Dimensions Definition and 1000 Threads

[b]1. For subsets U1, U2, U3 of a finite set, prove that dim(U1+U2+U3) = dimU1 + dimU2 + dimU3 - dim(U1∩U2) - dim(U1∩U3) - dim(U2∩U3) + dim(U1∩U2∩U3) [b]2. dim(U1+U2) = dimU1 + dimU2 - dim(U1∩U2) [b]3. I found that U1+U2 theorem in my book, and I think I should use that, but...

You throw a ball toward a wall at speed 25.0 m/s and at angle 40 degrees above the horizontal . The wall is distance d=22.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its...

A cart is propelled over an xy plane with acceleration components ax=4.0m/s^2 and ay= -2.0m/s^2 . Its initial velocity has components Vix=8.0m/s and Viy12 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate? im confused on how to get...

So we know some of the irreducibility criteria when we have one dimension X. But what about multidimensional abstract algebra? From Dummit Foote, we get that we can pair up every power of X with the powers of Y that happen to be associated with that power of X, and then treat those powers...

A hockey puck rebounds from a board as shown in Figure 16. Figure 16 looks like this. http://img174.imageshack.us/img174/2571/fig16vr6.png The puck is in contact with the board for 2.5ms. Determine the average acceleration of the puck over the interval. ------- So I know you have to use...

Hello Everyone! I have recently had an assignment given to me, concerning "Friction Problems in Two Dimensions." The only problem is, that I have no idea where to start or how to solve the problem... I would extremely appreciate it if I could have some help to point me in the right...

Homework Statement In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at an angle of 141d (Alex and Betty's angle). The tire remains stationary in spite of the three pulls. Alex pulls with force Fa of magnitude 208 N, and Charles pulls with force...

Why is it that it is thought that separate dimensions exist, as humans we can only exist in a volume, three so called dimensions, so why do scientists think that these three can be separated when in all probability and experimental AFAIK they can not, length, width and depth are just words to...

Homework Statement A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 800 km due north but discovers taht the plane must be headed 20.0 degree East of due North to fly there directly. The plane arrives in 2.00 h. what were the (a) magnitude and (b) direction of...

[SOLVED] Kinematics in two dimensions problem Homework Statement Chapter 3, Problem 20 Incorrect. A car drives horizontally off the edge of a cliff that is 48.1 m high. The police at the scene of the accident note that the point of impact is 195 m from the base of the cliff...

Anyone know what topic, branch of math, book, or subject I should look up in order to find a formulation for Maxwell's equations in higher spatial dimensions? I don't mean having time as a 4rth dimension. I mean a 4rth (and more) spatial dimension. This would require the maxwell exquations...

A small marble rolls horizontally with speed v0 off the top of a platform 2.75 m tall and feels no appreciable air resistance. On the level ground 2.00 m from the base of the platform, there is a gaping hole in the ground. The hole is 1.50 m wide. For what range of marble speeds v0 will the...

Consider that you have derived the Lorentz transformations in one space diomensions x=g(x'+Vt') t=g(t'+Vx'/c^2). In order to extend the problem to two space dimensions many Authors add y=y'. Please tell me if that is the best approach. Thanks.

I have read about the possibility of more than one time dimension but I never did really understand what the implications of that would be. What is going on in this idea? How can two dimensions of time be explained so that the layman will understand? Here's an example...

Detecting large extra dimensions via "mini black holes"? Occasionally I come across something explaining that one of the possible discoveries at the Large Hadron Collider might be the production of "mini black holes", which if found would demonstrate the existence of large extra dimensions. The...

Detecting large extra dimensions via "mini black holes"? Occasionally I come across something explaining that one of the possible discoveries at the Large Hadron Collider might be the production of "mini black holes", which if found would demonstrate the existence of large extra dimensions. The...

Hi, sorry if this is a daft question, but it's something I've often wondered about. why is it that the extra spatial dimensions in string theory have to be 'wrapped up' rather than extended like the 3 we experience? it seems to be that since we are 3D beings, 3 dimensions is the limitation of...

Homework Statement If we have a matrix in R^(2x3), what dimension does this matrix have? My book doesn't answer this question - it only tells me what the dimensions are of the different spaces, not of the matrix as a whole. The Attempt at a Solution I would think the dimension is the...

You have a box obviously it is three dimensional but hollow, using dimensions how would you turn this box into a solid object? The top, bottom, ends and sides of the box two dimensional.

Hello, I posted this several weeks ago in another forum, but I never really got a good answer. Could someone please take a look at this an tell me if it's mathematically valid? Thanks! Do Equations in More Than Three Variables Represent Graphs in Higher Dimensions...

Is there any validity to the Moving Dimensions Theory? I hang out at another forum where it has been discussed for about 2 months. It strikes me as a pure kook post. Just curious if it's been kick-banned from this site in the past.

Hey, first of all, I'd like to apologize if I'm posting this in the wrong forum. I wasn't sure whether I should post it here or in the mathematics forum. Recently I was going through an Algebra book, and I saw a chapter on solving linear equations in three variables. The book explained how these...

This question is going to be very weird, but bear with me please. The higgs, we believe is associated with the gravitron, correct? And it's possible that dimensions 5-7 could be the electromagnetic spectrums that can manipulate the higgs/gravitron? Or am I not even close? I am doing research...

Homework Statement A 0.321 kg puck, initially at rest on a horizon- tal, frictionless surface, is struck by a 0.227 kg puck moving initially along the x-axis with a speed of 2.51 m/s. After the collision, the 0.227 kg puck has a speed of 1.51 m/s at an angle of 31 degrees to the...

Homework Statement On a frictionless surface, a 0.35 kg puck moves horizontally to the right (at an angle of 0°) and a speed of 2.3 m/s. It collides with a 0.23 kg puck that is stationary. After the collision, the puck that was initially moving has a speed of 2.0 m/s and is moving at an angle...

Homework Statement Simplify the commutator [A,B] and give the expectation value of [A,B] in the ground state for an isotropic harmonic oscillator (mass m) that has the energy \hbar \omega /2 when A = xp_x B = y Homework Equations [AB,C] = A[B,C] + [A,C]B [p_i,x_j] =...

Homework Statement Suppose that a human head is a sphere with the bone thickness 10% of the radius of the head. Find the fraction of the volume of the head occupied by the brain. Make a similar estimate (forget about factors of pi) in the N-dimensional space (d = N) in the limit N ->...

Homework Statement The volume of a right circular cone is V = [(pie)(r^2)(h)]/3 and it ssurface area is S = (pie)(r)(r^2+h^2)^(1/2), where r is the base radius and h is the height of the cone. Find the dimensions of the cone with surface area 1 and maximum volume. The Attempt at a Solution...

An interesting question came up the other day. Someone asked how to visualize the tinier dimensions, and though I like to think that I can, it was pretty hard to put it into words. Here’s my attempt. Not saying it’s right, just saying it works for me. I’d be very interested to see what works...

I understand from popular books such as those by Brian Greene that among the stock in trade of string theorists are as-yet-unexplored dimensions that are squashed into tiny geometrical configurations called Calabi-Yao shapes. Do stringy folk ever consider a reverse process, which might be...

The partition function in the classical theory is an integral over phase space. Thus, the partition function is often not dimensionless. Then the formula F = -T \log Z can no longer be valid, as you can only take the logarithm of a dimensionless number. In the quantum theory, this...

I'm not sure if this should go here, or in electrodynamics, or in relativity, but never mind. I'm given to understand that Maxwell's equations are completely compatible with the theory of relativity, and apply over all distance scales. I've also heard of Kaluza-Klein theories in which adding a...

how do you if the collision is in 2 dimensions?

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.7m/s (E). After the collision, the velocities of the balls are 2.49m/s(62.8 N of W) and 2.37m/s (69.2 S of E). What is the initial velocity of the second ball? So i know that the masses are the same, and...

Well, I have been studying Work and Energy for a few days now. I started reading about momentum in 2 dimensions, but i can't seem to understand a thing! I would really appreciate it if someone could help me with this topic.

Homework Statement If we lived in a world with 2 spatial dimensions, would the solution to Poisson's equation for a singular charge be the same i.e. would it be 1/r radial dependence? I am doing a computer simulation and if I take out the third dimension, the results are manifestly...

Homework Statement Two lines in space are in the same plane. Line AB passes through points A(x,y,z) and B(x,y,z), and line CD passes through points C(x,y,z) and D(x,y,z). Determine if these two lines are parallel. If they are not, determine the x,y,z coordinates where these two lines...

Does anybody have information on the threaded cylinder port that a paintball pin valve threads into? I know it's a 5/8-18UNF-2B thread, but I need to know the dimensions for the o-ring surface of the port. Thanks

The question is: The driver of a car whose weight is 13000 Newtons traveling at 108km/hr slams on the brakes in order to undergo a constant acceleration, skidding to a complete stop in 4.5 seconds. What is the average force that the brakes must exert during braking? So far i have the...

Homework Statement At one instant a bicyclist is 26.0 m due east of a park's flagpole, going due south with a speed of 14.0 m/s. Then 35.0 s later, the cyclist is 26.0 m due north of the flagpole, going due east with a speed of 14.0 m/s. For the cyclist in this 35.0 s interval, what are the...

Homework Statement One of the fastest recorded pitches in major league baseball, thrown by Billy Wagner in 2003, was clocked at 101.0 mi/hr. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically ( in feet ) by the time it reaches home plate, 60.5 feet...

Hi, I'm sort of new to the calculation of limits of functions defined in R^2( or R^n, n>=2) exp. the limit of sqrt{hk/(h^2+k^2)} as (h,k) --> (0,0) I think it should be 1/sqrt(2) if we let h=k. but I'm not sure if this is the right approach. what about other limits in the form "0/0" as...

Hi, in my physics book (serway) they say "dimensions can be treated as algebraic quantities" but I don't understand this very well. If I sum meters I get meters, if I multiply meters I think I get meters^2 because the area of a rectangle is b.h. But if, for instance, I multiply seconds.seconds...

Can anybody tell me the known dimensions and how they are proved? I still can't understand how time is proved.

Homework Statement Water from a garden hose that is pointed 25 degrees above the horizontallands directly on a sunbather lying on the ground 4.4 m away in the horizontal direction. If the hose is held 1.4 m above the ground, at what speed does ithe water leave the nozzle? Homework...

Homework Statement A magnetic field has these components: x: B = 0.056 T y: B = 0.046 T The particle has a charge of +6.5e-5 C, has a velocity of 2.6e3 m/s, and is moving along the z axis. Questions: 1: What's the magnitude of the net magnetic force on the particle? 2: What's...

What are the properties of SO(4) group? , How this acts as a rotator in 4 dimensions?, What are the elements of Rotation matrix in a specific dimension among four dimensions?

What do electromagnetic waves look like in 3 dimensions? In my textbooks etc. they are always represented as the standard sine wave. But what about actual 3 dimensions? Are there waves with smaller wavelengths than gamma waves?

Scientists and mathematicians speak of extra dimensions that are "curled up" so small that it is impossible to detect them, but what exactly would an extra dimension look like:confused:? I realize that these extra dimensions have been detected mathematically, but the entire concept of something...

Hey, first I want to say my English & Math aren't the best yet, so ill be glad to explain myself again if I'll need to :smile: I hope this question belongs to this section. I want to ask, is there today a way to do calculations about vectors above fractal dimension? (and I would like to...