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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 Re: Help Me ! » Row space » 2007-03-12 11:36:01

I'm never sure what math people mean when they say "describe". I think they probably mean that they want you to find out if they are linearly dependent or not.

#2 Re: Help Me ! » in dire need of help » 2007-03-10 07:02:16

Do you only want a rough guess? Because the real deal involves phase changes and that can get messy. Or there's the less-rough guess, which ignores the phase changes and just deals with total energy.

What'll you have? smile

#3 Re: Help Me ! » Math problems!!! » 2007-03-10 06:57:47

Actually, it does. smile R is the ideal gas constant, which can be expressed in units of energy/ temperature*mole, which is also the units of heat capacity.

They've given you the heat capacity like it's a constant, which it isn't. Heat capacity is a function of temperature. Also, they've asked you to assume heating at a constant pressure, which you can't because the pressure is going to change when you heat the gas in a closed volume.

What class is this for? I ask because I don't know how far to go with the solution. It doesn't seem to be the type of problem that you'd get in a math class, but other classes (chemistry, engineering) don't usually make such gross oversimplifications so I'm wondering if this is really the whole problem.

Anyway, we'll take them at their word. Since we don't have Cp as a function of T, we can just multiply it by δT to get the specific internal energy change δÛ, which has units of energy/mol. Then just multiply that by the moles of gas, found as n = PV / RT = 0.1 (L*atm) / R (L*atm/K*mol) * 300K .

That should get you the very approximate solution. If you need the real solution I can get that for you too. (This is what I get for studying Chemical Engineering. tongue)

#4 Re: Help Me ! » Math problems!!! » 2007-03-09 19:34:36

Another heat problem that I have to wait until I can look stuff up tomorrow to do. smile

C sub p is the symbol for heat capacity. I'm not sure about the r though; I'm guessing it's short for rho, or ρ, meaning density. But then the units wouldn't make sense, so it must be something else.

#5 Re: Help Me ! » in dire need of help » 2007-03-09 19:29:31

Hmm...that seems much too nice and neat to work. tongue To check for sure, you'd need to find the total heat in the system and then convert that to temperature for 60g of water. I'll do that in the morning as I don't remember how off the top of my head and right now I don't have my book handy.

#6 Re: Help Me ! » please help » 2007-03-09 19:20:49

...and to do that, you treat the velocity as a vector quantity of magnitude 45 and making an angle of 50 degrees with the x-axis. You can then find the individual components as the legs of a right triangle, like so:

v = 45 * <sin(50), cos(50)>

I've bolded v to denote that it's a vector quantity, and the angle brackets (<>) denote a vector with the x portion first and the y portion second. The 45 distributes through to both.

This is your initial velocity. Because we're ignoring air resistance (you are usually allowed in these problems since modeling air resistance can get complicated), the x component does not change for the entire time. This lets us find the amount of time it will take the arrow to reach 150 meters:

t = 150m / (45*sin(50) (m/s))

This gives the time in seconds. We now know everything necessary to apply the formula for the position of an object under constant acceleration to find the height of the arrow.

The formula is: s = x0 + v0*t + (1/2)a*t²
...where s means "position" for some reason, and "x0" and "v0" are the initial position and velocity. Though I've given the vector form of the formula, in this problem we are only concerned with one dimension so we can use the scalar form. Now:
x0 = 0
v0 = 45 * cos(50)
t = 150 / (45 * sin(50))
a = -g = -9.8 m/s²

Plug those into the formula, and you'll have your answer. cool

#7 Re: Help Me ! » Profit and loss » 2007-03-04 16:36:34

Profit and loss both have the same formula. Profit is positive and loss is negative. I'll use the symbol "N" (for "net", as in "net profit" or "net loss") to denote that quantity.

N = Revenue - Costs

You may need to solve some equations for both the Revenue and Costs terms. If you need a percent, then do:

(N/Revenue) * 100%.

...which gives you the percent excess (or deficit) revenue.

#8 Re: Help Me ! » Crates of Fruit logic puzzle » 2007-03-04 13:44:53

The question is not specific enough. You said that all of the crates are labeled incorrectly, but not in what way. For all we know, one could contain kiwis and another a monkey in a cage.

Or, if you mean to say that there are only either Apples or Oranges in each crate, then if each is incorrectly labeled, then each contains the fruit opposite its label. However, this makes the simplifying assumption that the crates that are labeled as containing only one kind of fruit really only contain one kind of fruit. If any one of the three could contain both apples and oranges, then I don't see how we could ever tell what contains what by removing only one piece of fruit.

It's possible I'm just dense today, but this looks unsolvable to me.

#9 Re: Jokes » Brilliant mathematical minds » 2007-03-03 18:23:57

I'm with the student in the last image of Toast's post. (S)he answered the question as asked. It absolutely infuriates me when teachers ask things in such an ambiguous way that you have no idea what to do.

My other favorite is "discuss"--"Discuss the function f...". The only sensible response is, "What about it do you want to know?" But you can't very well put that if you expect points on the assignment.

Yes, I'm bitter. sad

#10 Re: Dark Discussions at Cafe Infinity » What kind of music do you like? » 2007-03-03 12:19:15

Toast, if you like video game music, check out the Cave Story Remix Project. Most of the tracks are really awesome, and best of all, it's free.

#11 Re: Help Me ! » Derivative of a spiral » 2007-03-03 07:20:18

D'oh! I forgot the chain rule. Thanks Jane.

#12 Re: Dark Discussions at Cafe Infinity » What kind of music do you like? » 2007-03-02 21:43:40

I just discovered Joshua James. You can listen to his most recent CD in its entirety on his web site, and it's quite nice. I think I may end up buying it, if I can scrape together the means.

#13 Re: Help Me ! » Synthetic Division » 2007-03-02 21:39:26

Gosh. It's late, but I'll have a go. (Sorry if some of my answers are snarky, but the questions are a bit redundant.)

1. Synthetic division is a quick way to perform polynomial division. It lets you determine the coefficients of the polynomial that will result from from dividing one polynomial into another.

2. Uh...Students? Math nerds? You? tongue

3. To perform polynomial division quickly. This is extremely useful for factoring higher order (degree 3 or more) polynomials, and can occasionally be useful for algebraically reducing some functions (those composed of a quotient of functions usually).

4. See 1.

5. Synthetic division is MUCH faster than polynomial long division, if you can remember how to do it (I never can; who factors polynomials by hand outside of algebra tests?).

6. Insufficient information to answer the question.

For more on synthetic division, see .

#14 Help Me ! » Derivative of a spiral » 2007-03-02 21:26:52

Replies: 5

Hey guys! Long time no post. I only come back when I've got a goofy problem. Sorry about that.

Anyway, I'll cut to the chase. A spiral is easy to describe in polar coordinates. It has the form r = aθ / 2π , where a is the amount by which r increases in each complete revolution. It's also not hard to map this equation to cartesian coordinates:
x = r*cos(θ)
y = r*sin(θ)

Here's the goofy problem: how do I find the (cartesian) slope of the line tangent to the curve at a given value of r and θ? I've tried implicit differentiation, like so:
dr/dθ = 1 / 2π

dx/dθ = (dr/dθ)*(-sin(θ))
dx/dθ = -sin(θ)/2π

dy/dθ = (dr/dθ)*(cos(θ))
= cos(θ)/2π

The slope of the line would then be dy/dx, and the angle said line makes with the x-axis would be atan( dy/dx ). Right? Am I getting this right? Because the angles produced from these expressions seem a bit off.


#15 Re: This is Cool » Death by Quicksand - Is It Possible? » 2006-09-27 03:48:20

I personally can float on my back in ordinary water. I would imagine quicksand would be the same.

#16 Re: Maths Is Fun - Suggestions and Comments » a programming forum? » 2006-09-21 14:40:07

The problem I see with that is that "programming" is too general; there are a bazillion and a half programming languages out there, and as many ways and contexts to use them, so someone looking for help with a specific system may not be best served here.

Other than that, it's a great idea and fits very well with the forum. smile

#18 Help Me ! » Linear Algebra: Check My Proof » 2006-09-19 19:07:32

Replies: 2

Will you please check this proof? It feels like I'm cheating.

Prove that two vectors, a and b are linearly dependent if and only if a is a scalar multiple of b.

If a = kb, then a - kb = 0, and the system is linearly dependent.

If, however, a ≠ kb, then a - kb ≠ 0, and the system is not linearly dependent.

My book gives the hint that we should consider separately the case where a = 0 (the zero vector), but that just seems superfluous and unnecessary to me.

What do you guys think?

#19 Re: Dark Discussions at Cafe Infinity » Magical Motor? » 2006-09-12 05:31:27

Antimatter production has at least one very worthwhile use: as rocket fuel. Not even just to power the warp drive on the Enterprise, but because it is the most energy-dense power source in the universe. We are currently limited in our space exploration by the energy density of our rocket fuel; if we had a reasonably priced way to produce antimatter, we could send a probe to neighboring star systems...

#20 Re: Dark Discussions at Cafe Infinity » Magical Motor? » 2006-09-07 07:56:17

Here's a good look at the Steorn bit from a blogger I trust (the Engineer-Poet):

#21 Re: Dark Discussions at Cafe Infinity » Magical Motor? » 2006-09-06 13:50:33

Ricky wrote:

I've said it once and I'll say it again, science happens with scientists.

Unless, of course, the scientists are too beholden to this "law" of conservation of energy to see the fundamental truth. Everyone knows that laws are really more like "guidlines" than actual rules.

Kidding! I'm with you. Their info page has this to say about independent verification:

During 2005 Steorn embarked on a process of independent validation and approached a wide selection of academic institutions. The vast majority of these institutions refused to even look at the technology, however several did. Those who were prepared to complete testing have all confirmed our claims; however none will publicly go on record.

None will publicly go on record? Why could that be? The only reason not to is that you are concerned about your reputation. Wait...either the technology works, or it doesn't. If it works, there is no danger (and actually a lot of prestige) in going on record to support it. If it doesn't work, then you should go on record to decry it. Which option did anyone choose?

This leads to the conclusion that the whole thing is a big, elaborate hoax. However, I'm having a hard time following the money here. What does Steorn stand to gain from the deception? They apparently have a history of doing business in an entirely different market (counterfeit prevention technologies). Why would they want to destroy their credibility with a lie?

#22 Re: This is Cool » Death by Quicksand - Is It Possible? » 2006-09-01 19:21:28

The maximum pressure your lungs can withstand and still breathe is determined by the strength of your diaphragm. I wonder how much "weight" this little muscle can lift? After all, it never gets a rest; it's always working.

If you're curious as to why scuba divers are able to withstand the pressures of the deep, it's because they are breathing from a pressurized tank. The regulator (mouthpiece) matches the pressure of the air they breathe to the pressure of the water outside (the "atmosphere"), so the balance is maintained and the diaphragm doesn't have to do any extra work. Breathing with a SCUBA feels just like breathing at the surface.

A standard scuba tank holds 3000psi of air. That pressure isn't matched until you get to a depth of about 7125 ft. Of course, at that depth you'd use up your whole 3000psi tank in 3 or 4 breaths. You'd also have a lot of other issues to deal with...

Sorry to go OT; I just love scuba diving. smile

#23 Re: Help Me ! » Maths » 2006-08-22 11:59:28

I'm not 100% sure, but I think batch files are more analogous to Unix shell scripts, which Macs can also run.

Applescript is for GUI applications. Think VBA in Microsoft Office, only on a global system level.

#24 Re: Help Me ! » Maths » 2006-08-21 08:08:11

Applescript is a scripting language created by Apple for scripting applications on the Mac. You can tie applications together and automate repetitive tasks - very handy! They also tried to make its syntax English-like in an attempt to make it friendly and easy to learn, but in fact it's just as rigid as any programming language and so is just as hard to learn.

#25 Re: Help Me ! » Help Needed on Odd Math Question » 2006-08-20 17:52:15

That's scarily coincidental and hilarious all at once... .. ....!

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