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Let's see if you guys can solve a math problem... :D
    #8631834 -

Alright, so I'm stumped, maybe one of you might find a different solution than I have, or you might agree. Anyways, I got this math question with four possible answers. Supposedly, one is correct, but I have my doubts. Here it is worded exactly:

Solve the problem

Find the average height of the paraboloid z=x^2+y^2 above the disk x^2+y^2 < or = 49 in the xy-plane
Which one is correct?
You may choose only one


Votes accepted from 07/13/08 11:19 PM until the end of time
You must vote before you can view the results of this poll


Edited by Cerius (07/13/08 11:24 PM)

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8631846 -

And here's my problem:

For one, it asks for average height "above" the disk. This, to me is infinite, seing how parabolas and paraboloids go on for infinity. Based on the definition of height, it usually corresponds to "z". Irregardless, this is only exemplified by the problem that it seemingly asks for the average height in the xy-plane, meaning height "above" the disk...which is still infinity. To make matters worse, if the question is indeed flawed, the flaw would be "below" instead of above, and the closest I can come up with is 7/2....ignoring "z" all together.

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8631855 -

Aww, need help on your elementary school homework?

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Re: Let's see if you guys can solve a math problem... :D [Re: Brugman]
    #8631864 -

invalid poll no '42'


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check out my music!
drowse in prison and your waking will be but loss

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Re: Let's see if you guys can solve a math problem... :D [Re: g00ru]
    #8631868 -

wha

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Re: Let's see if you guys can solve a math problem... :D [Re: g00ru]
    #8631876 -

guruu said:
invalid poll no '42'


:ilold:

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8631980 -

I could just be too damned tired, but the disk has a finite domain, doesn't it? The question only wants a solution for /that/ domain. No infinity about it.

(Granted my calc is rusty as all hell but I'm reasonably sure there's a simple theorem for this.)


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Wildflower seed on the sand and stone, may the four winds blow you safely home
Curriculum vapidum (dry herb vapes)

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Re: Let's see if you guys can solve a math problem... :D [Re: NizzyJones]
    #8632003 -

Well, this is what I was getting at, but the problem clearly states "above" the disk x^2+y^2 < or = 49.
So you basically have a parabola shape that's spun around the origin 360 with a disk that has a radius of 7 at (0,0) on the xy-plane and then another of the same size at z=49 on the xyz-plane, one smaller at z=48, z=47, etc., etc.

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8632008 -

The average height between the two disks is 49/2...but it isn't what the question asks for.

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8632011 -

The answer is......


















Blue! :laugh:

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Re: Let's see if you guys can solve a math problem... :D [Re: NizzyJones]
    #8632013 -

This is so easy. It's elementary really. The simple answer is...





                                                                                                            ...blue. :smirk:


--------------------
Question: Why do women wear make-up and perfume? 
Answer: Because they're ugly and they stink.

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Re: Let's see if you guys can solve a math problem... :D [Re: Le_Canard]
    #8632021 -

ToiletDuk said:
The answer is.....

Blue! :laugh:



HOW IN THE HELL DID YOU DO THAT!? Well there you have it, it must be true.


--------------------
Question: Why do women wear make-up and perfume? 
Answer: Because they're ugly and they stink.

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Re: Let's see if you guys can solve a math problem... :D [Re: BrandNewbie]
    #8632057 -

Um... maybe it's like a trick question and the answer is just 49?

have you arrived at these answers through integration or are you just guessing intuitively? Because it seems to me that some sort of integral is needed for this...

sorry, I'm a math minor, but I've been out of math classes for a few years now.. and am very tired.

I think that the phrase "average height above the disk" is too fucking ambiguous and you should just ask your professor to clarify it when you go back to class.


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"This day is a lover..."

~Rumi

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Re: Let's see if you guys can solve a math problem... :D [Re: Nunbuh_Chrubble]
    #8632078 -

It's an online class. This is from a quiz, and the answers provided are the ones given. Currently we're using double integration to find areas, but it doesn't come close to this. I mean, I could "use" these methods, but the question itself seems inherently flawed to me.


...and the average from 0 to 49 is 49/2. But this has nothing to do with anything on the xy-plane. :smile: I gots 'till eight am..and I'm not givin' up. :laugh:

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8632158 -

The equation in the xy plane defines a disc with radius 7.
The paraboloid truncated to the part above the disc is  a bowl with radius 7, it's value at the edge being 72 =49 and 0 at the center.

So now the question is how advanced is this course. The simplest answer would be (49+0)/2 = 49/2.

A more advanced course would ask for a answer weighted for the fact that there's more paraboloid near the edge than near the center, but that's not the case here since 49/3 is smaller than 49/2 and a weighted answer would be larger, and the other two options are both larger than 49 which means larger than the greatest height of the paraboloid so there is nothing average about those.

49/2 it is.

Edit (Or is it 49/3? I'm starting to doubt some of what I said above. The other two are still definitely wrong)

Edited by koppie (07/14/08 04:56 AM)

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Re: Let's see if you guys can solve a math problem... :D [Re: koppie]
    #8632440 -

my brain just imploded spontaneously after reading that

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8632519 -

Aw man, you should asked with a) more time to answer and b) in the science and technology forum... there's a lot of physics people there. I just get this feeling they might know math pretty well.

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Re: Let's see if you guys can solve a math problem... :D [Re: Gumby]
    #8632709 -

I get 49/2 as well.

This is how I set it up....

Formula: 0

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Re: Let's see if you guys can solve a math problem... :D [Re: Cerius]
    #8632713 -

attn: coaster

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Re: Let's see if you guys can solve a math problem... :D [Re: koppie]
    #8633209 -

This is what I've come up with, but the question seemingly asks for a parabola that goes on to infinity, not capped by a radius of 7. My problem is with the question itself, I suppose.

DieCommie, great solution, but could you please supply information on how you came up with upper+lower boundries, the f(r,thetha)=r^2 as well as the constant part 1/49pi?

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