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Thread: Assumptions in (calculus) word problems.

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    Assumptions in (calculus) word problems.

    HI there, Take a question like, (Q#) Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the radius is 2 feet.My question is, WHY do you assume a hole doesnt exist from which air leaves the balloon? Also think about this, when you do word problems yourself what is the reason you ASSUME that a hole doesn't exist in the balloon? My thoughts------------(1) Could it be that "the general method of word-problems" is that you assume the unstated things dont exist. Thanks a bunch guys =)

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    Quote Originally Posted by Amad27 View Post
    HI there, Take a question like, (Q#) Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the radius is 2 feet.My question is, WHY do you assume a hole doesnt exist from which air leaves the balloon? Also think about this, when you do word problems yourself what is the reason you ASSUME that a hole doesn't exist in the balloon? My thoughts------------(1) Could it be that "the general method of word-problems" is that you assume the unstated things dont exist. Thanks a bunch guys =)
    If there's a hole where the air is leaving, then the exercise becomes quite different. It's like the difference between a problem where you're filling a tub, and one where you're filling while a drain is emptying. In other words, it's not an "unstated assumption"; it's a fundamental property of the exercise.

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    stapel is quite correct, the problem would become much different. stapel's example points to the answer to your question as does your statement, "the general method of word-problems". That is, a word problem is supposed to provide all of the information necessary to solve it (except possibly some very basic assumptions). So, if there were a hole which was letting out air, the problem would need to give how much air was going out of the balloon also, otherwise there could be no answer to the question.

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    Quote Originally Posted by Ishuda View Post
    stapel is quite correct, the problem would become much different. stapel's example points to the answer to your question as does your statement, "the general method of word-problems". That is, a word problem is supposed to provide all of the information necessary to solve it (except possibly some very basic assumptions). So, if there were a hole which was letting out air, the problem would need to give how much air was going out of the balloon also, otherwise there could be no answer to the question.
    Hi, thanks to stapel and you. My question is,

    Is it like a "World-wide Accepted fact" that YOU ALL ASSUME that all information is given?

    But they also dont say that "there is no hole present"

    So, is it "a world-wide accepted fact" that you assume ALL EXISTING ITEMS (and information about them) is given?

    Thanks =)

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    In the formal sense, rather than say assume all the information is given to solve the problem, I would say it is defined that way.

    However there are some assumptions made. For example consider the rate initially mentioned, 4.5 feet3/minute. Everyone (well almost everyone) would assume that the 4.5 was base 10 rather than some other base like say, base 7. The difference being that, even if the numbers were base 7, the problem is still solvable whereas if there were a hole in the balloon the problem is not solvable without more information.

    On tests there is a strong assumption (one might almost call it a definition) that the students taking the test will make the same assumptions as the one making up the test. In fact, that assumption is so strong that it becomes part of the test itself in most cases.

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    It is a "world wide accepted fact" that if you are given a problem to solve, then you must be given sufficient information to be able to solve that problem.

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    Quote Originally Posted by HallsofIvy View Post
    It is a "world wide accepted fact" that if you are given a problem to solve, then you must be given sufficient information to be able to solve that problem.
    Hi, Thanks for this.

    But just a question here. When you are just given a word problem (dont automatically assume there MUST be an answer). But when you are given a word problem, is it a "world-wide accepted fact" that the problem you are given has ALL THE RELEVANT INFORMATION?

    Thanks =)

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    Quote Originally Posted by Ishuda View Post
    In the formal sense, rather than say assume all the information is given to solve the problem, I would say it is defined that way.

    However there are some assumptions made. For example consider the rate initially mentioned, 4.5 feet3/minute. Everyone (well almost everyone) would assume that the 4.5 was base 10 rather than some other base like say, base 7. The difference being that, even if the numbers were base 7, the problem is still solvable whereas if there were a hole in the balloon the problem is not solvable without more information.

    On tests there is a strong assumption (one might almost call it a definition) that the students taking the test will make the same assumptions as the one making up the test. In fact, that assumption is so strong that it becomes part of the test itself in most cases.
    Wait, so what you are saying is that the definition of a word problem is that you are given all the information about THE THINGS THAT EXIST?

    Thanks

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    Quote Originally Posted by Amad27 View Post
    When you are just given a word problem (dont automatically assume there MUST be an answer).
    On what basis then could the student be graded, if he's being told to find answers to questions that don't actually have answers?

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    Quote Originally Posted by stapel View Post
    On what basis then could the student be graded, if he's being told to find answers to questions that don't actually have answers?
    Hi, I'll give you an example from the textbook How To Solve Word Problems in Calculus by Eugene Don.

    Q: "A bicycle travels along a straight road. At 1:00 it is 1 mile fromthe end of the road and at 4:00 it is 16 miles from the end ofthe road. Compute (a) its average velocity from 1:00 to 4:00and (b) its instantaneous velocity at 3:00. "
    A: "
    We cannot solve this part of the problem since we do notknow the bicycle’s location at every point in time. Thereis not enough information given to compute its instanta-neous velocity. "

    Both Q & A have been QUOTED from the text.

    Therefore, this is an example of how some word-problems dont have answers.

    Can someone please answer the following question here,

    Is it an accepted fact (in the world of math) that you are always given ALL THE RELEVANT INFORMATION about the EXISTENCE of items in a word problem?


    ​Thanks

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