Expression Definition and 999 Threads

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

Homework Statement Express the repeating decimal as a series, and find the rational number that it represents 1) 3.2\overline{394} Homework Equations Geometric Series (a/1-r) The Attempt at a Solution I tried putting the value into a series by having n=1 as it goes to infinity Ʃ3.2...

Homework Statement find the magnitude and angle of the moment moment=-2.8i-1.53j+2.24k force tension=2.4 kNHomework Equations rxf=rfsin(theta)The Attempt at a Solution i used the cross product to get i j and k tried sin and cos of vectors but didnt work. inverse tan of vectors won't give...

Homework Statement A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b much greater than a and resistance R1. A Resistance dependent voltage is applied to the larger loop, having a slow sinusoidal variation in time given by...

Homework Statement Not long ago I had a similar problem, which I was able to solve after reading this thread, but for this question I'm stuck and I could use a small hint. Homework Equations The Attempt at a Solution Thanks

A bar of length l, breadth b, and depth d when loaded at the centre by a load W sags by an amount given by δ = W l^3/(4bd^3Y). Here Y is the young's modulus of the wire. My textbook says that we have to use little calculus to derive this expression. Can you please derive this?

"Waves" of sine expression So, I have been working with a lot of Math today(sorry if I am asking so many questions), and I found and expression. All sine functions use radians. sin(y) + sin(y) / sin(y) Now, assuming you start with 1, if you were to plot y on a graph with variable x...

I know that in an AC circuit at the steady state a capacitor behaves like a short and inductor behaves like an open. Since the inductor is open wouldn't that just mean the answer is 0?

what does it mean.

Homework Statement ℝ(3-7i)^4 Is this asking for just the real part of this complex expression? I suppose I could go about expanding the whole thing out, but is there a more convenient method? We've learned a few methods, such as expressing it in polar form and such. But here the angle...

Homework Statement A 300-foot-long cable, originally of diameter 5 inches, is submerged in seawater. Because of corrosion, the surface area of the cable diminishes at the rate of 1250 in 2 /year. Express the diameter d of the cable as a function of time t (in years). Homework Equations...

1. Homework Statement (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5) 2. Homework Equations Find an expression for the sum of the series. Give your answer as a product of linear factors in n. 3. The Attempt at a Solution I haven't tried it since I don't know what to do.

Homework Statement (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5) Homework Equations Find an expression for the sum of the series. Give your answer as a product of linear factors in n. The Attempt at a Solution I haven't tried it since I don't know what to do.

How do you come up with this approximation? [1+H(t-t_0)- \frac{1}{2}qH^2(t- t_0)^2]^{-1}\approx1+ H(t_0-t)+ \frac{1}{2}qH^2(t-t_0)^2+ H^2(t-t_0)^2 Is there a rule that leads to this approximation?

Hey folks, I'm using Molecular Dynamics to calculate the formation energy of an interstitial in FCC metal. Basically what I did is to minimize the perfects structure, and then find the minimized energy of the lattice with [100] dumbbell interstitial, to get the difference in energies. I...

How is it possible...that the integral performs an infinite amount of calculations to give the area under a curve. The integral expression has to find an infinite amount of areas of the (dx by f(x)) rectangles. I'm guessing there is a simple answer to this, I'm just not quite piecing it...

In the lab you place a beaker that is half full of water (density pw) on a scale. You now use a light string to suspend a piece of metal of volume V in the water. The metal is completely submerged, and none of the water spills out of the beaker. Give a symbolic expression for the change in...

Homework Statement According to the Debye theory of the specific heat of a three-dimensional solid, the internal vibrational energy of a volume V of a solid containing N atoms is: U=A(T)\int^{x_{D}}_{0}\frac{x^{3}dx}{e^{x}-1} where x=\frac{\hbar\omega}{k_{B}T} is the dimensionless form...

Homework Statement The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero. Homework Equations Electric Field...

Hello everyone, I have a bit of an issue regarding scaling of an expression. So, the scenario is as follows. I have a confidence value that can be associated with the solution given by an optimization routine and it is as follows: C = exp(-A)/(exp(-A) + exp(-B)) where A, B and C are...

Homework Statement Given vectors {\bf r}=\left[r_1,r_2,r_3\ldots{}r_n\right]^T {\bf e}=\left[e_1,e_2,e_3\ldots{}e_n\right]^T I need to write the sum \sum_{i=1}^{n}r_ie_i^2 in terms of {\bf r} and {\bf e} Homework Equations Nil. The Attempt at a Solution Without...

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 Suppose you have three functions, f_{1}(x_1),f_{2}(x_2),f_{3}(x_3). Consider the following expression: H=\int_{0}^{f_{1}(v_1)} G(f_2(\xi))G(f_3(\xi))d\xi, where G is some continuous function. What is \frac{\partial H}{\partial x_{j}}, j\neq 1? The Attempt at a...

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...