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**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?

Actually, it does. 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. )

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

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.

...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.

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.

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.

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.

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

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?

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 http://www.purplemath.com/modules/synthdiv.htm .

**ryos**- 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.

Thanks!

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

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.

Thanks; I got full credit.

**ryos**- 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**.

Proof:

If **a** = k**b**, then **a** - k**b** = 0, and the system is linearly dependent.

If, however, **a** ≠ k**b**, then **a** - k**b** ≠ 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?

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

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?

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.

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.

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