Challenge Definition and 942 Threads

I am looking for extremely challenging math equations/problems to solve. I would appreciate any problems in any field of mathematics (almost nothing is too difficult). Note that I am looking for straightforward problems with an answer (not proving someone else's conjectures). Who knows, others...

.. As I read the situation, DrChinese frequently challenges local realists -- of whatever hue -- here, in the Quantum Physics section of PF. As I understand the details: The challenge is delivered in the context of Aspect's experiment, the twinned photons are identically correlated (in the...

Hello, I am faced with a perplexing challenge in analyzing my results for an ecology experiment. All help is immensely appreciated. The situation: I have 6-month longitudinal mass data for 8 hummingbirds. From eye-balling the data, time definitely has an effect: masses tend to decrease...

This isn't even for the campus where I go to school, but as an amateur astronomer, I feel that this message should be spread everywhere. http://www.tdgogreenchallenge.com/video/p/1/playid/149/id/149/ Light pollution is something more than a nuisance to astronomers, it is also something that is...

Homework Statement A massless spring of constant k=78.4 N/m is fixed on the left side of a level track. A block of mass m=0.50-kg is pressed against the spring and compresses it a distance d from equalibrium position B to a compressed position A. The block, initially at rest, is then released...

I have a problem with calculating the concentration gradiant. Here is the question and the solution from the solution manual and the numbers don't add up. A 1-mm sheet of FCC iron is used to contain nitrogen in a heat exchanger at 1200℃. The concentration of N at one surface is 0.04 atomic...

Some matter (non-empty waves) formed a Black Hole. Black Hole emits Hawking Radiation. After a while, Black Hole dissapears, and there is nothing but radiation going in all directions. My question, How 'guided particled' managed to escape from the Black hole? Or, if they did not escape...

Homework Statement \sum_{k=0}^{4}\cos^2\left({\frac{2\pi k}{5}\right) = 5/2 The Attempt at a Solution I have to prove that. I don't know how. Maple gives 1+2*cos((2/5)*Pi)^2+2*cos((1/5)*Pi)^2 evaluated numerically it is equal to 2.499999. But I don't remember the trick to doing this...

Homework Statement I have to find all the partial limits {I hope this is how this term named in English} of a sequencesHomework Equations a_1=0 a_{2n}=\frac {a_{2n-1}} {3} a_{2n+1} = 1/3 + a_{2n} The Attempt at a Solution I have tried to prove first that sequences of all the even terms...

I'm looking for a formula to represent the idea that if I didn't have you, someone else would be equally nice or better. Suggestions? Thanks, Dian

Homework Statement Let I be an interval, and f: I --> R be a continuous function that is known to be differentiable on I except at c. Assume that f ' : I \ {c} --> R admits a continuous continuation to c (lim x -> c f ' exists). Show that f is in fact also differentiable at x and f ' (c) =...

In my engineering class, we were told to create a structure out of balsa wood (1/8"x1/8") and glue. The structure has to suport the weight of 3 15lbs. weights (donut shape). We are only give 72" of balsa wood, and the structure must hold the 3 15lbs. weights for 1min. Sorry I am new to this...

can anyone help me please can anyone solve this problem for me please Q) The Binomial distribution allows the calculation of the probability of k successes in n trails where there are only two outcomes: success or fail with probabilities p and q respectively. The Binomial probability is...

Homework Statement This is just a problem i came up with while doing in equations, and recently saw in a book too. Find the smallest integer n, for which n! > 10n The Attempt at a Solution The trial method (with help from the computer) yields 25 to be the answer. After a...

Got some exciting news from a PF Mentor: And the actual paper: http://iopscience.iop.org/1367-2630/12/12/123007 Violation of Leggett inequalities in orbital angular momentum subspaces J Romero, J Leach, B Jack, S M Barnett, M J Padgett and S Franke-Arnold J Romero et al 2010 New J...

This isn't a homework problem. I challenged myself to see if I could make this work... but I couldn't. Now I'm asking for help on it. The question is simple. \int \frac{W(x) W_1(x)}{x} \left(\frac{1}{W(x)+1} + \frac{1}{W_1(x)+1}\right) dx Now I have what this equals right here (W(x)...

I have been trying to plot a vector and it's derivative for a while now, but I cannot figure out why I can't get them to plot. Here is what I put for my code... a[t_] := Sin[t] Cos[2 t] b[t_] := Sin[t] Sin[2 t] c[t_] := Cos[t] V[t_] := {a, b, c} I tried this...

Hi Physics forums, I have been approached by an interesting challenge proposed by my colleagues. The goal is to build a structure completely out of newspaper with the longest span to support a 1500.0g weight at its centre point, duct tape allowed to connect ends. The point scheme is as...

Hi all! Good evening Here is the Question: This question is given as a challenge extra credit task, and is a part of a course called solid mechanics 2 that deals more with shear strain and strain matrices. While trying to translate the question I used the term "strength" instead of...

Homework Statement Let V a subset of the real line be called a vitali set if V contains precisely one point from each coset of the group of rational numbers. Prove: Homework Equations 1) every lebesgue measurable subset of V is a nullset. 2) V is not lebesgue measurable 3) every set of positive...

Homework Statement You are crossing a narrow bridge 1km long when you notice a truck approaching at 90km/h. If you can run at 5m/s, how far from the far end must you be if you could reach either end just before being hit by the truck? My attempt Displacement between the two...

Homework Statement Calculate the radius of convergence of \sum_{n=0}^\infty a_{n}^{2}z^{n} let \sum_{n=0}^\infty a_{n}z^{n}RADIUS R Homework Equations \limsup|a_n|^{\frac{1}{n}}=\limsup |\frac{a_{n+1}}{a_n}|The Attempt at a Solution the latex is killin me please help....

challenge question! whay does not monossacharides come less than three carbon atoms?? (I mean they just come triose to hexose)>>thnk you

Homework Statement So the goal is to reach a distance H in the x-direction, starting from a height H in the y-direction, and you need to minimize the speed, and find the smalest and angle. Homework Equations i did: dx = V cos(theta) *t and y = y_0 +V sin(theta)*t-1/2*g*t^2 Vx =...

Homework Statement Just when a Frisbee passes over the head of a student at a speed of 4m/s and decelerating at a rate of 1.5 m/s2, she starts to run accelerating at a rate of 1 m/s2. [neglect vertical motion of Frisbee] a)How long will it take the student to catch the Frisbee? b) If...

How would you solve this without using decisional blocks?

I just need a hint to solve the problem. The method used is illustrated in the example problem as follows: I am supposed to imitate the method used in the example problem to solve the challenge problem in the book as follows Imitate the method used in the last problem to find a formula...

Ever attempt a "food challenge"? Just looking for a laugh at the moment? I'm not usually one to just post a blog-link, but I am not running into any of my particular friends soon who would get a kick out of this... so I'll just share it with a random crowd! This is well written for a blog...

Homework Statement sin(α+45) = ? The Attempt at a Solution Dunno. Really dont. Need it in simplification.

Homework Statement Solve the following parametric equations for y = f(x) x(t) = e^{-t} + t y(t) = e^{t} - t The Attempt at a Solution I'm completely stuck on this one. I've noticed x + y = e^{-t} + e^{t} and also y = \frac{1}{x-t} - t but that's about as far as I've gotten.

Does the fact that a car burns fuel to keep it moving mean that we can truly say that the car is moving and not the earth? If so does this disprove the 1st postulate that maintains ALL uniform motion is relative? *I know that objects in space don't require fuel to move at a constant speed...

Okay, I am totally baffled here. For our final project in Algebra we have one class period to build an egg drop carrier. The egg will be dropped from 8 feet, and we have VERY LIMITED materials. - 8 Straws - 1 6x6 Piece of Thick Paper - 3 Tissues - 2 ft. of Masking Tape Another rule is that...

Dear readers, At my webpage: http://domingogomez.web.officelive.com/brocotfraction.aspx I have posed a challenge entitled "To PI or not to PI", it deals with a generalized continued fraction (bifurcated fraction) whose coeficients are all the Stern-Brocot fractions, that is, all...

Homework Statement A flexible, circular conducting loop of radius 0.15m and resistance 4 ohms lies in a uniform magnetic field of .25 T. the loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m^2. it takes .30s to close the loop. what...

Homework Statement find \int\int_D sin\left(\frac{y}{x}\right)dA bounded by x=0, y=\pi, x=y^2The Attempt at a Solution I've only studied calculus 1, this problem is for my friend. I did read up briefly on double integrals however and this is why I'm stuck: From the limits and where the graphs...

I have teenaged daughters, and like many of their peers, they're obsessed with their body weight. Unfortunately, since I have access to accurate scales at my gym, I've never bothered buying a bathroom scale at home, and this is now becoming a source of friction. Rather than simply surrender...

Right now we show that we have 197,293 PFers. Do we have any guesses as to the date and time that we hit the 200,000 mark?

I've been working on this for years; self determination; there IS a time to say "Help"; this is it. Equations of motion; I'm well acquainted with them, but THIS one is unique, and I can't get to first base. V is Velocity X is distance/location t is time X = 4*(t^2) - 15 - K*V so I...

Homework Statement A particle of mass 1kg is projected in XYZ space, where Gravity (g=10m/s2) acts in -\hat{k} direction. The initial velocity of a particle is \vec{u}=(-3\hat{i}+4\hat{j})m/s. x-component of acceleration = 3t/4 y-component of acceleration = -1 - 3t/4 If total work done in...

A real challenge to all physicsist! In order to experience free fall a student walks off the top of the CN Tower which is 553m high and falls freely. His initial velocity is zero. The rocketeer arrives at the scene 5 seconds later and dives off the top of the tower to save the student. The...

..sucks. I have the Sky-Watcher 10" dob (got it for xmas). All around, it's a great scope for the cost, and produces some very crisp visuals of surprisingly distant objects... when it can center on them. I find myself having to constantly aim higher than the object so my telescope will "fall"...

Okay so we are going to drop an egg from three stories high. The only materials we are allowed to use is popsicle sticks, glue, string, and garbage bags...HELP!

I found on wikipedia that the following statements are equivalant: 1. Matrix A is left invertible 2. Ax=0 => x=0 I couldn't find the proof so I try to do it myself. From 1. to 2. is easy. Assume A is left invertible. If Ax=0, then x=Ix=A-1Ax=A-10 = 0 . I can't figure out how to do 2=>1. Any...

Homework Statement Every 2km power is reduced by half. Initial power = 10watt. What is power after traveled 8km? C = 3x108. What is speed of light passing through optic fibre? n = 1.55Homework Equations P = \frac{w}{T} ? The Attempt at a Solution I don't know where to start

Homework Statement So I'm trying to find the integral of P = 2xyz^2 along the curve c which is defined by: x=t^2 y=2t z=t^3 t goes from 0 to 1 So the q says that it is the integral of P dr along c Homework Equations The Attempt at a Solution So I know that this...

Mouse trap car! i need to make a mouse trap car that goes 7 meters forward and then goes 7 meters back.

I have a challenge for anyone gifted enough to communicate with a stupid layman in terms that I can understand. I'm struggling in my attempt to understand the concept of "spin" with regard to fundamental particles. 1.) How can a fundamental particle that has no spatial dimension have an axis...

My cousin challenges me with a tough limit problem. Compute the limit as x->0 of (sin(tanx)-tan(sinx))/(arcsin(arctanx)-arctan(arcsinx)). This limit seems impossible to do. I used L'Hopital's rule but it didn't help at all. Can anyone find a way to do it?

Prove that: F_{n} = \frac {\varphi^n - (1-\varphi)^n}{\sqrt5} holds true for any number in the Fibonacci Sequence. Who can answer the fastest?

Prove that this is the equation of a straight line; -\frac{\zeta(x)\zeta(2)y\Gamma(x)}{\int_0^\infty \frac{u^{x - 1}}{e^u - 1} du \int_0^1 \frac{\ln(1 - x)}{x} dx} - \nabla \cdot (\nabla \times \vec{A}) = \frac{L^{-1}[\frac{F(t)}{t}] \int_{k = 0}^1 \int_{\theta = 0}^{\pi /2} \frac{d\theta...