Expression Definition and 999 Threads

if you have a sequence of events {A_1, A_2, ...} then an expression for the event that "infinitely many A_i's occur" is: U(n = 1 to inf, U(m = n to inf, A_m) ) but wouldn't U(n = 1 to inf, A_n) also satisfy this?

1. Simplify ei6x(1+e-i10x)/(1+ei2x) 2. i have no idea how to simplify this its supposed to be in terms of cosines 3. i don't how i can simplify this such that i can use the 1/2(e^x +e^-x) = cosx formula

ok .lets say the expression we have is ex the taylor expansion becomes 1+x+x2/2+... integrating becomes x+x2/2+x3/6+...+c so how do we know that c = 1? for it to become back to ex becos it is said that integral of ex = ex do we just let x be 0 to find c = 1? does it work for all...

Homework Statement Hi I have an expression on the form \frac{\tau }{{\alpha - \varepsilon + i\eta }}\left( {1 + \frac{\tau }{{\alpha - \varepsilon + i\eta }}G} \right) where i denotes the complex i. I have to bring this into the form \frac{\tau }{{\alpha - \varepsilon +...

Given 2NO(g) + Br2(g) <--------_____> 2NOBr(g), Concentration (M) [NO] [Br2] [NOBr] Initial 2.5 5.0 1.0 Change P Q...

Homework Statement The expression {\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}} has a volume integral equal to 4\pi for arbitrary "a". Homework Equations The Attempt at a Solution \int_0^R {\int_0^{\pi /2} {\int_0^\pi {{\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}}...

Homework Statement Compute and plot the entropy S(T) for the truncated system. My actual question is what the function S(T) should be. Homework Equations Consider a bound single-particle system with a discrete, equidistant (spectral constant = delta e) energy spectrum. epsilon_j...

Homework Statement I'm looking for a closed form expression for the partition function Z using the Canonical Ensemble Homework Equations epsilon_j - epsilon_j-1 = delta e Z = Sum notation(j=0...N) e^(-beta*j*delta e) beta = 1/(k_B*T) t = (k_B*T)/delta e N is the number of excited...

Homework Statement Rearranging an equation...can't quite see how it's done. Homework Equations r=\sqrt{2.5^{2}cos^{2}(t/2)+5^{2}sin^{2}(t/2)} r=2.5\sqrt{cos^{2}(t/2)+4sin^{2}(t/2)} r=2.5\sqrt{1+3sin^{2}(t/2)} The Attempt at a Solution I know that cos^{2}(x)+sin^{2}(x)=1 but...

Hi, I have a problem on how to convert the imaginary parts of expression into all real parts. For example: x1 = - (a + ib) x2 = (a + ib) x3 = - (a - ib) x4 = (a - ib) My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used...

[/tex]1. Homework Statement [/b] Given: \phi(x)=\phi^+(x)+\phi^-(x) Where: \phi^+(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a(\mathbf{k}) \mathrm{e}^{-\mathrm{i}kx} and \phi^-(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a^\dagger...

Homework Statement That's basically the whole question in the title there, ie; Derive an expression for the fermi energy of a 2d structure at 0 kelvin. 2. The attempt at a solution Basically the first part of the question had us sketching the Fermi-Dirac distribution function at 0K for...

Books for self-teaching previously taken math courses, and other problems :) What I want to focus on: While I am a CS student, I am also interested in mathematics subjects as a whole and want to re-familiarize myself with some of the courses I took in the past. I received high grades, but to...

Hello everyone...can anyone tell me what is the modified expression for the gravitational potential in GR which takes into account the fact that the speed of gravity is finite (c, to be precise)...In fact, it may be a non-sense question as I haven't started to read GR yet...Is there any...

Factoring a very long expression! please help (x^6) - (4x^5) + (x^4) + (10x^3) - (4x^2) - (8x) then: x((x^5) - (4x^4) + (x^3) + (10x^2) - (4x) - 8) my teacher skipped many steps and ultimately found: x * [(x+1)^2] * [(x-2)^3] I guess he's assuming we know how to get through it. Can...

how to solve this hamilition? and Does this expression has an exact solution?

I must derive the 1/4th life expression for a first order rxn. ln(\frac{[A]_{\circ}}{[A]_{t}})=kt ln(\frac{[A]\circ}{\frac{1}{4}[A]_{\circ}})=kt_\frac{1}{4} ln(4)=kt_{\frac{1}{4}} do I set t=1/4 ? \frac{ln(4)*4}{k} \frac{5.545}{k} What am I doing wrong here? The answer is allegedly...

Homework Statement Sketch the graph of a function g(x) with a corresponding domain on (-5, infinity) whose first derivative is always positive and whose second derivative is always negative. Then come up with and algebraic expression to model your graph. Homework Equations The Attempt at a...

Homework Statement Convert the following expression into sum of products and products of sums (AB+C)(B+C'D) Homework Equations Distributive Property The Attempt at a Solution for product of sums it would be (AB+C)(B+C'D) since it is already in this form. When calculating sum of...

Homework Statement Show that the expression A, T(dP/dT)|V - P is equal to expression B, T^2 * [d(P/T)/dT]|V Also, show that expression C, -[d(P/T)/d(1/T)]|V is also equal to expression B Homework Equations A: temperature * (dPresure/dTemperature at constant volume) -...

Homework Statement Given z(t) as above, write out the expression for the vertical velocity Homework Equations z(t)=Asin(vt) where z(t) is the vertical position of a test particle, A is the amplitude of its motion, and t = 0 is the time when the particle is at the midplane The...

I need the following expression simplified. 36/[64.4*(0.5+(2+ x)*((1-(1/4)*x^2 )^0.5)) ]-x*((1-(1/4)*x^2 )^0.5)=0

Homework Statement Black body radiation inside a cavity at temperature T may be thought of as a gas of photons with an energy distribution given by the function n(E) given by n(E)dE = A [E^2 / (e^(E/kT) - 1) ] dE Where A is independent of E and T. (k is Boltzmann constant) The...

Homework Statement Today I had a physics lab. It involved a hanging mass on a string that hung off the table. It went through a pulley and the string was then spooled around a rotating spool on the table. We first measure the radius of the spool. Then we figured out the mass it took to...

The Attempt at a Solution I'm attempting to solve a question with a few unknowns, and I managed to get it to the following form: tanx(1-cosx)=0.25 I just can't seem to simplify it further and thus solve.. Any ideas?

Homework Statement Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.Homework Equations The Attempt at a Solution Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I...

Homework Statement The limit of \frac{8x^3+x^2-5x}{3x^4-5x^2+2} as x goes to 1Homework Equations Evaluate this limit algebraically.The Attempt at a Solution Tried using 1 instead of x. The denominator becomes 0. Divided denominator by (x-1) but couldn't continue.

Homework Statement Derive an expression for the temperature of an ideal blackbody so that its radiated light at the peak intensity wavelength has exactly enough energy to excite the ground state to fourth excited state. Homework Equations I = σ*T4 λm*T = 2.9 * 10-3 m * K E = hf = hc/λ...

I understand how to compare 2 functions and tell which bound they are in... but what I cannot comprehend is, given a single function... how do you write which bound it is in? Given a simple for loop like : for(int i = 0; i<n; i++) { for(int i = 0; i<j; i++) { System.out.println("Haha.")...

Homework Statement f(x) = \frac{x}{x-1} + \frac{x+1}{3x} Homework Statement need to take the first derivative of this expression... I can do it but I am curious as too why i cannot take the derivative of \frac{x}{x-1} and then just add it to the derivative of \frac{x+1}{3x}...

By 'equivalence', I mean of the computational kind -- i.e. in the same way any universal computer can emulate any other. First of all, hi there, I'm not sure I put this question in exactly the right forum, but it seems to me that most dualities currently being discussed fall under the...

Ship A is located 3.3 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B? (b) Write an expression for the position of A relative to B as a...

Hello, geniuses! :) I am having a problem in chemistry... What is this systems equilibrium constant expression? And under what conditions (temperature, pressure, concentrations) you can most fully get rid of SO2? I really have no idea with what to start... :/

Homework Statement What is the totaly power emitted by the sun over all wavelengths (frequencies) according to the (incorrect) classical Rayliegh-Jeans expression for ρt(v) Homework Equations ρt(v)dv=8piv^2kT/c^3 dv The Attempt at a Solution I'm not sure how to start this one...

ln(-1)/i=pi this equation does not use limits or integrals, as you can see, but it does involve imaginary numbers. Does this make it an open expression, or does the fact that it uses i not matter?

So is there any set of defined rules that help in the simplification of regular expressions? Because till now I would simply try and look at the patterns and see whether this or that simplified version would generate the same.Intuitive, but now always fast or correcct. So is there any...

Homework Statement Find dP/dt of 2048000(t^2)(e^1600t)+5120t(e^-1600t)+3.2(e^-1600t) Homework Equations The Attempt at a Solution 2048000(2t(e^-1600t)-1600(t^2)(e^-1600t))+5120((e^-1600t)-1600(e^-1600t))+3.2(-1600(e^-1600t)) After moving the t over to simply the first part and...

Homework Statement hi I'm new and thanks in advance! I'm trying to work out a problem I've been given but having difficulties! I am given a scope for the current in a capacitor and I'm trying to determine the expression of charge in the capacitor firstly, then when t = 10ms Homework...

Hi all, Anybody pls help me to convert cosmic time to conformal time (numerically)... is there any analytical expression for conformal time, \tau , except d\tau=dt/a(t) ? can we approximate \tau \approx -1/aH ?? pls help... Anuradha

Here's the question: Let f be the function satisfying f'(x)=x\sqrt{f(x)} for all real numbers where f(3)=25. a. Find f''(3) b. Write an expression for y-f(x0 by solving the differential equation \frac{dy}{dx} = x\sqrt{y} with the initial condition of f(3)=25. For a, I got...

Homework Statement Expression is p^3-(x^2+xy+y^2)p+xy^2+x^2y=0 where ^ shows power Homework Equations The Attempt at a Solution the solution is (p-x)(p-y)(p+x+y)=0

Hi all, I'm trying to fill in some mathematical steps from a derivation I'm reading in a research paper. I want to see that the following expression \text{Div}\left(\nabla u\frac{ \phi ' \left(|\nabla u|\right)}{|\nabla u|}\right) is equivalent to (\frac{\phi '...

Homework Statement I have 2 charges: Q1 = 300 uC located at (1, -1, -3) m Q2 = ?? uC located at (3, -3, -2) m Q1 feels a force from Q2 of F1=(8i - 8j + 4k) N 1. Find Q2 2. Find the expression of the E-Field at (3, -3, -2) m (at Q2) Homework Equations F=(k|Q1*Q2|) / r^2 E=(k|q|)...

a.cos(wt) + b.sin(wt) = M.cos(wt + ϕ) Can you give me M and ϕ in terms of a and b?

Hi, I am doing an experiment. I am heating a sample and changing a temperature on one surface of the sample as a sine function of time. Measuring heat flux I am trying to predict heat response of the sample. After some sine cycles heat response is in every next sine cycle the same. How do you...

I'm going over the Landau's Mechanics, and can't get over two hurdles. The first is the following(I'm not good with latex here, so please bear with me): Landau asserts that the action S' between t1 and t2 of a Lagrangian L such that L is a function of (q+dq) and (q'+dq') minus the action S...

Hi! This is my first post, so i apologise if i leave out any information. I need to derive an expression for the theoretical velocity of flow in an open channel using the Bernoulli Equation. I realize it is probably a simple question but i am sort of a beginner. Any help appreciated...

Homework Statement Write the Trigonometric Expression as an algebraic expression. cos(2arccos 2x) Homework Equations Probably the inverse properties, I'm not sure. The Attempt at a Solution I know I can rewrite this equation as. u= arccos 2x cos(2cos u=2x) I can also...

Ok, I have an Expression which is attached and it needs simplifying. What I have done is got 12logx But I don't think this is correct. Another possible place I got to is logx4/logx1/3 Which one is it?

Simplify the attached expression using any relevant logarithmic rules I haven't really done much with logarithms, so i didnt know where to start?