Change Definition and 1000 Threads

With the change of variables-method for a many-to-one transformation function Y = t(X), what's the logic behind summing the different densities for the roots of x = t^-1(y)? Probabilities should be ok to add, but densities? Also, is there no way to extend this method for many-to-many...

I have two n-vectors e_1, e_2 which span a 2D subspace of R^n: V = span\{e_1,e_2\} The vectors e_1,e_2 are not necessarily orthogonal (but they are not parallel so we know its a 2D and not a 1D subspace). Now I also have a linear map: f: V \rightarrow W \\ f(v) = A v where A is a given n...

Homework Statement The following series are not power series, but you can transform each one into a power series by a change of variable and so find out where it converges. ∑∞0 ((3n(n+1)) / (x+1)n Homework Equations a power series is a series of the form: a0 + a1x + a2x^2 ... + ... The...

Homework Statement A mass m is thrown from a height of h. Find the entropy change of the mass, the surroundings and the universe. The temperature of the surroundings is T. Homework Equations dS=dQ/T ΔU=Q+W The Attempt at a Solution The main thing I don't understand in this question is how we...

I understand that the change in Gibbs Free Energy at equillibrium is 0 and this leads to the equation -deltaH=TdeltaS. My questions here is that if a reaction is at equillibrium, how can there be any change in enthalpy or entropy at all? Why wouldn't these terms be 0?

consider an irreversible cycle. There will be no changes in the state variables (like U, S) of the system undergoing the cycle, but for the surroundings, there will be change in the state variables, in fact, entropy increases. my question is, what happens to the internal energy of the...

My understanding is that matter tends to converge and form stars and in those stars fusion creates heavier atoms from lighter atoms, and this process repeats continuously. if this is true wouldn't it imply that throughout these star cycles the average atomic mass will just increase, and as the...

I don't know what I did wrong for this question, but I assume something is wrong as my solution is extremely simple and this is a 20 marks question... 1. Homework Statement Refer to uploaded image. Homework Equations Pressure = h ( density in kg/m^3 ) ( gravitational acceleration) The...

Basically, if the size of the event horizon(EH) of a black hole is R (radius) can the rate of change of this R or dR/dt be faster than the speed of light(c)? When it comes to expansion of an EH of a black hole: Does the event horizon immediately expand? For example, if one black hole consumes...

I built a pressure chamber to test small parts for leaks at 1000 psi. I can measure the pressure with an accuracy of ± 1 psi. I found that small changes in ambient temperature ± 2 °F can result in a slow but profound change in the pressure in the system, say 25 psi. Insulating the chamber...

Light travels more slowly through light-transmitting substances such as air or glass, otherwise no lens would refract light. so does this mean that the speed of light is not a universal constant?

Homework Statement Using change of summation index show that: $$\sum_{k=1}^{n} (k + 1)^3 - \sum_{k=1}^{n} (k-1)^3 = (n + 1)^3 + n^3 - 1$$Hence show that: $$\sum_{k=0}^{n} k^2 = \frac{n}{6} (n + 1)(2n + 1)$$ 2. The attempt at a solution For the first part I changed the summation index like...

Homework Statement I want to change integral variable to jx it means (w=jx) Homework EquationsThe Attempt at a Solution but as you see the bounds of integral are different from the book text , what is my mistake?

Homework Statement On shifting the origin to a point P, the axes remaining parallel to the old axes,the equation ax+by+c=0 is transferred to ax+by+c+k=0.Show that the locus of P is the straight line ax+by=k. 2. Relevant equation 1. ax+by+c=0 2. ax'+by'+c+k=0 The Attempt at a Solution In the...

Homework Statement in this question , it's not stated that whether the temperature change from 20°C to -20°C or -20°C to 20°C . I'm confused... Homework EquationsThe Attempt at a Solution I think it should be changing from 20°C to -20°C so delta T = (-20-20) = -40°C , am i right ?

Homework Statement (a)How much heat must be added to a block of 0.120kg of frozen ammonia initially at 100oC to convert it to a gas at 80oC given the following information? (b) assuming this could be done using a reversible process what would be the total entropy change associated with this...

So i am 18 years old , and i just graduated high school with a high score . recently i got accepted into medical school and my parents are pushing me hard to study there . aside from school work , i have been extremely interested in technology , i did some extensive research on programming...

Dear all, The Hamiltonian for a particle in a magnetic field can be written as $$\hat{H} = \frac{1}{2}g\mu_B\textbf{B}\cdot\boldsymbol\sigma$$ where ##\boldsymbol\sigma## are the Pauli matrices. This Hamiltonian is written in the basis of the eigenstates of ##\sigma_z##, but how is it...

Homework Statement in the notes , i was told that ∂A is the resistance of aluminium rod...I'm wondering the change length of steel rod that we can 'see' is ∂ st or ∂T(st) ? Homework EquationsThe Attempt at a Solution I think the change length of steel rod that we can 'see' is ∂ st ?

Why isn't ##\frac{\partial L}{\partial t}\frac{\partial t}{\partial \dot{q_m}}## included in (5.41), given that ##L## could depend on ##t## explicitly?

Okay, best to provide some background here. I am trying to understand the light coming from the LED's over my aquarium. I have blue moon lights I think at about 540nm and 450nm. Oddly enough, when they are on, there is a green tinge to the light. I had assumed that this was because the light...

Homework Statement A rope has an end fixed and the other is passing through a pulley and has a body attached to it. The fondamental frequency of the rope is initially ##f_1=400 Hz##. If the body is then put in water the fondamental frequency of the rope becomes ##f_2=345 Hz##. If the linear...

Homework Statement Find the change in diode voltage if the current changes from 0.1 mA to 10 mA. Ans. 120 mVHomework Equations V2-V1=VTln(I1/I2)The Attempt at a Solution That is all the information given. The only equation I can think to use is the diode voltage/current relationship, but a...

I just have a simple question to ask people of physics since I keep on forgetting to ask my physics teacher. Does changing your direction while in motion affect your velocity? If so why? What forces cause it's velocity to decrease. Assuming that friction is present.(Also would it affect an...

I get two different answers, ##a^2## and ##0.5a^2##, by using two different methods. Which is the correct answer? The family of curve for ##y^2=4u(u-x)## is given by the blue curves, and that for ##y^2=4v(v+x)## is given by the red curves. Method 1: Evaluate the integral ##I## directly in...

Hi there, I was just trying to perform a change of variable on a differential equation as shown below. The original second order ODE is written in terms of a dependent variable ## \theta ## and independent variable ##q##. I have used the expression ## q = \sqrt{\frac{z\tau'}{LT_R}} ## and...

How are the intensity of a sound wave and the Doppler shift of frequency related togheter? That is, if the source or the observer are in relative motion, how does the intensity change? For a sound wave $$I=\frac{1}{2} \rho \omega^2 A^2 c=2 \pi^2 \rho f^2 A^2c$$ (##c## is sound speed, ##\rho##...

Homework Statement A particle with a charge of 2e moves between two points which have a potential difference of 75V. What is the change in potential energy of the particle? Homework Equations U = (75 V)(2e) The Attempt at a Solution [/B] When a particle with charge e moves through a...

Homework Statement Let $$\vec H = ih_4^{(1)}(kr)\vec X_{40}(\theta,\phi)\cos(\omega t)$$ where ##h## is Hankel function of the first kind and ##\vec X## the vector spherical harmonic. a) Find the electric field in the area without charges; b) Find both fields in a spherical coordinate system...

Homework Statement An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle...

Question regarding different percentage changes. If I have a monthly rental fee of \$100 in July with a discount of 60%. I will pay \$40. In the month of August the monthly rental fee is \$100 with a discount of 45%. I will pay \$55. My discount has decreased by %15. However my...

Homework Statement The diagram below shows an electrolysis cell which contains 1L of an aqueous 1M copper(II)sulfate solution. If 0.4 moles of electrons pass through the cell, the concentration of copper ions after passage of the charge will be A) 0.4 M B) 0.8 M C) 1.0 M D) 1.2M...

Homework Statement Cu2+ ions react with Fe2+ ions according to the following reaction. Cu2+ + 2Fe2+ --> Cu + 2Fe3+ At equilibrium, the concentration of Cu2+ ions is not changed by the addition of A) Cu2++B) Fe2+C) CuD) Fe3+. Homework EquationsThe Attempt at a Solution I chose A through...

I have Windows 2010 with the corresponding Microsoft Word. Both left-to-right and right-to-left text directions are available upon click (the paragraph sign pointing one way or the other), because I live in a country where both are common. I use both directions, but mostly I use the...

Hey, working on something for a personal project and was wondering if you could point me in the right direction. I have a 47 inch hollow steel tube that I'm going to cut the end 6 inches into a half circle tube . I have a load of 200 lb at the top and am wondering how about I would quickly...

Imagine potential well which in t=0 switches to a different potential well (instantly), like in the picture below. So in negative times the wavefunction density should tend to be localized in the first well, in positive times to be localized in the second well...

The pink spheres cause an acceleration of 1 cm per second squared towards themselves. The aqua spheres cause an acceleration of 2 cm per second towards themselves. All spheres have the same mass. The spheres are attached to a massless, yet mysteriously solid perfectly circular green...

Homework Statement Consider having a battery, its voltage let's say 20 volts. If you connect this battery to a wire. Its resistance is zero. If you precisely measure the voltage at the end of the wire, Would it equal 20 volts or no? Homework Equations dV = I R The Attempt at a Solution Well...

Homework Statement http://imgur.com/Sk6YkIf . You can take Va to be volume of cavity and Di to be density and Vo to be volume of cube and A to be surface area of container and h to be height of liquid column and Vi to be volume of immerser part of cube. Prove if water level will rise or will...

What is the change in entropy of thermodynamic environment if it changes its temperature during the process and the process is not reversible? I'm slightly confused because, on the one side, in that case ##\Delta S_{gas} \neq -\Delta S_{surroundings}##, since ##\Delta S_{universe} >0## but on...

Homework Statement Hi I know my picture has 2 problems, but let's just focus on the first problem parts a and b. So for part a it ask for the final frequency after the ant landed, and part b is the kinetic energy difference. Basically the ant=.01kg, diameter of cylinder is .115m, the weight of...

I'm a 3rd year graduate student doing atomic physics experiment. I was thinking of changing my group to do theoretical biophysics for a few reasons. Did any experimentalist here change to theory? What was the transition like?

Homework Statement You have a ukulele and you change the strings tension so that it becomes tighter. First the frequency was 431 Hz and after we tightened the string the frequency. how much bigger does the force have t be to get that frequency? Homework Equations PA*V^2 = F (P = density, A =...

Does quantum gravity play role inside brain in ever changing perception of time?

I have a problem to understand the de Broglie wavelength. We know that also particles undergo scattering and interference at a double slit. The interference pattern is calculated by the use of the de Broglie wavelength which is defined as lambda = h / p ; p is the momentum of the particle. This...

Given a sample of nitrogen gas (assume ideal gas conditions), the following conditions were observed inside the container. n = 0.75 moles at 253 K, and pressure = 0.5 atm. Then, an ISOTHERMAL IRREVERSIBLE COMPRESSION on the system forced by a constant Pexternal = 10 atm reduced the initial...

I am trying to prove that the above is true when performing the change of variable shown. Here is my attempt: What I am not quite understanding is why they choose to isolate the partial derivative of ##z## on the right side (as opposed to the left) that I have in my last line. This ultimately...

Assuming incompressible uniform streamlined flow, with fluid flowing from a wide tube into a tapering section then on into a narrow section... Would the be a little kink in the pressure at the junction of the tubes and the taper? Each flow line is accelerating towards the central line, so one...

Production function Q(K,L) without equation However partial derivatives are given Partial derivatives: Q(K,L) = (K^2 - KL + L^2)/(K+L) + 4K . ln(K+L) Derivative to K Q(K,L) =( K^2 + L^2) / (K+ L) Dervative to L A. Calculate the derivative in point (10,L) If I am correct...

Homework Statement Calculate ΔH for 2 mols of Nitrogen for the following transformation: 1 bar, 21°C → 200 bar, 21°C Given that molar Cp = 4R 2. The attempt at a solution How am I supposed to find the ΔH? From what I learned, there can only be a change in enthalpy when there's a change in...