Jedo's School Help Thread

[Guest]

Not in the mathmatical sense.

[Digit Ne]

I never got that the fourth dimension was time anyway. I mean, as far as I understand it, time is one-way linear.. which would be the first dimension, not fourth. The fourth would be the third squared. How is that possible? I dunno. But if we were 2D people (like on a piece of paper) and some 3D person picked us up, we would have no idea what the hell was going on, because we wouldn't be able to comprehend "up". So a fourth dimension would, logically, move in a way we can't comprehend, and NOT be a one-way linear concept.. right?

And Jedo, I took Precal last year. Radians are, indeed, your friend.

[doormouse11]

[Guest]

Each dimension is independently linear. Depth without length and width is still 1 dimensional.

Alot of the confusion people are having is from using terms like length width and height to refer to dimensions. These terms are practical in the real world, but irrelevant on the theoretical level.

On a grid you an determine length with an X value, and height with a y value. It's only numbers. On a 3d grid you could refer to depth with Z. In a 4D grid you could just add another number for the 4th dimension. W or something.

[jadesmar]

[Old Father]

Using time as an example of a fourth dimension, is quite a good way of teaching beyond the thre dimensions. I always liked the concept that no two things can exist in the same 4 dimensions, (x,y,z,t) yet they can in any 3 of the 4.

[Courk]

*uses thread for intended purpose*

For my english class we have to do a presentation of George Washington's views on various things. Mine is western expansion. Most of our information comes from a book of what seems like every letter that Washington ever wrote. I've been doing rather well with figuring out what he was saying and "translating" 1700s English into 2000s English, but one passage has be utterly stumped.

Washington is talking about the Land Ordinance of 1785, which determined how to divide and sell the land in the Northwest Territory (Now Ohio, Indiana, Illinois, Wisconsin, Michigan, and part of Minnosota). Here's the quote I cannot grasp:

"Many think the price which they [Congress] have fixed upon the Lands too high; and all to the Southward I believe, that disposing of them in Townships, and by square miles alternately, they will be a great let* to the sale: but experience, to which there is an appeal, must decide."

(Pg. 306 of George Washington: a collection, ed. W.B. Allen)

*I determined that "let" here means "hinderance," but after that I'm at a loss. A) Does he think the people to the South will hinder the sale of land (i.e., won't buy them)? B) Does he think that the method of dividing them into 1-mile square plots, with 36 plots in a 6mi x 6mi square township is a bad idea and will hinder sale? C) Or, does he think that this method might work in the NW territory, but in more southern territories it would be a bad idea?

I'm leaning towards B, but I'm not overly confident in it. Any help would be appreciated. Thank you!

[doormouse11]

I get the impression that they are going to do whatever they have done in the past from the bit about letting experience decide. It sounds like Washington is questioning whether that is really the best plan of action, especially for the South. But that is all I can gather (so I guess I vote B).

Do you know what kind of hinderance he is talking about? It would help if he elaborated on why it's a bad idea. Is the land too pricey for people to buy? is there something bad about the way the land is being divided that would keep customers uninterested?

wish I could give better input

[doormouse11]

Has anyone used Maxima, Maple, or any similar programs?

I'm using Maxima for the first time and am having trouble graphing f(x,y)=xy(x^2 - y^2)/(x^2 + y^2).

This is what I typed:

[Lucky Wizard]

I'm not 100% percent certain about this, but this sounds right:

D) Perhaps the part before the colon is a description of how these "many", particularly in the South, feel about the Ordinance, and Washington is saying that "many", particularly in the South, feel that the proposed system will hinder the sale; and the part after the colon is Washington's own opinion of the Ordinance, namely that experience must decide, which he seems to be contrasting with the feelings of this "many".

BTW, kevin, your last post in this thread reminded me of a Foxtrot comic, where Peter (a junior in high school) is talking to a teacher who has just graded one of Peter's tests. The teacher goes into the bizarre answers Peter gave in the test, saying at one point, "And in problem 4, you use 800 million as the value of pi! Is this your idea of a joke?" In the punchline, we see a conversation between Jason and Marcus (two younger characters, of which the former is Peter's brother) in which Marcus says "So did you ever tell Peter you spilled root beer on his calculator?" (or something like that, can't remember exactly what was spilled) and Jason says "No, I figure what he doesn't know can't hurt him."

[Courk]

That makes a bit of sense, but earlier in that letter Washington said he didn't like the Ordinance.

[doormouse11]

yay! it worked. I finally e-mailed my professor and found out I was leaving out the asteriks between xy and immediately after.

[Courk]

Looks like we both solved our problems. Washington wrote another letter that same day saying the same thing, but in different words.

LW was closest. Sorry to have doubted you.

[doormouse11]

If anyone is bored and feels like looking at a probability problem I would appreciate it so much!

[The Ragin' South Asian]

I think you've misunderstood the question. leave out case B and it comes out right.
or rather case A, not that it matters
there aren't master keys and specific keys, just specific keys that are for some reason called master keys

[Antrax]

MIT Tools for multiple-variable functions - graph xy/(x^2+y^2) here!
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[Chuck]

The probability of not having the key is 5/8. The probability of the door being locked is 3/5. The probability of not getting in is 5/8 times 3/5 which is 15/40, or 3/8. The probability of getting in is 1 minus 3/8 which is 5/8.

[doormouse11]

Thanks Chuck, RSA! I thought about that one all night. It makes sense now. *stops thinking about it* So only the master key will work if the door is locked. ack, I'm thinking about it again.

And thanks for the nifty site, Antrax.

[doormouse11]

why does 0!=1 ?

[Courk]

Because.

[Lucky Wizard]

Several reasons.

One is that, when you calculate how many ways are there to choose k objects from n objects, you do so by this formula: (n!)/(k!)(n-k)!

When k=0 or n, the formula becomes n!/n!0!=1/(0!). Since there is clearly one way to choose no objects from (say) 8 objects, or 8 objects from 8 objects, this expression should equal one. So 0!=1. (Similarly, since there is one way to arrange zero people, 0!=1.)

Also consider that:

4!/4=3!
3!/3=2!
2!/2=1!

So, to keep this recursion working, 1!/1=0!, and therefore 0!=1.

This, by the way, is a specific case of the fact that the product of no numbers is 1. It can be shown that multiplying any group of numbers is equal to taking another number and raising it to the power of the sum of the logarithms of the numbers in the group. If the group is empty, there are no logarithms to sum up, and it can be agreed that the sum of no numbers is 0. Hence, we have a^0, or 1.

[extro...]

Barely relevant thought......
In the LISP programming languages, the functions +, *, AND and OR take any number of arguments. All functions are used in fully parenthesized prefix notation. Thus:

(+ 2 3 4) = 9
(* 2 3 4) = 24

Now,
(+) = 0
(*) = 1
(AND) = true
(OR) = false

[doormouse11]

[doormouse11]

asked my professor about it and am now feeling much more kindly towards vectors, as they reduced my proof by almost a page in length. yay

[doormouse11]

In probability/statistics we are looking at normal distributions. I'm trying to figure out where the z-values (the values that tell you the area to the left of a certain value on a normal curve) come from (other than the table in the back of the book). Does anyone know how they are calculated?

[ZutAlors!]

The normal distribution itself has a standard formula, but the area under that curve does not have a simple closed form solution. So the values are computed numerically. Cite.

[doormouse11]

thanks

[Jedo the Jedi]

Well, it turns out that Physics gets harder as the year goes on. This was news to me. Anyway, I need some help with one of my problems.


An avalanche is traveling down a mountain with a coefficient of friction of 0. The acceleration due to gravity is 9.8 m/s ² .

If you were on a 21.4 ^o slope and an avalanche started 483 m up the slope, how much time do you have to get out of the way? (Assuming that the 483 m is the distance between yourself and the avalanche, and that initial velocity is 0 m/s.)

That's all of the relevant information, I think. These problems are usually quite easy, but my teacher added some new stuff in to the lesson yesterday so the...less understanding people might understand it. Unfortunately, this extra info confused me.

Just could someone please tell me the answer to 6 significant figures, and explain how you got it. Thanks.

[Courk]

What equations do you have?

[Jedo the Jedi]

Almost any you can think of for high school.

I have F _friction =F _Normal *u; x=1/2at ² +V _initial t*; and F _// =F _gravity sinO. Those are the only ones I can think of that could be used for this problem.

If there is one that anybody else can think of, then just post it. We may or may not have learned it yet, but I can file it away for later use. Nothing too complicated, though, please.

*x is distance, a is acceleration, t is time, and v is velocity. The second half of that equation doesn't get used because velocity initial is 0. The u in the first equation is the coefficient of friction, but since it's zero in this problem, it doesn't matter much.

[CrystyB]

So what's wrong with sqrt(2x/gsinO) ~ 16.43623755 s ?

[Courk]

What's F //?

[CrystyB]

I think it's supposed to be along the slope. Perpendicular to the normal component of G. (In my language, we call it "tangential".)

[extropalopakettle]

[Jedo the Jedi]

F// is parallel, or the force parallel to the surface. I don't know what it is that CrystyB said. I'm going to try that answer, CB.

[Jedo the Jedi]

It was correct, CB. Thanks alot. I ended up making a 94 on that homework.

[Neo]

Extro, it makes no difference how wide it is. You still have the same amount of time to get out of the way.

First, draw a picture and pick your axis-orientation. You can flip them around any way you want, so long as they are perpendicular to eachother. I usually choose to put an axis along the path something is traveling in these types of problems.



Next, draw a free-body diagram using the same set of axes. Treat the avalanche as a point-mass.



(are the pics required for this problem? No, but it's a great habit to get into before the more complicated problems start coming)

Now, since this is contained to travelling along the x-axis, we can use a kinimatics formula.

x _f - x _i = v _i,x *t + .5*a*t ²

Well, we're solving for time (t) and the initial velocity is zero, so the formula is now:

sqrt(2(x _f - x _i )/a)

acceleration (a) does not fall on an axis. So, it is 9.8*sin(21.4) for the x-direction.

sqrt(2(483 - 0)/9.8*sin(21.4)) = 16.44 seconds.
_________________
_{Ad Astra}

[Jedo the Jedi]

Thanks, Neo. I try to draw diagrams for every problem I do, but my diagram for this one was insufficient. I'll keep all of that in mind.

[extropalopakettle]

[Guest]

Indeed, extro, my initial thought was too "But how quickly do i run down the slope? I might not outrun it, but i might be able to delay its reaching me..."

I can't understand how you two could insist on your point of view and not realize there is a fundamental difference...