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Is it possible to make t the subject of x=t^3-8t? Watch

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    (Original post by studentro)
    You mean rearrangements should be equivalent - equivalence relations refer to something else entirely.
    What I said was exactly what I meant. Taking the relation on equations in any number of variables to be equivalent if anf only if one can be rearanged into the other should be an equivalence relation.
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    (Original post by TeeEm)
    I have nothing else to say ...
    I have never seen rearangement used in a context that causes the loss of information.
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    (Original post by james22)
    I have never seen rearangement used in a context that causes the loss of information.
    I do not mean to offend but I totally disagree...

    I am no purist but I have been involved with mathematics teaching/lecturing for 27 years and this is my opinion ...

    is the function F(t) = t3 - 8t, for all real t, invertible?
    definitely not

    Is it possible to make t the subject of x=t3-8t?
    (as the poster asked)

    yes, plain and simple.

    Any computer algebra system will give you 3 rearrangements ...

    in the same way

    F(x)= x2 is not invertible over the reals.

    but it is possible to rearrange y=x2 for x as 2 separate rearrangements
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    (Original post by TeeEm)
    I do not mean to offend but I totally disagree...

    I am no purist but I have been involved with mathematics teaching/lecturing for 27 years and this is my opinion ...

    is the function F(t) = t3 - 8t, for all real t, invertible?
    definitely not

    Is it possible to make t the subject of x=t3-8t?
    (as the poster asked)

    yes, plain and simple.

    Any computer algebra system will give you 3 rearrangements ...

    in the same way

    F(x)= x2 is not invertible over the reals.

    but it is possible to rearrange y=x2 for x as 2 separate rearrangements
    Would you say that you can rearange y=sqrt(x) into y=-sqrt(x)?
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    (Original post by james22)
    I have never seen rearangement used in a context that causes the loss of information.
    You probably have. Try reading a GCSE textbook
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    (Original post by notnek)
    You probably have. Try reading a GCSE textbook
    I may well be totally wrong, but I thinks it's a bit weird if rearangements don't form an equivalence relation. If A can be rearanged to B then I would hope B can be rearanged to A, and I A can be Rearanged to B and B to C then A to C as well. Obviously A can be rearanged to A.
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    (Original post by james22)
    I may well be totally wrong, but I thinks it's a bit weird if rearangements don't form an equivalence relation. If A can be rearanged to B then I would hope B can be rearanged to A, and I A can be Rearanged to B and B to C then A to C as well. Obviously A can be rearanged to A.
    I think it's fine that you have that definition of a rearrangement. I don't think anyone can say that you are "wrong".

    But as a GCSE teacher, I cannot always use your definition since for example,



    The answer given in the mark scheme is

    \displaystyle y=\sqrt{\frac{\pi x^2 - A}{\pi}}
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    (Original post by notnek)
    I think it's fine that you have that definition of a rearrangement. I don't think anyone can say that you are "wrong".

    But as a GCSE teacher, I cannot always use your definition since for example,



    The answer given in the mark scheme is

    \displaystyle y=\sqrt{\frac{\pi x^2 - A}{\pi}}
    Would they also accept the negative of that answer?
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    (Original post by james22)
    Would they also accept the negative of that answer?
    Hopefully, although only the positive answer is shown in the mark scheme.
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    (Original post by notnek)
    I think it's fine that you have that definition of a rearrangement. I don't think anyone can say that you are "wrong".

    But as a GCSE teacher, I cannot always use your definition since for example,



    The answer given in the mark scheme is

    \displaystyle y=\sqrt{\frac{\pi x^2 - A}{\pi}}
    I'm very late to the party, but I think that's just plain wrong, for reasons we've discussed on here before about the meaning of the square root symbol.

    You can only deduce that formula for y if you're provided with additional information e.g. that y must be non-negative IMHO.
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    (Original post by davros)
    I'm very late to the party, but I think that's just plain wrong, for reasons we've discussed on here before about the meaning of the square root symbol.

    You can only deduce that formula for y if you're provided with additional information e.g. that y must be non-negative IMHO.
    How do you feel about the answer

    \displaystyle y=\pm \sqrt{\frac{\pi x^2 - A}{\pi}} ?

    Would that be a "rearrangement" of the initial equation?
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    (Original post by notnek)
    How do you feel about the answer

    \displaystyle y=\pm \sqrt{\frac{\pi x^2 - A}{\pi}} ?

    Would that be a "rearrangement" of the initial equation?
    I think that that - like the standard quadratic formula that we all know by heart - is probably better as an answer to the question "if x = blah then what are the possible values of y in terms of x?" or "Solve the following equation for y",

    I'm not trying to be ridiculously pedantic here - I haven't made a scientific study of GCSE papers but all the examples I've seen of "rearranging an equation" - rather than "solving an equation" - have been unambiguous in the sense that there is only one possible answer.

    Is the question you quoted in your earlier post from a "real" GCSE or IGCSE paper?
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    (Original post by davros)
    I think that that - like the standard quadratic formula that we all know by heart - is probably better as an answer to the question "if x = blah then what are the possible values of y in terms of x?" or "Solve the following equation for y",

    I'm not trying to be ridiculously pedantic here - I haven't made a scientific study of GCSE papers but all the examples I've seen of "rearranging an equation" - rather than "solving an equation" - have been unambiguous in the sense that there is only one possible answer.

    Is the question you quoted in your earlier post from a "real" GCSE or IGCSE paper?
    That was from a 2010 IGCSE Maths paper. I see questions like this quite often in GCSE/IGCSE papers.

    Here's another example from a 2013 AQA GCSE paper:

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    (Original post by notnek)
    That was from a 2010 IGCSE Maths paper. I see questions like this quite often in GCSE/IGCSE papers.

    Here's another example from a 2013 AQA GCSE paper:

    I really despair when I see nonsense like this in a Maths exam

    What on earth is the point of the "Julie and Phil" scenario? If you want to test students' ability to do maths, ask them to do some maths!

    (And I bet if Julie had the 'wrong' answer and Phil had the 'right' one, there would be howls of protest from equality campaigners! No wonder boys feel alienated by a lot of the current exam system.)

    Here is what I would write:

    Given that E = mv^2 and that v > 0, express v in terms of E

    Or, if you want to be a bit more challenging:

    Given that E = mv^2 and that v < 0, express v in terms of E

    I'll get off my soapbox now, because I suspect nothing is going to change for the better any time soon!
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    (Original post by Mr M)
    He's been at it all day.
    I really don't think banning members of an already extremely small community, for such minor offences, is beneficial to TSR.
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    (Original post by anonwinner)
    I really don't think banning members of an already extremely small community, for such minor offences, is beneficial to TSR.
    You may consider it minor

    Perhaps the people who's threads he was derailing with his nonsense did not
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    (Original post by anonwinner)
    I really don't think banning members of an already extremely small community, for such minor offences, is beneficial to TSR.
    Small community?! Think again my friend.
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    (Original post by Mr M)
    Small community?! Think again my friend.
    The fact that I see the same users over and over again in each thread shows that this is a relatively small community.
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    (Original post by anonwinner)
    The fact that I see the same users over and over again in each thread shows that this is a relatively small community.
    http://tsrmatters.com/facts-and-figures/
 
 
 
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