Assumptions in (calculus) word problems.

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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?

Hi,

There is no mention of the problem being a bad problem at all. So I suppose it was a bad question.
 

Hi Ishuda, I actually talked to someone else about this "fact" he said,

The basic assumption needed is that the author is providing all the relevant (existence) facts needed.

So then I asked him why you would assume this, he stated,


If this assumption isnt made then communication between people is impossible.

What do you think about this? Here's what I think

The author is trying to communicate to the student (you), so because he is trying to communicate you
can make that "basic assumption"

​What do you think?
 
Hi Ishuda, I actually talked to someone else about this "fact" he said,

The basic assumption needed is that the author is providing all the relevant (existence) facts needed.

So then I asked him why you would assume this, he stated,


If this assumption isnt made then communication between people is impossible.

What do you think about this? Here's what I think

The author is trying to communicate to the student (you), so because he is trying to communicate you
can make that "basic assumption"

​What do you think?

Paraphrasing something I said earlier, there is a strong assumption that the person listening/reading is making the same assumptions as the one talking/writing.

For example, what is 1+1? Most people would answer 2 but some, maybe suspecting a 'trick question' might answer 10. Both answers are correct under the proper assumptions. But, if that question were on a test and you answered 10, you would very likely have it marked as the wrong answer because it is generally assumed that, unless specifically otherwise stated, numbers in test problems are written in base ten.

However, in the formal sense the other person is correct because every 'well posed' word problem also carries with it the unwritten assumptions (unless stated otherwise) of numbers are in base ten, the writing is to be interpreted in a straight forward manner, the problem is solvable with the conditions given, ... If fact, when the other person gave their answer, they were in fact making some assumptions about your question.
 
Paraphrasing something I said earlier, there is a strong assumption that the person listening/reading is making the same assumptions as the one talking/writing.

For example, what is 1+1? Most people would answer 2 but some, maybe suspecting a 'trick question' might answer 10. Both answers are correct under the proper assumptions. But, if that question were on a test and you answered 10, you would very likely have it marked as the wrong answer because it is generally assumed that, unless specifically otherwise stated, numbers in test problems are written in base ten.

However, in the formal sense the other person is correct because every 'well posed' word problem also carries with it the unwritten assumptions (unless stated otherwise) of numbers are in base ten, the writing is to be interpreted in a straight forward manner, the problem is solvable with the conditions given, ... If fact, when the other person gave their answer, they were in fact making some assumptions about your question.

If people did consider the different number bases there would be way to many correct answers

But the bottomline is was the person correct about the author trying to communicate --> therefore the assumptions all relevant information is given.

I mean the person said it is impossible to communicate others. Cant you still communicate?


A question for you.Why did you assume unstated items didnt exist before me asking this question?
 
...A question for you.Why did you assume unstated items didnt exist before me asking this question?

With questions like this, you appear to read into what I have written what you thought I said or assumed. With other questions, you appear to ignore answers given so that you can ask the same questions in different ways. Discussions are nice, IMO, but statements about what I have said which are opposite to what I actually said (wrote) make for a poor discussion.

As a (possibly) final statement, I will leave you with your original question
"(1) Could it be that "the general method of word-problems" is that you assume the unstated things dont exist."
and (part of) my initial reply
"That is, a word problem is supposed to provide all of the information necessary to solve it (except possibly some very basic assumptions)"
 
"That is, a word problem is supposed to provide all of the information necessary to solve it (except possibly some very basic assumptions)"

When you said this, my question is why? Is it the definition or a rule or an accepted fact?


"...Ask the same question in different ways..."

No, I did not ask the same question. I asked for your opinion, and what you did BEFORE ALL THIS, just so I can see your thoughts.
 
So I guess we need to ask "exactly what do you mean by a 'word problem'?". I assumed that you meant a word problem that was given as an exercise, perhaps in a text book, or on a test. Certainly, if you are expected to be able to answer such a problem, you must have been given all necessary information. Of course, if you are talking about problems that occur as part of work or research or otherwise, that we NOT designed to have a specific answer, then it might well happen that you are NOT given all of the information- but if you are in a job where you have to do such research or work, you will have to learn to recognize that you need more information and learn how to find it.

Going back to your original post, if you really are trying to fill a balloon, rather than just doing a textbook problem, you certainly should check to be sure there are no holes in the balloon!
 
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So I guess we need to ask "exactly what do you mean by a 'word problem'?". I assumed that you meant a word problem that was given as an exercise, perhaps in a text book, or on a test. Certainly, if you are expected to be able to answer such a problem, you must have been given all necessary information. Of course, if you are talking about problems that occur as part of work or research or otherwise, that we NOT designed to have a specific answer, then it might well happen that you are NOT given all of the information- but if you are in a job where you have to do such research or work, you will have to learn to recognize that you need more information and learn how to find it.

Going back to your original post, if you really are trying to fill a balloon, rather than just doing a textbook problem, you certainly should check to be sure there are no holes in the balloon!

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.
 
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.

Really? The volume V of the spherical balloon is given by
V = \(\displaystyle \frac{4 \pi}{3}\) 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 = \(\displaystyle \frac{4 \pi}{13.5}\) r3
or
r = {\(\displaystyle \frac{27 t}{8 \pi}\)}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.
 
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 =)

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....
 
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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
 
Really? The volume V of the spherical balloon is given by
V = \(\displaystyle \frac{4 \pi}{3}\) 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 = \(\displaystyle \frac{4 \pi}{13.5}\) r3
or
r = {\(\displaystyle \frac{27 t}{8 \pi}\)}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?
 
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!
 
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.
 
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!
 
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...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
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).
 
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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,

(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)
 
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
 
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.
 
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