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 Jedo's School Help Thread Goto page Previous  1, 2, 3, 4, 5, 6  Next
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Guest

 Posted: Sun Aug 29, 2004 8:45 pm    Post subject: 41 Not in the mathmatical sense.
Digit Ne
Daedalian Member

 Posted: Mon Aug 30, 2004 12:57 am    Post subject: 42 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
Daedalian Member

Posted: Mon Aug 30, 2004 1:12 am    Post subject: 43

 Quote: MIT has this Java thing that lets you plot multiple-variable functions, surfaces, vector fields etc. If you're interested, I could dig up the link.

ooooh, that would be awesome!!
Guest

 Posted: Mon Aug 30, 2004 2:41 am    Post subject: 44 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.

Posted: Mon Aug 30, 2004 5:33 am    Post subject: 45

 Digit Ne wrote: 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.

I don't think there is a valid foundation for this understanding. It may simply be due to the way that your conscious mind has evolved.

 Digit Ne wrote: The fourth would be the third squared. How is that possible?
Three squared is nine.

 Digit Ne wrote: 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.

Here is a simple demonstation of the theory.

A point is zero dimensional.
Taking a point and extending in infinitely in any direction will produce a one dimensional line.
Taking a one dimensional line and extending it similarly will produce a plane.
Extending a plane will produce a 3 dimensional space.
Extending the three dimensional space infinitely along the time axis will produce a 4 dimensional space. It may appear "linear", but it is an entire 3 dimensional space that is being extended along this line.

The uni-directional aspect, may be illusional and an evolutionary trait developed in order to increase the likeliness of survival of a species based on Chemical reactions moving in this direction on this timeline.
Old Father
Guest

 Posted: Tue Aug 31, 2004 2:49 pm    Post subject: 46 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
Daedalian Member

 Posted: Sat Sep 11, 2004 8:46 pm    Post subject: 47 *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
Daedalian Member

 Posted: Sat Sep 11, 2004 9:17 pm    Post subject: 48 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
Daedalian Member

Posted: Sat Sep 11, 2004 9:58 pm    Post subject: 49

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:
 Quote: (C1) plot3d((xy)((x^2)-(y^2))/((x^2)+(y^2)),[x,-10,10],[y,-10,10]);

And this is my error message
 Quote: Error: ((MTIMES SIMP) 0.0050000000000000001 ((|\$xy| SIMP) 0.0)) is not of type (OR RATIONAL LISP:FLOAT). Fast links are on: do (si::use-fast-links nil) for debugging Error signalled by LISP:FLOAT. Broken at LISP:FLOAT. Type :H for Help. MAXIMA>>
Lucky Wizard
Daedalian Member

 Posted: Sat Sep 11, 2004 11:05 pm    Post subject: 50 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
Daedalian Member

 Posted: Sat Sep 11, 2004 11:41 pm    Post subject: 51 That makes a bit of sense, but earlier in that letter Washington said he didn't like the Ordinance.
doormouse11
Daedalian Member

 Posted: Sun Sep 12, 2004 11:26 pm    Post subject: 52 yay! it worked. I finally e-mailed my professor and found out I was leaving out the asteriks between xy and immediately after.
Courk
Daedalian Member

 Posted: Sun Sep 12, 2004 11:44 pm    Post subject: 53 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.Last edited by Courk on Fri Oct 20, 2006 4:17 am; edited 1 time in total
doormouse11
Daedalian Member

Posted: Tue Sep 14, 2004 6:21 am    Post subject: 54

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

 Quote: A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?

This is what I've done... I'm wrong somehow. So any of it could be messed up. I can't pick out where I'm going wrong.

I decided that there are 56 total combinations of 3 keys she could choose on her way out of the door (8!/(5!8!)).

21 of those combinations have the master key. (6+5+4+3+2+1)
21 of the combinations have the key that will open the door to whatever house she is going to.
6 combinations have both the master key and the specific key to the house.

case A: one of the keys she chooses is the master key; P(A)=3/8
case B: one of the keys she chooses is the key to the house; P(B)=3/8
case C: the door to the house she is going to is unlocked; P(C)=2/5

The intersection of A and B =3/28 (from the 6 combinations/56 from earlier)
I used the theorem that says that if two events A&B are independent of each other, P(intersection A&B)=P(A)*P(B) to find the intersections of A&C and B&C.
Intersections A&C and B&C=3/20
I used the same theorem to say that the probability of the intersection of A&B&C would = P(A&B)*P(C) = 3/70.

I assumed that the probability of the union of A and B and C would represent the odds of her being able to open the door when she gets to the house.
P(Union(ABC))= P(A) + P(B) + P(C) - Intersection(A&B) - int.(A&C) - int. (B&C) + int. (A&B&C)
=3/8+3/8+2/5-3/28-3/20-3/20+3/70= 11/14 <--my final answer. The first thing I noticed was that it looks really high. And the right answer is 5/8.
The Ragin' South Asian

 Posted: Tue Sep 14, 2004 6:32 am    Post subject: 55 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
ESL Student

 Posted: Tue Sep 14, 2004 9:52 am    Post subject: 56 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
Daedalian Member

 Posted: Tue Sep 14, 2004 2:54 pm    Post subject: 57 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
Daedalian Member

 Posted: Tue Sep 14, 2004 4:48 pm    Post subject: 58 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
Daedalian Member

 Posted: Wed Sep 22, 2004 4:46 am    Post subject: 59 why does 0!=1 ?
Courk
Daedalian Member

 Posted: Wed Sep 22, 2004 8:05 pm    Post subject: 60 Because.
Lucky Wizard
Daedalian Member

 Posted: Thu Sep 23, 2004 2:08 am    Post subject: 61 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...
Guest

 Posted: Thu Sep 23, 2004 2:17 am    Post subject: 62 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
Daedalian Member

Posted: Fri Sep 24, 2004 8:24 am    Post subject: 63

 Quote: Because.

Hahah, that is what my probability and statistics teacher said.

This calculus problem is scaring me . *resists hiding under blanket*

 Quote: Show that the lines joining the centroid (the intersection point of the medians) of a face of the tetrahedron and the opposite vertex meet at a point 1/4 of the way from each centroid to its opposite vertex.

I have shown satisfactorily that the medians of an equilateral triangle meet at a point 1/3 of the way from the base of each side to its opposite vertex. (I used trigonometry/basic geometry though, and I think I was supposed to use vectors since the section is called "displacement vectors.")

My professor last semester skipped over center of mass, but my current professor says that I don't actually need to know how to find the center of mass to solve the problem. He says that you can do it all with vectors (we just started with vectors, so I guess that's probly the point of the problem).

I guess I am experiencing vector resistance or something.
doormouse11
Daedalian Member

 Posted: Tue Sep 28, 2004 3:45 am    Post subject: 64 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
Daedalian Member

 Posted: Wed Nov 03, 2004 9:14 pm    Post subject: 65 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!
Daedalian Member

 Posted: Thu Nov 04, 2004 3:22 pm    Post subject: 66 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
Daedalian Member

 Posted: Sat Nov 06, 2004 8:04 am    Post subject: 67 thanks
Jedo the Jedi
Paragon in Training

 Posted: Sat Feb 05, 2005 5:26 pm    Post subject: 68 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
Daedalian Member

 Posted: Sat Feb 05, 2005 8:18 pm    Post subject: 69 What equations do you have?
Jedo the Jedi
Paragon in Training

 Posted: Sat Feb 05, 2005 8:50 pm    Post subject: 70 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
Misunderstood Guy

 Posted: Sat Feb 05, 2005 9:20 pm    Post subject: 71 So what's wrong with sqrt(2x/gsinO) ~ 16.43623755 s ?
Courk
Daedalian Member

 Posted: Sat Feb 05, 2005 9:21 pm    Post subject: 72 What's F //?
CrystyB
Misunderstood Guy

 Posted: Sat Feb 05, 2005 9:28 pm    Post subject: 73 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
No offense, but....

Posted: Sat Feb 05, 2005 9:38 pm    Post subject: 74

 Jedo the Jedi wrote: 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?

It depends on how wide the avalanche is. If it's narrow, you can sidestep it as it's about to hit you. If it's very wide, you better start moving sooner.

Or just wait till it hits you and let it knock you out of the way.
Jedo the Jedi
Paragon in Training

 Posted: Sat Feb 05, 2005 11:10 pm    Post subject: 75 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
Paragon in Training

 Posted: Sat Feb 05, 2005 11:12 pm    Post subject: 76 It was correct, CB. Thanks alot. I ended up making a 94 on that homework.
Neo
Daedalian Member

 Posted: Sat Feb 05, 2005 11:45 pm    Post subject: 77 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
Paragon in Training

 Posted: Sat Feb 05, 2005 11:56 pm    Post subject: 78 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
No offense, but....

Posted: Sun Feb 06, 2005 2:40 am    Post subject: 79

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

If the avalanche is very wide, you have to start getting out of the way a lot sooner than if it's narrow (if it's really narrow, you can sidestep it at the last second). Or, if by "amount of time to get out of the way", they don't mean how soon you'll have before you must start moving, but how soon you'll have to complete the move, then it depends on which direction you move. If you get out of the way by skiing downhill very fast, you'll have longer than if you're moving horizontally across the slope.

Maybe they should have asked how long until it hits you. That would have been a lot less ambiguous.
Guest

Posted: Sun Feb 06, 2005 4:47 am    Post subject: 80

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...
 Neo wrote: Treat the avalanche as a point-mass.
How wide is that?
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