Expression Definition and 999 Threads

Homework Statement In this pattern, what is the algebraic expression for the term t? -15, 30, 90, -360 Homework Equations t= term number The Attempt at a Solution no idea

Homework Statement \lim_{x \rightarrow 0} \frac{(1+tan(3x))^{1/3} x^2}{log_2(arcsin(x^3)+1)} Homework Equations The Attempt at a Solution i tried to use l'hopital twice but i get a very weird function, so there another way to calculate it?

Homework Statement prove that: 1-exp(-iwt)= 2i*sin(wt/2) Homework Equations exp(iwt)= cos (wt) + i*sin(wt) The Attempt at a Solution I attempted to express the exponential into sum of cos and sin and considering t=2*t/2 in order to obtain an argument like (t/2) (using...

Homework Statement There's a problem that involves triple integrals, but basically, I've boiled all of it down to the following single integral but cannot proceed any further. ∫u2 sqrt(a2-u2) du from 0 to a where a is a constant Homework Equations The Attempt at a Solution I attempted to use...

Homework Statement Find the exact value of the following expression. \sqrt[3]{10+6\sqrt{3}}+\sqrt[3]{10-6\sqrt{3}} Homework Equations The Attempt at a Solution Don't know where to start. I guess we can factor out a 21/3 but I don't see how that would help. Any clues? Perhaps some factoring...

simplify and answer should be in positive exponents. (((4x^6)^3(4y^-8))/((2x)^4(12y^3)^2))^1/2 please help and thanks

Homework Statement Derive an expression for the rate of interactions in a fixed target experiment, for which the beam of incoming protons has a current I, the target density is ρ(g/cm^{3}), the target thickness is d and the interaction cross-section is σ. You assume that the beam particles...

Homework Statement A solid body at initial temperature T0 is immersed in a bath of water at initial temperature Tw0. Heat is transferred from the solid to water at a rate \dot{Q}=K\bullet(Tw-T), where K is a constant and Tw and T are instantaneous values of the temperatures of the water and...

How would I write 1 + n + n(n - 1) + n(n - 1)(n - 2) + ･･･ + n! in sigma notation? If it's possible.

I am trying to simply G1 = G1(1+F1) / (1 + G1F2(1+F1)) in terms of G1, G2, H2, and H3 where F1 = G2/(1-G2H2) and F2 = G3 / (1-G3H3) i got the result (G1(1-G2H2)(1-G3H3) + G1G2(1-G3H3)) / ((1-G2H2)(1-G3H3) + G1G3(1-G2H2) + G1G2G3) however, the book gives the result with a +1 in the...

Homework Statement A self propelled vehicle of mass m travels in a straight line. The vehicle has an engine which provides constant power P so that the acceleration 'a' at an instant is given by a=P/mv where v is the speed of the vehicle and all frictional resistance is neglected. Determine...

Homework Statement Consider three univariate distinct functions f_1(x),f_2(y),f_3(y). Let H be given by the following integral: H=\int_{0}^{f_1(x)} G(f2(\xi))G(f3(\xi))d\xi The Attempt at a Solution Then, computing dH/dy should give zero. However, I am not certain of this because...

Homework Statement a,b,c,d are real numbers ab+bc+cd+da=16 Find the minimum value possible for a²+b²+c²+d² Homework Equations ab+bc+cd+da = (a+c)(b+d) x^2 \ge 0 for some real x The Attempt at a Solution 1st approach:2(a^2 +b^2 +c^2 +d^2) + 2(ab+bc+cd+da) = (a+b)^2 +(b+c)^2...

Dear all, If someone could help me solve this mathematica NDSolve problem, that would be really nice. Here is a related, simpler problem to the one I am having. Suppose I want to solve the nonlinear ODE \left(2 r + f(r) f'(r) \right) (1 + f'(r)^2) + r f(r) f''(r) = 0 subject to the...

Homework Statement A metronome is a device used by musicians to help them adjust the timing of their music to a standard number of beats per minute. The position of the moveable slider determines the frequency. It is possible to build a simple mechanical metronome using a light stick...

Newtons first law should not be termed an expression of inertia LAW I. EVERY BODY PERSEVERES IN ITS STATE OF REST, OR OF UNIFORM MOTION IN A RIGHT LINE, UNLESS IT IS COMPELLED TO CHANGE THAT STATE BY FORCES IMPRESSED THERON. - «Isaac Newton`s Principa» In case inertia could be removed from a...

Hi guys, I'm having a bit of trouble splitting the RHS of the following expression into real and imaginary parts: (χ'+iχ")/A = \frac{1}{ω-ω_{0}-iγ/2} (It's to find expressions for absorption coefficient and index of refraction, but that's irrelevant). I've defined a = ω-ω_{0} and b =...

Homework Statement Three charges with values + 20 μC, -10 μC and -10 μC are placed at the corners of a 0.10m square, as shown. c) Consider a sphere of radius 0.3m which totally encloses all three charges. Using Gauss's law derive an expression for the flux through this surface. Homework...

Homework Statement Here is the question: Homework Equations The Attempt at a Solution I know that SHM is: accel = -(constant) (displacement) Linear from my book says: Ax = Ftotal/m (dont quite get this) Any help? THanks!

Hello everybody, I have some problems in finding an analytical expression for this product: \sum_{j=0}^{N}(N-j)e^{-ijy}\cdot\sum_{k=0}^{N}(N-k)e^{iky} . I have solved the problem for several Ns, applying the Euler rule 2\cos(x) = e^{ix} + e^{-ix} Now, I'm trying to express the...

Homework Statement http://img513.imageshack.us/img513/88/71893688.png Homework Equations Not applicable. The Attempt at a Solution http://img441.imageshack.us/img441/846/14479081.png I'm already stuck! I calculated both expressions and they don't equal each other. :(

Hi all, Let f:[0,\infty)\rightarrow\mathbb{R} be a bounded measurable function such that \lim_{x\rightarrow\infty}x^2f(x)=1. Find an integral expression for \lim_{\lambda\rightarrow 0^+}\frac{\int_0^{\infty}(1-\cos(x))f(\frac{x}{\lambda})dx}{\lambda^2}. This one is really bizarre to me...

When sketching a graph I'm told to assume that the expression: f(x) =( e^x)/x Tends towards the infinite as x tends towards the infinite. Can someone show me how to check this? Thanks

Homework Statement (xy’+z)’.((xz)’+y') The Attempt at a Solution (xy’+z)’.((xz)’+y’) =(x'+yz’).(x’+z’+y’) =x’x’ + x’z’ + x’y’ + yz’x’ + yz’z’ + yz’y’ =x’ + x’z’ + x’y’ + yz’x’ + yz’ + z’ Can it be further siplify?

Hi guys... this problem is really annoying me How to find: \displaystyle{\sum_{k=0}^{n}\frac{1}{2^k+3^k}} I can clearly see that it converges \frac{1}{3^k+3^k}<\frac{1}{2^k+3^k}<\frac{1}{2^k+2^k}...

Which of the two is a better expression for the time period of a simple pendulum? t-=2∏\sqrt{(l/g)} or t=2∏\sqrt{(1/T/m)} ; l=length of the pendulum T=time period of the pendulum m=mass of bob...

Homework Statement Prove: for any real number x, -|x|\leqx\leq|x|. Homework Equations Only the definition of absolute value is allowed. The Attempt at a Solution Don't even know where to start

Homework Statement Prove: |ab|=|a||b|. (Hint: Consider the cases separately for various signs of a and b.) Homework Equations I think it asks me to prove it only from the definition of absolute value (if it is possible). The Attempt at a Solution |ab|= \frac{(ab), if (ab)\geq0}{-(ab), if...

A rope of negligible mass is wrapped around a uniform solid cylinder, of radius R, that can rotate freely about its axis, which is horizontal and fixed. A block hangs vertically from the rope and causes the cylinder to spin. The blocks mass, M_B is 4 times the mass, M, of the cylinder. Find an...

Homework Statement 1+2x+(4!x^(2))/((2!)^(2))+(6!x^(3))/((3!)^(2))+(8!x^(4))/((4!)^(2))+... Homework Equations Uhhhhh... The Attempt at a Solution Well, the denominator looks like it's going to be (n!)^2. And this expression appears to be using values of N≥0. But I'm not so sure...

Homework Statement Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x Homework Equations Trig identities. The Attempt at a Solution I used the identity: 1 + tan^2(x) = sec^2(x) I get for numerator: 1 + tan^2(x/2) I kept denominator same: 1 - tan^2(x/2) I get the...

problem solved, thanks

Hello, I am reading this paper about quantum gravity, trying and failing to follow along in the derivation of this, eq (204) p. 72, expression for the scale factor: a(t) = a_1 \left( 1 + \frac 3 2 ( 1 + \omega ) H_1 (t - t_1) \right)^{\frac 2 {3(1+\omega)}} (I'm not sure what the...

Hey guys, I was wondering how to get the expression for pauli matrices. I know that for one electron: S_i = \frac{\hbar}{2} \sigma_i But I also know that you can get to the above expression by explicitly calculating the matrix elements of the Sz, Sx and Sy operators (in the basis generated...

In Ramakrishna's paper, http://arxiv.org/ftp/arxiv/papers/1111/1111.1922.pdf , he derived equation (9), page 5. It is a difference of two square-roots using an approximation method. Can anyone help in how this is done? Thanks

hi, let's take something simple, for example: (a>b) && ((b>c) && c>d) || (d > c) Intuitively, it's easy to work out given the values of a, b, c and d and just evaluating the brackets in order of precedence. i.e. Is b > c?? then is c > d Then in addition to the above answer being...

I am trying to understand how, for a given physical system it is possible to come up with the correct expression for the lagrangian and thence the least action formulation from which the governing equations can be derived by application of the euler lagrange equation. From what I have seen so...

Homework Statement The ground state wave function for a particle of mass m moving with energy E in a one-dimensional harmonic oscillator potential with classical frequency omega is: u(subscript 0) (x)= N(subscript 0) exp((-alpha^2)(x^2)/2) and alpha=sqrt (m *omega/h-bar) where...

Homework Statement Reduce the expression to one that just contains xor and/or xnorHomework Equations (A'B'C')+(A'BC)+(ABC')+(AB'C)The Attempt at a Solution C'(A'B'+AB)+C(A'B+AB') C'(A\ominusB)+C(A\oplusB) not really sure what to do next.Do the C' and C cancel each other out?

Is there a simple way to find the integer values of f(x)=(a+5x)/(6x+1) with a, x integers.

Homework Statement With f(x)=-\lgroup\frac{a}{2}-\frac{x}{2b}\rgroup\ln\lgroup\frac{a}{2}-\frac{x}{2b}\rgroup-\lgroup\frac{a}{2}+\frac{x}{2b}\rgroup\ln\lgroup \frac{a}{2}+\frac{x}{2b}\rgroup and z=\frac{df}{dx}=\frac{1}{c} find an expression of x in terms of c. Homework...

Homework Statement Simplify the following expressions (x'y'+xy'+x'y) (p+q'p)(p+qr) Homework Equations Laws of boolean algebra The Attempt at a Solution For the first one I've found many ways to solve it... something isn't right here (x'y'+xy'+x'y) =x'(y'+y)+xy' =x'+xy'...

Homework Statement Reduce, x(w+y'+z') + (w+x)y'z + wx'yz + wxy Homework Equations + stands for OR * (multiplication) stands for AND ' NOT The Attempt at a Solution I tried to combine some terms but I cannot find a good start... x(w+y'+z') + (w+x)y'z + wx'yz + wxy = xw + xy'+...

Homework Statement I need to simplify the boolean expression by algebraic manipulation as much as possible. (a+b+c)*(a'+c)*(a'+b') Homework Equations + stands for OR * stands for AND (or no operator between variables) ' Stands for NOT The Attempt at a Solution I tried but I do not...

Homework Statement A toy cart of mass M1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass M2 rests on top of the cart. The coefficient of static friction between the block and cart is μ. The cart is moving up a ramp at angle θ. Find an expression for...

A toy cart of mass m1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass m2 rests on top of that cart. The coefficient of static friction between the cart and block is μ. Find an expression for the maximum tension T that will not cause the block to slide on...

A flat, circular plate (mass Mp, radius Rp, thickness Tp) rotates parallel to the surface of the Earth on a frictionless axle. As it spins, a point on the top of the disc traces a circle each time the plate completes a rotation. in terms of the number of rotations per minute (N/min), create...

Homework Statement csc(cos^-1 u) Homework Equations Fundamental identities properties The Attempt at a Solution The book is incredibly vague on how to do this. I tried multiplying csc by (cosθ/cosθ) to get cotθ*secθ. I'm not sure if this is the right thing to do, or what to do...

I'm having trouble trying to decipher this: A number U is on the unit interval. Write the algebraic expression for "U differs from 0.5 by more than 0.25" This is what I did...am I doing this correctly? 0.5-U > 0.25 after doing the algebra U < 0.25

Homework Statement The position of an object of mass m is given by: http://imageshack.us/photo/my-images/62/20110920161443.jpg/ Find expression for the velocity and the acceleration and deduce the force components acting on the particle. Homework Equations W = vr, v = u+at , f = ma v = d/t...