attempted the question I made the mistake of thinking we were working in degrees in which case the answer to the first part of the question, at least, is trivial. We are working in radians.
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    Yes it converges, but some lemma about bounded sums and terms tending to 0.

    What does it converge to, probably some argument by Fourier methods is going to solve this.
    Consider the fourier series of \frac{\pi-x}{2} then we get

    \frac{\pi-x}{2} = \sum \frac{\sin k x}{k}

    Subbing in x = 1, we find \frac{\pi-1}{2}

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