Good catch. Edited.

And yes. I can't think of any physical reason why this equation should be undefined at A=1. In addition, I can't figure out how to solve it for just H/C, regardless of restrictions.

## Search found 71 matches

- Wed Dec 05, 2012 9:44 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

- Wed Dec 05, 2012 7:30 pm UTC
- Forum: Site/Forum issues
- Topic: What happened to LaTeX?
- Replies:
**8** - Views:
**11474**

### Re: What happened to LaTeX?

Here's a handy site to replace the LaTeX functionality. Once you render the equation, it creates a permalink to the image (either copy and add .png, or copy link location on the image). You can even edit it later if you made a mistake.

- Wed Dec 05, 2012 6:38 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### Re: problems for fun! Volume of a cone as a function of heig

I tried changing around the variables a little to make this easier to look at: Let R 2 /R 1 = A, V/v = B, and H/h = C. Let R 1 = R. Then, http://mathurl.com/agf9w83.png However, trying to solve for H/C leads me to a dead end, and Wolfram Alpha to garbage. Thoughts? Edit: is the math not rendering fo...

- Mon Dec 03, 2012 11:39 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### Re: problems for fun! Volume of a cone as a function of heig

I've just done it both ways, by which I mean doing it as cones and similar triangles with the little cone subtracted from the others, and doing it as an exercise in integration. I got the same result both ways, though the integration exercise seemed rather less messy when it came to tidying up the ...

- Fri Nov 30, 2012 8:24 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### Re: problems for fun! Volume of a cone as a function of heig

I'm still getting major ugliness for a result. Is this what I should expect? h is the height of the "water" and has a range of (0->H), and v is the volume of the "water" and has a range of (0->V). h(v)= -\frac{-\sqrt{3 \pi} \sqrt{-H(R_1-R_2)^2(\pi H R_1^2-4v&#...

- Fri Nov 30, 2012 6:44 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### Re: problems for fun! Volume of a cone as a function of heig

Volume of a frustrum of a cone: V=\frac{\pi H}{3}(R_1+R_2)^2 Just to be a little bit helpful, the actual volume is V=\frac{\pi H}{3}\frac{R_2^3 - R_1^3}{R_2 - R_1} Not according to Wolfram Mathworld . See step 8. By the way, my original volume was off as well (I had an extra 2R 1 R 2 term).

- Thu Nov 29, 2012 9:45 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### Re: problems for fun! Volume of a cone as a function of heig

@dudiobugtron: I already know the volume of a frustrum of a cone. I want the volume as a function of height. What I've done so far: Volume of a frustrum of a cone: V=\frac{\pi H}{3}(R_1+R_2)^2 Let us imagine a second frustrum superimposed on the first, with height h, smaller radius R 1 , lar...

- Thu Nov 29, 2012 8:45 pm UTC
- Forum: Mathematics
- Topic: problems for fun! Volume of a cone as a function of height
- Replies:
**33** - Views:
**4255**

### problems for fun! Volume of a cone as a function of height

Here's an interesting problem I've been working on: there is a frustrum of a cone (a cone with the pointy bit chopped off) with height H, smaller radius R 1 , and larger radius R 2 . Hey look, it's a glass! If you fill the glass to the brim with water, at what height h (large side up) have you drunk...

- Fri Sep 21, 2012 1:58 am UTC
- Forum: Science
- Topic: Velocity dependent acceleration
- Replies:
**6** - Views:
**3609**

### Re: Velocity dependent acceleration

I guess this second question is a little tougher, huh? (I'm bumping a little because a post was made while I was editing the second question in. In retrospect, I probably should've made a new post.)

- Thu Sep 20, 2012 4:55 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1110:"Click and Drag"
- Replies:
**595** - Views:
**674610**

### Re: 1110:"Click and Drag"

I don't know if this has been posted yet, but here's a google maps-esque version with zoom buttons and all. It even loads quickly!

http://xkcd-map.rent-a-geek.de/#10

http://xkcd-map.rent-a-geek.de/#10

- Thu Sep 20, 2012 1:23 am UTC
- Forum: Science
- Topic: Velocity dependent acceleration
- Replies:
**6** - Views:
**3609**

### Re: Velocity dependent acceleration

I knew it was something like that. Thanks! EDIT: Here's another one for the fora. I've solved this equation properly as far as I can tell, but I'm having trouble figuring out where the parameter for v 0 goes. Here's what I've got: This one's similar to the previous problem, except that I've added a ...

- Wed Sep 19, 2012 10:11 pm UTC
- Forum: Science
- Topic: Velocity dependent acceleration
- Replies:
**6** - Views:
**3609**

### Velocity dependent acceleration

This should be a very simple question, but for some reason, I'm struggling with it. Rest assured, it's for my own fun, and not for homework. A certain object has a velocity-dependent acceleration, such that the acceleration at any given time is given by a=-Dv, where D is a constant. Finding an equat...

- Mon Jul 23, 2012 9:10 pm UTC
- Forum: XKCD Meetups
- Topic: [US] Cambervillains (Boston Area)
- Replies:
**3400** - Views:
**616737**

### Re: Cambervillain Indecipherable Meetup Thread (Boston Area)

I'll be there!

EDIT: I won't. My parents are in town and demand my presence.

EDIT: I won't. My parents are in town and demand my presence.

- Sat Jul 14, 2012 11:32 pm UTC
- Forum: XKCD Meetups
- Topic: [US] Cambervillains (Boston Area)
- Replies:
**3400** - Views:
**616737**

### Re: Cambervillain Indecipherable Meetup Thread (Boston Area)

Hey all! I just relocated to Boston and I'm trying to meet some geeks in the area. Anybody want to get coffee or a drink sometime soon?

- Wed Jul 11, 2012 4:30 pm UTC
- Forum: Science
- Topic: Looking for 3D modeling software recommendation
- Replies:
**6** - Views:
**3645**

### Re: Looking for 3D modeling software recommendation

Thanks for the suggestions, everyone! Sketchup addons look like a pretty attractive option, so maybe I'll give that a look. @Gorcee, I actually do need the stress analysis. One upcoming project involves either a really nasty cantilever or a vertical load hung from horizontal wire. The load could be ...

- Tue Jul 10, 2012 9:36 pm UTC
- Forum: Science
- Topic: Looking for 3D modeling software recommendation
- Replies:
**6** - Views:
**3645**

### Looking for 3D modeling software recommendation

Hi all! Long time no post. I'm in the market for 3D modeling software. I've looked at Google Sketchup and the plethora of Autodesk products, and I'm having trouble telling what will fit my needs. For the most part, I'd be using the software to plan personal projects (a spice cabinet, a bookshelf, et...

- Mon May 28, 2012 2:39 pm UTC
- Forum: Mathematics
- Topic: at what height is half the volume?
- Replies:
**10** - Views:
**4083**

### Re: at what height is half the volume?

Thanks pizzazz, that looks like it's it. That sounds much more reasonable!

EDIT: an interesting implication of this is that if you drink half the height, you've drunk 7/8 of the volume.

EDIT: an interesting implication of this is that if you drink half the height, you've drunk 7/8 of the volume.

- Mon May 28, 2012 4:55 am UTC
- Forum: Mathematics
- Topic: at what height is half the volume?
- Replies:
**10** - Views:
**4083**

### Re: at what height is half the volume?

Without actually working out any of the math, I see that you mark the radius r as a constant. Our variable of integration is h, so think about starting at the bottom (tip) of your cone and working up. The radius obviously increases with increasing height, so we can't express this as a constant in t...

- Mon May 28, 2012 3:21 am UTC
- Forum: Mathematics
- Topic: at what height is half the volume?
- Replies:
**10** - Views:
**4083**

### at what height is half the volume?

Here's a slightly odd math conundrum for you all. I amuse myself in restaurants by marveling at how poorly-equipped the human brain is for measuring volume. For example, if you eat "half a bowl of soup," or reduce the height of the liquid in the bowl to one-half, you've actually eaten a go...

- Mon Feb 06, 2012 4:10 pm UTC
- Forum: Mathematics
- Topic: A Probability Conundrum
- Replies:
**7** - Views:
**1314**

### Re: A Probability Conundrum

Thanks for the help! ConMan, is that the standard deviation for a single card, or for a 5-card hand?

- Mon Feb 06, 2012 4:55 am UTC
- Forum: Mathematics
- Topic: A Probability Conundrum
- Replies:
**7** - Views:
**1314**

### A Probability Conundrum

Here's a probability conundrum that I've stumbled across in a personal project. Suppose you have a deck of cards with numbers of cards and values as follows: value # of cards 1 12 2-6 8 each 7 4 In a hand of 5 cards, what is the mean sum of the card values? What is the standard deviation from the su...

- Tue Mar 29, 2011 11:05 pm UTC
- Forum: Science
- Topic: truss cantilever design
- Replies:
**3** - Views:
**1498**

### truss cantilever design

Yes, it's a boomilever, no, it's not for Science Olympiad. I am a physics student working on an independent research project in which I'm taking another stab at the good old boomilever. I've been working through Hibbeler's Statics and Mechanics of Materials all semester, and I figure that since I'm ...

- Wed Dec 29, 2010 4:25 pm UTC
- Forum: Science
- Topic: Walking on an escalator
- Replies:
**15** - Views:
**15563**

### Re: Walking on an escalator

By the way, at first I also thought the the escalator should provide extra energy, but I now see that this is not the case. If the upward force of the escalator to the walker were greater than his weight, there would have been acceleration. So this force is exactly equal to this person's weight as ...

- Thu Dec 16, 2010 7:04 am UTC
- Forum: Science
- Topic: Telepathy, ESP, Psychics and The Occult.
- Replies:
**50** - Views:
**7039**

### Re: Telepathy, ESP, Psychics and The Occult.

@poxic: I have had a similar experience, but only with colors, and only with my girlfriend. Early on in our relationship when we were just beginning to get really close we tried doing some mental exercises to open up more to each other (nothing particularly notable scientifically, totally placebic a...

- Wed Nov 17, 2010 7:51 pm UTC
- Forum: Science
- Topic: Chemistry Safety
- Replies:
**24** - Views:
**2423**

### Re: Chemistry Safety

I feel this is necessary in any discussion of chemistry safety:

http://www.flickr.com/photos/blacklovei ... 2556853/#/

http://www.flickr.com/photos/blacklovei ... 2556853/#/

- Tue Nov 16, 2010 9:53 pm UTC
- Forum: Science
- Topic: Mechanical Engineering, or, A Crisis in Profession
- Replies:
**8** - Views:
**1506**

### Re: Mechanical Engineering, or, A Crisis in Profession

My 101, 102 and modern physics were lab courses, as will be my dynamics and E&M classes. My school also offers two courses called Intermediate and Advanced lab which cover experimental design and data analysis through experiments in every (and I mean every) field of physics. I'm taking both. Tha...

- Tue Nov 16, 2010 6:58 am UTC
- Forum: Science
- Topic: Mechanical Engineering, or, A Crisis in Profession
- Replies:
**8** - Views:
**1506**

### Mechanical Engineering, or, A Crisis in Profession

I am a physics major who wants to become a mechanical engineer. As a junior, I'm starting to freak out about grad school and the rest of my life and all that fun stuff. Since there's no one at my school who could give me guidance as to how to best achieve this, I turn to the fora's collective experi...

- Mon Nov 15, 2010 6:36 pm UTC
- Forum: Science
- Topic: Undergraduate Statics Textbook
- Replies:
**19** - Views:
**3106**

### Re: Undergraduate Statics Textbook

So looking at the Pearsons site, Hibbeler has a completely separate book on structural analysis. What the heck is that, and how is it different from statics and mechanics of materials?

- Mon Nov 15, 2010 4:45 am UTC
- Forum: Science
- Topic: Undergraduate Statics Textbook
- Replies:
**19** - Views:
**3106**

### Re: Undergraduate Statics Textbook

My school doesn't have a class on deformable bodies either... Any suggestions on specific books? I'm currently eyeing Hibbeler's combined Statics and Mechanics of Materials. Has anyone heard anything about Morrow and Kokernak? http://www.pearsonhighered.com/educator/product/Statics-and-Strength-of-M...

- Thu Nov 11, 2010 5:48 pm UTC
- Forum: Science
- Topic: Undergraduate Statics Textbook
- Replies:
**19** - Views:
**3106**

### Re: Undergraduate Statics Textbook

I took a look at Hibbeler on Google Books and it looks like it doesn't really cover anything that my Physics 101 class didn't. I'm looking for something a little more advanced, as this is going to be a 300-level class taught alongside Dynamics (which has things like Hamilton's principle, Lagrangian ...

- Wed Nov 10, 2010 4:30 am UTC
- Forum: Science
- Topic: Undergraduate Statics Textbook
- Replies:
**19** - Views:
**3106**

### Undergraduate Statics Textbook

I am an undergraduate physics student, but I want to go into mechanical engineering in grad school. Since my school doesn't offer a course in statics, I'm doing an independent study. Anybody have recommendations on textbooks?

- Fri Jul 30, 2010 2:24 am UTC
- Forum: Science
- Topic: Explain This Engine
- Replies:
**12** - Views:
**1623**

### Re: Explain This Engine

All you guys are missing one big thing: the video showed that if the engine was not allowed to spin, it would not function. How do you explain that?

- Tue Jul 27, 2010 4:22 pm UTC
- Forum: Gaming
- Topic: Board games anyone?
- Replies:
**962** - Views:
**258405**

### Re: Board games anyone?

My two current favorites are Pandemic and Carcassonne. Pandemic is interesting because all of the players are on the same team and win or lose together. Carcassonne's just simple and fun and doesn't take too long to play.

- Fri Jul 23, 2010 5:27 am UTC
- Forum: Science
- Topic: Help with near-lightspeed travel
- Replies:
**21** - Views:
**2914**

### Re: Help with near-lightspeed travel

Something to consider (and maybe even to use to your advantage in making your desired plotline work out) is that the positions of objects in our universe are not static: in the four years between when the first and second ship leave, the star could've become a light year or more closer (or more like...

- Thu Jul 22, 2010 5:16 pm UTC
- Forum: Science
- Topic: Dyson Sphere / Ringworld (in)stability
- Replies:
**36** - Views:
**8046**

### Re: Dyson Sphere / Ringworld (in)stability

Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.

- Wed Jul 21, 2010 10:51 pm UTC
- Forum: Science
- Topic: 'Seeing' Around Objects
- Replies:
**12** - Views:
**1902**

### Re: 'Seeing' Around Objects

Yeah, if you put it 5 feet up in the air, there'll be nothing blocking it. Then again, you couldn't put it in your garage. Maybe a telescoping pole?

- Wed Jul 21, 2010 10:48 pm UTC
- Forum: Science
- Topic: LaTeX and other markup!
- Replies:
**30** - Views:
**18856**

### Re: LaTeX and other markup!

Yes there is: http://www.codecogs.com/latex/eqneditor.php ...And that's about it. The problem is that the part that's huge isn't the frontend that you see, it's the giant hulking backend that does all the work (formatting the text, typesetting it, interpreting code, etc.) You can't have a lite backe...

- Wed Jul 21, 2010 12:50 am UTC
- Forum: General
- Topic: economics and personal finances question
- Replies:
**3** - Views:
**772**

### economics and personal finances question

I didn't really think this fit in the mathematics forum, so here it is: Let's say I have 8 savings bonds: 2 from 1990, 2 from 1991, etc. up through 1993. The current value of the 1990 ones is $555, the 91's $535, the 92's $515, and the 93's $490. I need $2000 now and I'll need $2000 again in 4 years...

- Tue Jul 20, 2010 10:27 pm UTC
- Forum: Mathematics
- Topic: Interest calculation more complex than f=p(1+i)^n
- Replies:
**3** - Views:
**903**

### Interest calculation more complex than f=p(1+i)^n

Note: this is NOT for homework. Everybody knows how to calculate interest using F=P(1+i)^n for finite compounding periods or F=Pe^{rn} for interest compounding continuously. But how would one find the future value of a loan that accrues and compounds in different periods? An example: a loan ...

- Sat May 22, 2010 10:04 pm UTC
- Forum: Science
- Topic: LaTeX and other markup!
- Replies:
**30** - Views:
**18856**

### Re: LaTeX and other markup!

Just to be curious, i heard of latex in the past but never gave it any attention... Is latex useful if you are writing reports and papers about biochemical subjects? Because in my mind using Pages i thought i could achieve the same thing but correct me if im wrong :) *which i probably am* Absolutel...