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Thread: Assumptions in (calculus) word problems.

  1. #31
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    Quote Originally Posted by Subhotosh Khan View Post
    Another unstated assumption is that the ballo0n (that started as a sphere) remains a sphere - as air is being pumped in.

    For a Ph.D. thesis, I'll be explicit and state my assumption and do the problem. Then I'll do the problem as a perturbation to the spherical shape.

    Also air in this problem is "assumed" to be incompressible - since we do not have pressure mentioned.

    For a problem in first calculus class - all these assumptions are unstated.

    Problems require different level of assumptions as the degree of "importance" changes....
    Hi Subhotosh, can I ask you something.

    There are two solutions to the problem,

    (1) You assume nothing else exists (eg. the balloon remain Spherical) From this you can work out solutions.
    (2) You can assume there is a hole and other possibilities, so this "solution" is that there are no "answers"


    They are both 100% correct. Then why is the second solution always ignored?

    Thanks

  2. #32
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    Quote Originally Posted by Ishuda View Post
    Really? The volume V of the spherical balloon is given by
    V = [tex]\frac{4 \pi}{3}[/tex] r3
    where r is the radius. We are also given that that volume is changing at the rate of 4.5 ft3/min or
    V = 4.5 t
    where t is in minutes. Thus
    t = [tex]\frac{4 \pi}{13.5}[/tex] r3
    or
    r = {[tex]\frac{27 t}{8 \pi}[/tex]}1/3
    Take the derivative of r, compute t when r is two, compute the derivative of r at that time to find your answer.
    r = (27t/8pi)^(1/3) = 3t^(1/3)/[8pi]^(1/3)

    dr/dt = (3/2pi^(1/3)) * (1/3)(t)^(-2/3)

    dr/dt (t = 2) = 3/[2pi^(1/3)] * 1/[4^(1/3)]

    What was the point of this?

  3. #33
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    Quote Originally Posted by Amad27 View Post
    Hi Subhotosh, can I ask you something.

    There are two solutions to the problem,

    (1) You assume nothing else exists (eg. the balloon remain Spherical) From this you can work out solutions.
    (2) You can assume there is a hole and other possibilities, so this "solution" is that there are no "answers"


    They are both 100% correct. Then why is the second solution always ignored?

    Thanks
    But that answer is incorrect - that's why it is given a 0 (which you called ignored).

    The correct "answer" for the second case would be to state the extra "unstated" assumptions - and solve the problem!
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  4. #34
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    Quote Originally Posted by Subhotosh Khan View Post
    But that answer is incorrect - that's why it is given a 0 (which you called ignored).

    The correct "answer" for the second case would be to state the extra "unstated" assumptions - and solve the problem!
    That wasn't point.

    It is 100% correct to write both answers. If you write BOTH it is 100% correct, I dont see why people DONT write the second alternative on tests or homework.

  5. #35
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    It's hard to believe you are serious and not just having a joke. Given any problem you could always speculate that there is missing information and simply say the problem cannot be solved. But that is not in any sense a "solution" to the given problem. If you took your car to a mechanic because it was losing power and he, after looking over it, said that he thought he had found the problem but that "of course, there might be other symptoms that you haven't told me about" and so refused to fix what he believed was the problem. Would you pay him for such a diagnosis?

    In any case, the point of homework or test problems is to see if you can solve the problem- see what the problem is, determine what needs to be done and do it. To simply declare that there might be other things that you were told and so declare that it is impossible to solve, won't show what you can do.

    If your reaction, when faced with a problem, whether mathematics or not, is to throw up you hands and say "There might be other information that I don't know about so there is nothing I can do", you are not going to get far in life!
    Last edited by HallsofIvy; 08-07-2014 at 11:26 AM.

  6. #36
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    Quote Originally Posted by Amad27 View Post
    ...What was the point of this?
    Maybe you made a typo [see part in red], but your original post in relationship to my answer was
    Quote Originally Posted by Amad27 View Post
    Hi,

    This was a textbook problem. I came to a final conclusion.

    Both answers are correct.

    1)If you assume there is no hole, no elephant, no air leaving etc.. then there is no answer.
    2) dont assume anything else exists.

    Both are 100% correct, it just depends on context. In this case it was the textbook where you are taught to use ONLY the information given.
    As far as your 'reworded' statements
    ...There are two solutions to the problem,

    (1) You assume nothing else exists (eg. the balloon remain Spherical) From this you can work out solutions.
    (2) You can assume there is a hole and other possibilities, so this "solution" is that there are no "answers"


    They are both 100% correct. Then why is the second solution always ignored?...
    you have been told the answer to that several times in several different ways.

    Possibly you will understand the following which is a rewording of what you have already been told:

    There are (at least) two answers to your question (as reworded in your post referenced above).

    (1) In the formal world of students taking a test/being asked to solve a problem/... the second solution is not always ignored. It is understood by those answering the questions that, at the general level of those asking questions in this forum, it is a (partial) answer to every question and thus it is unnecessary to state it. This is the world in which you were initially given answers because the forums here are generally for that kind of world (those kinds of assumptions are made for the conditions under which questions are generally asked in this forum).

    (2) In the informal (real) world and sometimes at a higher level than that assumed for questions in this particular forum (for example the answer containing a reference to a Ph.D. thesis),the answer to your question depends on what assumptions you make but, as a general answer, part of the answer is 'Do pay attention to the unstated assumptions'. What this means is that there may be one answer, many answers, or no answer depending on what additional assumptions you make. Thus, again, your second solution is not ignored. However it is incomplete (and both statements are not 100% correct).
    Last edited by Ishuda; 08-07-2014 at 12:46 PM.

  7. #37
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    Quote Originally Posted by Ishuda View Post
    Maybe you made a typo [see part in red], but your original post in relationship to my answer was


    As far as your 'reworded' statements
    you have been told the answer to that several times in several different ways.

    Possibly you will understand the following which is a rewording of what you have already been told:

    There are (at least) two answers to your question (as reworded in your post referenced above).

    (1) In the formal world of students taking a test/being asked to solve a problem/... the second solution is not always ignored. It is understood by those answering the questions that, at the general level of those asking questions in this forum, it is a (partial) answer to every question and thus it is unnecessary to state it. This is the world in which you were initially given answers because the forums here are generally for that kind of world (those kinds of assumptions are made for the conditions under which questions are generally asked in this forum).

    (2) In the informal (real) world and sometimes at a higher level than that assumed for questions in this particular forum (for example the answer containing a reference to a Ph.D. thesis),the answer to your question depends on what assumptions you make but, as a general answer, part of the answer is 'Do pay attention to the unstated assumptions'. What this means is that there may be one answer, many answers, or no answer depending on what additional assumptions you make. Thus, again, your second solution is not ignored. However it is incomplete (and both statements are not 100% correct).
    That is an excellent explanation, I must say. When you said,

    Quote Originally Posted by Ishuda View Post
    (2) In the informal (real) world and sometimes at a higher level than that assumed for questions in this particular forum (for example the answer containing a reference to a Ph.D. thesis),the answer to your question depends on what assumptions you make but, as a general answer, part of the answer is 'Do pay attention to the unstated assumptions'. What this means is that there may be one answer, many answers, or no answer depending on what additional assumptions you make. Thus, again, your second solution is not ignored. However it is incomplete (and both statements are not 100% correct).
    I am talking about GENERAL Level math, no where NEAR a P.h.D.

    When I said they are ignored I meant when you look at AP Calculus problems for example, when you look online at the scoring guidelines, The second solution is always ignored.

    My point is look at SAT Math questions, with the multiple choice, those questions have answers, which are based upon the assumption that unstated items DONT exist. This ALWAYS happens.

    Everyone is disagreeing when I say there are TWO ways to interpret this. BOTH interpretations are 100% correct IF PUT TOGETHER. If you write BOTH these down when answering a question, it SHOULD be given full marks.

    The problem is, in SAT questions for example it is always based upon the assumption that nothing else exists (Besides the stated)

  8. #38
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    Quote Originally Posted by Amad27 View Post
    ...If you write BOTH these down when answering a question, it SHOULD be given full marks. ...
    What is it about NO you don't understand?

  9. #39
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    Quote Originally Posted by Ishuda View Post
    What is it about NO you don't understand?
    Thanks.

    One thing I've asked but seem to have no reply.

    From before when you said you can expect all relevant information has been given.


    On what basis can you accept this?

    ALSO
    ------
    Before this confusion,
    I used to solve word problems when I assumed all information is given WITHOUT a reason.

    So
    Is there really no reason for assuming the "expect all relevant..... given"?

    Thanks

  10. #40
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    This is getting battle with semantics .... I am locking the thread. If you have irrepressible desire to continue this futile battle - PM me and I'll unlock the thread.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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