Posting Worked Solutions - Comments Please

Steven G

Steven G

Elite Member
Joined
Dec 30, 2014
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Heretohelpyou said:
Hi,

So they are asking to us optimize cost in terms of the surface area of the tank.

The equation for the surface of the tank is the surface of a sphere (2 hemispheres put together) and the surface area of the cylinder (ignoring the circle top and bottom);

SA=4Pir^2+2Pirh

Now to make the cost equation we just have to multiply the surface ara of the sphere by two, indicating the cost:

C = 8Pir^2+2Pirh

We can see we have 2 variables so we need to make a second equation. We are given the volume, 200m^3, so we can create the equation for the volume of the tank by adding the volume of the cylinder plus the volume of a sphere to give:

200 = 4/3Pir^3 + Pir^2h

Solve for h so we can input it in the cost equation, giving us only one variable;

h = (600 - 4Pir^3)/3Pir^2

Input this equal into the h in the cost equation, giving us;

C = 8Pir^2+2Pir((600 - 4Pir^3)/3Pir^2)

find the derivative of it and set it equal to zero. Your final derivative should be;

C' = 93Pir^3 - 3600

r should be 2.3 m, so 230 cm. Put 2.3 into the h equation to find h to be 8.96 m or 896 cm, which can be rounded to 900 cm.

The 16 m length of the tank is for the maximum and minimum, which we can ignore.

I hope this helps
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Hi,
This being a math help forum, I do not understand why you would post the solution to a problem.
 
Are we no longer allowed to post worked solutions, after giving OPs a reasonable opportunity?

[imath]\;[/imath]
 
mmm4444bot said:
Are we no longer allowed to post worked solutions, after giving OPs a reasonable opportunity?

[imath]\;[/imath]
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I believe ~1 month after OP, posting complete solution is pedagogically correct. Cheaters will find a way to cheat!! We should not stop teaching in open forum, due to this "imaginary" yet well-founded concern.

I have not seen any official dictum about this problem. Any other opinion ?
 
I would say the primary purpose here is to teach. Anyone trying to cheat who is reasonably skilled will be able to get an answer from someone in a month or so. So I'd say it's fine to post a full solution later on to help out anyone else who might come across the problem.

-Dan
 
Good to know. The unwritten dictum used to be a week, then it changed to four days, then it changed to 10 days. (I can't seem to keep up.)

Anyhoo, I'd been telling members one week for some time, but one month it is then!

(It ought to be in the forum guidelines -- which may get updated this year, heh.)

?

[imath]\;[/imath]
 
I loathe blanket rules. Circumstances alter cases. The helpers here are sensible people interested in educating people. Few are going to blurt out full answers without what seems to be a good reason. Let’s trust each other.
 
JeffM said:
The helpers here are sensible people … Let’s trust each other.
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For the regular helpers, yes. When a new helper posts a worked solution where the OP hasn't responded (within a week), I delete the post and bounce their text back by PM. I need to provide new helpers some sort of time frame, for reposting. I've been telling people to wait at least a week; I'm going to start telling them to wait a month, if the OP hasn't responded to initial replies.

?
 
topsquark said:
I would say the primary purpose here is to teach.

-Dan
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No, I disagree. People should not be coming here expecting to be taught, nor should we be expecting to teach people.
That is the role for the educators that the students who are sitting in the classrooms and/or who are learning remotely.
We are here to reinforce concepts that they should already have been exposed to in their classrooms, and help guide
them to the solutions.
 
lookagain said:
We are here to reinforce concepts that they should already have been exposed to in their classrooms, and help guide
them to the solutions.
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It's a good comment, and I'm not against it, but to me that's merely semantics. I consider this to be "teaching" as well. Perhaps "tutoring" would be a more agreeable word for me to have used here? Either way you want to call it I still would prefer to be able to post a full solution after a given time period so that others that have questions may benefit from them. Otherwise we are going to have to lock all the threads after some "resolution time" in order to make sure other members post new threads to ask questions about them and I don't agree with that policy. That's my take on it, anyway.

-Dan
 
topsquark said:
Either way you want to call it I still would prefer to be able to post a full solution after a given time period so that others that have questions may benefit from them.
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Don't you think posting a full solution will give others too much benefit? They wouldn't have to go through the trouble of doing the problem but simply copying the solution.
 
BigBeachBanana said:
Don't you think posting a full solution will give others too much benefit? They wouldn't have to go through the trouble of doing the problem but simply copying the solution.
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I believe that a full solution should be able to be posted. Note, though, that I have almost never actually done it. I don't view the Fora I work on to be problem banks. But if someone feels the thread deserves one I have no problem with it.

-Dan
 
Has the membership decided on a shorter waiting period for posting answers, or is it still 30 days after an OP's most-recent post?

:)

[imath]\;[/imath]
 
Otis said:
Has the membership decided on a shorter waiting period for posting answers, or is it still 30 days after an OP's most-recent post?
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This whole controversy depends upon what is a compete solution?
Does any one else remember SOROBAN ? He once told us to ?-off. That he was always going to give the fullest-complete solution possible.
His rational was that as a community college instructor he knew best how students learned mathematics.
For me as a product of three of R.L.Moor's students I too think that I understand the discovery method of question/answer learning.
But guess not in the eye of some site moderators here. I have to learn that complete solutions are in the eye of the beholder.
 
Otis said:
Has the membership decided on a shorter waiting period for posting answers, or is it still 30 days after an OP's most-recent post?

:)

[imath]\;[/imath]
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I personally think we should wait at least a week - unless it's obviously not a student/ homework question.

--

A problem with waiting a month before providing a worked solution is that you can't easily view messages from that long ago.

If you view "new posts" and then skip to the last page - the posts there aren't over a month old (on the occasions that I've tried)
In "search" -> "advanced search" there's an option for specifying a date but you also have to provide a keyword or username

Perhaps a facility to browse older posts would be nice (if this facility exists then please let me know :) - entering SK for the user in the "advanced search" is a workaround because he frequently responds - but obviously this isn't guaranteed to catch all the interesting old posts)
 
Cubist said:
I personally think we should wait at least a week - unless it's obviously not a student/ homework question.
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This strikes me as a reasonable solution in two ways.

If it is not a homework problem but a problem from someone in a jam or frustrated at a practical problem, it is simple courtesy to provide an answer with or without an explanation. If someone asks me where the nearest gas station is, I would not start by asking what he knows about location economics and the local road network.

If it is a homework problem, no student I ever knew did homework a week in advance. If such a creature exists, it will almost certainly have found the solution on its own within a week.

How far to go in leading the way for students seems impossible to define in the abstract. We should exercise reasonable charity in assessing each others’ judgments in specific cases, and moderators should be the ones to express privately the judgment that a specific helper went too far too fast in a specific case.
 
JeffM said:
If it is a homework problem, no student I ever knew did homework a week in advance. If such a creature exists, it will almost certainly have found the solution on its own within a week.
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I once had a student do the whole semester's homework problems in the 1st two weeks of the semester. I was a bit concerned about that thinking that she would not redo her homework in preparation of her upcoming exams. I guess that she did because she aced all her exams. After getting A's on her first two exams she wanted to do extra credit work to ensure that A. I advised her that if her grades slip, then she should ask me again. She didn't listen and kept asking me if she could do extra credit work. Finally I told her that if she kept asking me to allow her to do extra credit work I would fail her. I guess that she believed me since she never asked again.

You can write a book about students.
 
Steven G said:
I once had a student do the whole semester's homework problems in the 1st two weeks of the semester. I was a bit concerned about that thinking that she would not redo her homework in preparation of her upcoming exams. I guess that she did because she aced all her exams. After getting A's on her first two exams she wanted to do extra credit work to ensure that A. I advised her that if her grades slip, then she should ask me again. She didn't listen and kept asking me if she could do extra credit work. Finally I told her that if she kept asking me to allow her to do extra credit work I would fail her. I guess that she believed me since she never asked again.

You can write a book about students.
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I doubt that student came here often.
 
pka said:
This whole controversy depends upon what is a compete solution … complete solutions are in the eye of the beholder.
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I'd asked about the answer only, not a set of steps.

Cubist said:
we should wait at least a week
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JeffM said:
This strikes me as … reasonable
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I'm okay with a seven-day threshold for posting 'the answer', too.

Are there any objections?

⚖️

[imath]\;[/imath]
 
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