Terms Definition and 1000 Threads

Homework Statement A sphere of radius R, centered at the origin, carries charge density ρ(r,θ) = (kR/r2)(R - 2r)sinθ, where k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere. Homework Equations...

whether or not it is shrinking or expanding the origin and how long the universe has existed and whether or not there is more than one universe ?

Homework Statement The roots of x^2 + bx + c = 0 are r_1 and r_2, where |r_1 - r_2| = 1. Express c in terms of b. Homework Equations x^2 + bx + c = 0 |r_1 - r_2| = 1 The Attempt at a Solution Im not even sure where to start with this problem, and i don't see how the roots...

Homework Statement A speciality coffee shop sells Cuban coffee beans for $5.50 each bag and Colombian coffee beans for $3.80 a package. 1.If the cost of sales is $1450 plus $0.95 per bag, write down the function which calculates the profit in terms of the number of bags of coffee beans sold...

Homework Statement A toy rocket consists of a plastic bottle which is partially filled with water. the space above the water contains compressed air. At one instant during the flight of the rocket, water is of density\rho is forced through the nozzle of radius r at speed v relative to the...

The links I pull up assume that the reader knows what null dust is. Which I don't. An explanation would be appreciated. The question came up when looking for an (equally absent) clear explanation of Vaidya spacetime. This, in turn, came up while looking at the article...

This will sound like a very amateur question but please read: I have been puzzled for a while about the *precise* mathematical meaning of "quantum fluctuation". I know what a classical fluctuation is (as found in classical statistical dynamics). I also know what a superposition is. These seem...

Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2 and bB=49...

Homework Statement If Logb2=A and Logb49=B, what is logb397, in terms of A and B. This is one of the bonus question in my geometric quiz and i don't remember if the number is 397. I wonder if anyone get this? Homework Equations The Attempt at a Solution here is what i did bA=2...

Homework Statement Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? \sum^{\infty}_{n=1}\frac{(-1)^{n}}{n*9^{n}} (|error| < 0.0001) Homework Equations Alternating Series Test General knowledge of adding...

Ok, I've been trying to follow what you guys have written about this. Is it sort of like protein folding in biology, only instead of proteins you have space time, and you spin it around, and most of it is quantum foam vacuum stuff, but in some places it clumps in sort of oscillating ways...

Homework Statement Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t). Express dV/dt in terms of dr/dt. 2. The attempt at a solution Volume of a Sphere = 4/3 pi r3 I took the derivative of the formula...

Homework Statement The function f is defined by f(x) = x^3 Find an expression for g(x) in terms of x in each of the following cases. (a) f [ g(x) ] = x+1 (b) g [ f(x) ] = x+1 Homework Equations The Attempt at a Solution I got the same answer both times. g(x) = cubic route...

Homework Statement A 1150 kg boat is traveling at 100 km/h when its engine is shut off. The magnitude of the frictional force k between boat and water is proportional to the speed v of the boat: f_k = 73v, where v is in meters per second and f_k is in Newtons. Find the time required for the...

Homework Statement A liquid-level transducer consists of two parallel plates of conductor immersed in an insulating liquid. When the tank is empty the capacitance of the plates is 200pF. The relative dielectric constant of the liquid is 25. Determine an expression for the capacitance C as a...

I was doing my differential equations homework. I had to solve y'' -4y = (e^(2x))/x. While doing this I ran into an integral\int\frac{e^{4x}}{4x}dx. I tried integrating my times but I couldn't; my guess is that this cannot be integrated in terms of elementary functions but I'm not sure. Is...

This is for a first year university question in Physics (Mechanics). 1. Write each vector in terms of the unit vectors i(hat) and j(hat). Use the unit vectors to express the vector C\rightarrow where C\rightarrow = 3.00A\rightarrow - 4.00B\rightarrow. Find the magnitude and direction of...

Calculate the polarizability "a(lpha)" of atomic hydrogen in terms of R Homework Statement A simplified model of a hydrogen atom is that the electron cloud is a sphere of radius R with uniform charge density and total charge -e (The actual charge density in the ground state is nonuniform)...

Homework Statement express cos^4 x in terms of cos 4x and cos 2x given that cos^ x = 0.5(1 + cos 2x) The Attempt at a Solution i did some playing around for a minute and came to this; cos^4 x = 0.25 + (cos2x)/2 + (cos 4x +1)/8 and thought, great! now i'll just check it on...

Hello, I have created a multiple linear regression fit (using least squares) for a project. The regression has two independent variables, rainfall and time, and fits these to groundwater level. The regression was calculated automatically in Excel. I have been asked to report on the P-value and...

Homework Statement By using the Euler's constant (0.577...), express the limit of the sum 1/n + 1/(n+1) + ... + 1/2n explicitly as n goes to infinity. Homework Equations The limit as n goes to infinity for [1/1 + 1/2 + ... + 1/n - In (n)] is the Euler constant, 0.577... It has been...

Homework Statement I'm given acceleration as a=-1.5*s where s is position, and I need to derive an expression for acceleration as a function of time. I am also given an initial velocity of 20 m/s and initial position of 0 m. Homework Equations a=-1.5*s Characteristic Equation...

Hey, so I have a question that states that a particle is subject to an acceleration of a=-3.0*v (m/s^2), and I need to find the acceleration, the velocity, and the position of the particle in terms of time. The initial velocity, Vo, is 15 m/s, and the initial position, So, is 0m. Attempt at...

So by manipulating two of the kinematic equations you can find this relationship: a= acceleration t = time v = velocity v0 = initial velocity x = displacement eq (1) = v = v0 + at --> at = v - v0 eq (2) x = 1/2*(v - v0)*t --> 2x/t = v - v0 substituting 2x/t for v -...

I have a basic under standing of what it is but does anyone know in kid-friendly terms of how it is used, what it is and where it can be found? Thanks, Chase:smile:

Explain/solve the "Matching Problem" in the simplest terms How would you explain and solve the "Matching Problem" to a HS math club? give the simplest explanation and solution you know.

http://www.ph.qmul.ac.uk/phy108/CM2008_week2_exercise1_solution.pdf The L-J Potential Curve in question 2), V(r) = V(r) repulsive + V(r) attractive Is the ^12 term the repulsive term and ^6 is the attractive term?

Homework Statement Ok, so I have a 2nd order differential equation, I can get the complimentary function no problem, its getting numerical values for terms in the particular integral that I can't do. Homework Equations y'' - y' - 2y = t2 The Attempt at a Solution...

Suppose the infinite series \sum a_v is NOT absolutely convergent. Suppose it also has an infinite amount of positive and an infinite amount of negative terms. Say we want to prove it converges by proving the sequence of partial sums, A_n, are Cauchy. Then we need to prove that for every...

I would like to compute the power distribution that maximizes the sum data rate of a certain communication scheme. The expression follows from the sum of the rate of four messages which interfere with each other. A certain amount of power (here 1 Watt) is assigned to these messages, and there is...

WARNING: THIS POST WAS WRITTEN BY A PERSON WHO IS A NOOB AT PHYSICS. Can somebody compare and contrast what people mean when they say the following terms? 1. Quantum Mechanics 2. Quantum Field Theory 3. Quantum Electrodynamics 4. Quantum Chromodynamics Any helpful posts would be...

i know this is possible to find with iteration, but is it possible to find it algebraically?

The definition of a sequence of real numbers is : a function from N to R. What is the standard way to handle a sequence like (1/log n) where the first term is undefined? Do we instead write (1/log (n+1)) so that the first term is defined? Or leave the first term undefined? The definition...

I'm trying to work through an introduction to Lagrangian mechanics. I get the idea. You have a particle at point A traveling to point B. You have a functional which maps every path between those points to a scalar called the action of the path. The universe then does some number crunching...

Hi guys, I bought a high-torque DC motor, that says at the back: 6,000 (gf.cm). I am intending to use this motor to power a plinth on a turntable. So the motor will be upright, with its shaft pointing up. My question is - What is the maximum weight i can put on this turntable, where the...

my math teacher said that the arctan can be setup in terms of logs does anyone know how to do this.

I am looking at the following application note that goes into nodal analysis of op amps: http://www.maxim-ic.com/appnotes.cfm/an_pk/1939/ and down at the bottom where they're analyzing the Wien bridge oscillator the equation at the negative input of the op-amp taken from the output in terms of...

Which pair of constructs best embodies your philosophy of physics?

I am calculating the likelihood of a hierarchical model and am having trouble distributing the product sign. Here are the two expressions that I'm interested in: Product from j=1 to j_k of: (t_jk)^(sum(Z_ijk) + a_k - 1) and Product from k=1 to K of: (b_k)^(j_k*a_k). The tricky...

I am calculating the likelihood of a hierarchical model and am having trouble distributing the product sign. Here are the two expressions that I'm interested in: Product from j=1 to j_k of: (t_jk)^(sum(Z_ijk) + a_k - 1) and Product from k=1 to K of: (b_k)^(j_k*a_k). The tricky...

Hello, I am attempting a past exam paper in preparation for an upcoming exam. The past exam papers do not come with answers and I'm a little unsure as to whether I'm doing all of the questions correctly and would like some feedback if I'm going wrong somewhere. Any help is greatly appreciated...

Terms of "second order" and "fourth order"...what does this MEAN?! I am reading the paper written by Born and Oppenheimer that explains the development of the Born-Oppenheimer approximation. The paper contains the following cryptic (to me) statement: "The nuclear vibrations correspond to terms...

Hi everyone I'm trying to express each term of the Hamiltonian H = \int d^{3}x \frac{1}{2}\left[\Pi^2 + (\nabla \Phi)^2 + m^2\Phi^2\right][/tex] in terms of the ladder operators a(p) and [itex]a^{\dagger}(p). This is what I get for the first term \int d^{3}x...

Interesting analysis of human behavior as to why belief in the supernatural has evolved: http://www.scientificamerican.com/article.cfm?id=skeptic-agenticity

I was wondering if there was a computer algebra system (like Math'ca, Maple, or Maxima) that could handle manipulations with big O error terms. Mathematica has an O function, but it doesn't work properly: > x^2 Log[x] + x Log[x]^2 + x / Log[x] + O[x] O[x^1](it should be "x^2 Log[x] + x...

I am trying to write the term "Sin^2 theta * Sin 2 phi" in terms of spherical Harmonics (they form a combination of Y(2,-2) and Y(2,2)) but the term I get contains the imaginary number 'i'. Am I doing something wrong.. In fact this term is a part of a Hamiltonian and when I get the eigenvalues I...

grad(A*B)=(A*grad)B + (B*grad)A + A curl B + B curl A i'm not sure how to read the RHS to begin to work out the index definition.i'm thinking if add and subtract terms this will work out. i think i can see the first two terms, but the last two maybe "A cross nabla" is what they mean acting on...

Like university researchers measuring the force of Ricky Hattons punch with a special bag, or when programs talk about the force of crashes and ballistic impacts like shells and so on. But force is the mass x the acceleration. That indicates how strong something had to be to accelerate that...

Hello there, my physics friends. I was hoping ye could answer a wee question I have on the phonon spectrum. Mainly,what is it? I know one of the mediations is sound but that's about it. If possible could you put it in terms similar to that of the electromagnetic spectrum. Thanks in...

Hello, I need to find the sum(as a function of x) of the power series \Sigma^{\infty}_{n=0}\frac{(x+1)^n}{(n+2)!} The hint i was given was compare it to the Taylor series expansion of ex. Im not sure even how to start this problem and any help is much appreciated.