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 =)
Assumptions in (calculus) word problems.
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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.
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 =)
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.
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.
HallsofIvy
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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.
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 =)
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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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? :shock:
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
No, didn't you read the last two paragraphs and especially the last paragraph.
One other thing, having to do with your answering HallsofIvy's last comment, in what context are you asking these questions? Are you assuming a formal test environment (which your initial question seemed to imply) or are you assuming an environment in which word problems may not be answerable or some other environment. As indicated above, the answers given have assumed a formal test environment where one part of the definition of word problems is that they are solvable.
Maybe we have 'failed the test' by not making the same assumptions you have made. If you are going to make non-standard assumptions, then those have to be pointed out if the question (problem) is to have an answer. With the question above, it appears that you have made at least one non-standard assumption (word problems may not be solvable). What other non-standard assumptions have you made? Hopefully, one of them isn't 'my question can't be answered'
Is that a quote of all of the relevant information? In other words, there is no mention of this being a poorly worded problem or anything indicating that? If so, I would not be quoting Eugene Don as an authority on word problems in this situation, but that may be just me.
However, notice the difference between what you are asking and the example you gave. In the one case, without adding other assumptions there is not enough information given to answer the question. The case you presented was asking, in a sense, why isn't adding other assumptions ok for word problems.
No, didn't you read the last two paragraphs and especially the last paragraph.
One other thing, having to do with your answering HallsofIvy's last comment, in what context are you asking these questions? Are you assuming a formal test environment (which your initial question seemed to imply) or are you assuming an environment in which word problems may not be answerable or some other environment. As indicated above, the answers given have assumed a formal test environment where one part of the definition of word problems is that they are solvable.
Maybe we have 'failed the test' by not making the same assumptions you have made. If you are going to make non-standard assumptions, then those have to be pointed out if the question (problem) is to have an answer. With the question above, it appears that you have made at least one non-standard assumption (word problems may not be solvable). What other non-standard assumptions have you made? Hopefully, one of them isn't 'my question can't be answered'
Hi Ishuda, thanks a lot, you are awesome. Just a thing here,
From what you and HallsOfIvy stated earlier, he said and I quote,
"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."
What would you say about this statement?
So basically, the Eugene Don question was a Bad Question?
And what you said,
"However, notice the difference between what you are asking and the example you gave. In the one case, without adding other assumptions there is not enough information given to answer the question. The case you presented was asking, in a sense, why isn'tadding other assumptions ok for word problems."
My whole point here was tha IF YOU ASSUMED THE EUGENE DON problem WAS Solvable then you may be ALLOWED to add facts.
SO was that a bad question (the eugene don text)?
LASTLY
I've been asking this for a while, can you please answer it? So is it an accepted fact or convention of a word problem that you are given all the information?
Can you please answer this question?
Thanks
As I mentioned previously, under what assumptions? Tell us the assumptions you are making when asking the question.
Oh, and would you answer the question "Is that a quote of all of the relevant information?"
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Hi Ishuda, thanks =)
LEts consider two cases
(C1) Assumption that it is a test/homework/exam problem
(C2) Textbook problem Or Random Problem for example on Yahoo!Answers
Thank you so much =) I really appreciate it Ishuda.
Are you assuming that there is enough information in your assumptions to answer the question? How about, are you also assuming the question is well posed?
Oh, and how about the answer to the other question?
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Are you also assuming the problem set you want the answers for are all well posed problems? If not, there is no answer to your question.
To refresh your memory a bit, a post above said "Is that a quote of all of the relevant information? In other words, there is no mention of this being a poorly worded problem or anything indicating that? If so, I would not be quoting Eugene Don as an authority on word problems in this situation, but that may be just me." The question was in response to a quote by you from a book by Eugene Don (according to you). I've been asking this for a while, can you please answer it?
Thanks @Ishuda. The question you asked, I can answer. What I quoted was ALL the problem was. So that IS ALL THE RELEVANT Information. That is really ALL the Information in the problem.
SECOND PART - Where you asked if the question is well posed.
On the basis of the author having a P.h.D from a respectable university, yes I do think the question is well posed. But how does this relate to the issue at all?
THIRD PART - The basic assumption that all relevant data is given
@Ishuda, I want your opinion/ideas here.
One other person (not on this forum) said that you must assume all relevant data is given or else, IT IS IMPOSSIBLE TO COMMUNICATE.
So I suppose it is okay to accept the fact all relevant information is given because the author is trying to communicate. Otherwise take the other latter.
Thanks
No
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