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    Also, if I took the height of cone as the radius of the circle instead of the diameter (silly mistake IK), how many points should I expect to lose? 2-3?
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    (Original post by zemaitistrys)
    @DrSebWilkes

    Lol nice symbols.As a future physics student, you should really try to acquire intuition for what is asked of you. Only way you can integrate the function is if t isnt a function of x - then you take t^4 out of the integral. And there is no evidence why it would be expected of us to treat t as t(x). Differentiating shouldn't cause anyone any problems.
    Hmm sorry I'm not buying that. "t" here was a constant value which was used as a limit of the integration (that's what limit means, surely?)

    So you integrate, presumably on some other plane or what have you, and your left with a constant with the same value as what we are changing ... so ... erm ... that's nothing?

    Intuition is one thing; being able to do things properly is another. Either the question was poorly worded, or the expectations of the question were poorly understood.
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    (Original post by DrSebWilkes)
    Hmm sorry I'm not buying that. "t" here was a constant value which was used as a limit of the integration (that's what limit means, surely?)

    So you integrate, presumably on some other plane or what have you, and your left with a constant with the same value as what we are changing ... so ... erm ... that's nothing?

    Intuition is one thing; being able to do things properly is another. Either the question was poorly worded, or the expectations of the question were poorly understood.
    t doesnt change it just makes tx a family of functions, thus t is a parameter, integrating with a parameter is perfectly fine
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    (Original post by Quantum42)
    for the circles question, if I got one of the radii wrong but the centres of both and the other radius right and correctly drew in all four tangents but was unable to work out their lengths, how many marks do you think that would be?
    Anyone know about this?
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    (Original post by Quantum42)
    Anyone know about this?
    Depends if they value the working out of circle equations or finding the correct tangent lengths more, either way it should be at least 3/9
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    Your limits of integration can be anything - a variable, a function, a number.

    What matters is you integrate a function with respect to x and your limits of integration involve t.
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    If the average offer holder scored 71 last year, what do you guys think that figure will be this year?
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    (Original post by Tomyil12345)
    t doesnt change it just makes tx a family of functions, thus t is a parameter, integrating with a parameter is perfectly fine

    Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

    So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.

    (Original post by zemaitistrys)
    Your limits of integration can be anything - a variable, a function, a number.

    What matters is you integrate a function with respect to x and your limits of integration involve t.
    Yes but not when that "t" then must switch from a constant to a variable - that's not how it works. The only way it can work is if you move to a different plane or something but even then I can't really see how that'd work. You can integrate y=rootx ... or you could rearrange y=2at, and x=at^2 and integrate that way ... the key thing is that the x,y plane is determined by a third plane t, but integrating and differentiating t on the t plane is a different matter to that on the x-y plane.


    (Original post by Quantum42)
    Anyone know about this?
    You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?
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    (Original post by DrSebWilkes)
    Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

    So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



    You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?
    4 tangents but 2 lengths
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    (Original post by Tomyil12345)
    4 tangents but 2 lengths
    Yeah I'm not sure there would be two tangents? I asked my maths savy friend and he didn't seem to think so. Again we might have made a mistake though so I'm definitely willing to hear if someone thinks there are are indeed more than 2 tangents.
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    Name:  IMG_20171106_190411-compressed.jpg.jpeg
Views: 85
Size:  96.8 KB which of these values is wrong for how much each question was worth because this adds up to 101 not 100?
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    (Original post by DrSebWilkes)
    Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

    So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



    You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?
    Yes there's 4 tangents.

    Yes you can treat t as a constant, but when you differentiate with respect to t, t becomes a variable. The "variable'ness" of a quantity depends on the context.
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    (Original post by DrSebWilkes)
    Yeah I'm not sure there would be two tangents? I asked my maths savy friend and he didn't seem to think so. Again we might have made a mistake though so I'm definitely willing to hear if someone thinks there are are indeed more than 2 tangents.
    The circles didnt touch so one at the bottom one on top and two ‘diagonal’
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    (Original post by Quantum42)
    Name:  IMG_20171106_190411-compressed.jpg.jpeg
Views: 85
Size:  96.8 KB which of these values is wrong for how much each question was worth because this adds up to 101 not 100?
    Paramatics is 8 i think
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    (Original post by Quantum42)
    Name:  IMG_20171106_190411-compressed.jpg.jpeg
Views: 85
Size:  96.8 KB which of these values is wrong for how much each question was worth because this adds up to 101 not 100?
    Whoa!

    Also, Binomial is 4 I think!!
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    (Original post by DrSebWilkes)
    Okay so you've lost me now: why is integrating with a parameter okay? I can't integrate the "function" x=at^2? What would that get me? That only maps out the values of x in the x-t plane surely? But I can integrate x with respect to t, that's fine (but still begs the question of why?)

    So for the function (xt)^4, that to me looks like 1 variable and a constant; then, we integrate that to a constant ... okay ... and then boom it's a variable? Either this is some seriously fancy maths or my (and 2 separate maths teachers) understanding about the meaning of basic calculus is wrong.



    Yes but not when that "t" then must switch from a constant to a variable - that's not how it works. The only way it can work is if you move to a different plane or something but even then I can't really see how that'd work. You can integrate y=rootx ... or you could rearrange y=2at, and x=at^2 and integrate that way ... the key thing is that the x,y plane is determined by a third plane t, but integrating and differentiating t on the t plane is a different matter to that on the x-y plane.




    You got 4 tangents? I nearly did that but I have this horrid feeling that they don't exist. Can anyone else say that they got 4 tangents?
    Well say you want to integrate a general line from 0 to 1 , y=ax+b so integral y=a/2 x^2 +bx +c
    Integral 0 to 1 = a/2 +b
    a and b are not constants, but you did nothing illegal while integrating
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    (Original post by Tomyil12345)
    Paramatics is 8 i think
    Great thanks, if for that question I solved it except for the fact that I forgot that the 1/2 in the general solution would only be negative in one of them how many marks do you think I would lose?

    I left it as a(n(2pi) +- pi/6 -1/2)
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    (Original post by Tomyil12345)
    Well say you want to integrate a general line from 0 to 1 , y=ax+b so integral y=a/2 x^2 +bx +c
    Integral 0 to 1 = a/2 +b
    a and b are not constants, but you did nothing illegal while integrating
    Look I promise myself this is the last I wade into this ... the a and b are variables in as much that they can take values that we can assign them BUT BUT BUT when they are going through the integration they are coefficients with one value; they are just values that multiply the variable.

    After that, we can "assign" a numerical value to them but that's kinda a shortcut.

    What is different though is saying "Okay, well "t" can equal ... idk ... 3 ... and then with it that equaling 3 let's integrate x ... good now let's differentiate to t"

    As I say I really can't be arsed arguing with you guys. You don't accept the basics and you don't try to explain things either.
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    I can confirm the circle has 4 tangents - my friend made a mistake haha

    http://mathworld.wolfram.com/Circle-CircleTangents.html
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    I'm applying to oxford physics in 2020 any advice?
 
 
 
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