Expression Definition and 999 Threads

Taken from Hobson's book: How did they get this form? \dot u^{\mu} = - \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u^{\mu} g_{\mu \beta} \delta_\mu ^\beta = - g_{\mu \beta} \delta_\mu ^\beta \Gamma_{v\sigma}^\mu u^v u^\sigma \dot u_{\mu} = - \frac{1}{2} g_{\mu \beta} \delta_\mu ^\beta...

Homework Statement For the circuit in (Figure 1) , suppose va=10cos16,000tV vb=20cos4000tV. Suppose that R = 700Ω . Write the steady-state expression for io(t) as io=I′ocos(ω′t+ϕ′)+I′′ocos(ω′′t+ϕ′′), where −180∘<ϕ′≤180∘, −180∘<ϕ′′≤180∘, and ω′>ω′′. Find the numerical value of I′o. Find the...

Simplify the expression below: $\dfrac{w^2(z-x)(z-y)}{(w-x)(w-y)}+\dfrac{x^2(z-y)(z-w)}{(x-y)(x-w)}+\dfrac{y^2(z-w)(z-x)}{(y-w)(y-x)}$

Homework Statement Identify and fix all hazards in ##f = (ab + \bar{a}c)(c + \bar{b}) + ab##. Re-check if the final expression obtained is hazard free. Homework EquationsThe Attempt at a Solution So I used a binary tree and found a static 1 hazard present for ##bc = 11##. The hazard was ##a...

Hey! :o How can we find the regular expression of a language given by an automaton M?? Could you give some hints?? (Wondering) Which are the steps that we have to follow so that we convert an automaton into a regular expression?? (Wondering)

How did they arrive at this expression? I understand the ##Q^2## term in the nominator and the ##r = r_0 (A)^{\frac{1}{3}}## term in the denominator. Where did the ##\frac{\alpha}{2}## term come from? Putting in Z=40, A=100 gives ##3.3 \times 10^{14} J##, not ##65 MeV##. The energy term...

Simplify $\left(\sqrt{3}\sec \dfrac{\pi}{5}+\tan\dfrac{2\pi}{5}\right)\tan \dfrac{2\pi}{15}$.

Homework Statement I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x) I want to simplify this expression.Homework Equations None The Attempt at a Solution I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it...

Find a closed form expression for $$\sum_{k=1}^{n^2}\dfrac{n-\lfloor\sqrt{k-1}\rfloor}{\sqrt{k}+\sqrt{k+1}}$$.

This is from from Sakurai and Napolitano HW Prob #2.6. I've done the HW problem and can fit all the pieces together with the mathematical formalism, but even afterwards I'm still scratching my head wondering what I'm looking at. I start with the commutator [[H,x],x]. If I take...

Homework Statement According to my textbook, the electric flux through a disk of radius R situated at a height d from the xy plane is given by: ##2 \pi k_0 Q [1- \frac{d}{\sqrt{R^2+d^2}}]## Where ##k_0 = \frac{1}{4\pi \epsilon_0}## I'm having some difficulty obtaining this answer. Homework...

What is this asking for? Is it asking for the trig expression in the form of x and y? Or is it asking for something else?

Hi, this is my online homework exercise. I think I did it right, but the system gives me wrong answer... Can someone please check what I did y=$\sqrt{x+\sqrt{x+\sqrt{x}}}$...

Hi Folks, I have a symbolic A=18*1*18 array containing symbols/expressions. I want to populate certain entries of this array into another matrix. For example K(1,1)=A(1,1,1) I get the following ? The following error occurred converting from sym to double: Error using ==> mupadmex Error in...

If A is an additive subgroup of a ring R, A is said to be an ideal if Ra is contained in A for all a in A; that is, if every multiple of an element of A is again in A. Is it true that A is an ideal of R if Ar is contained in A for all r in R? To me it seems like they are equivalent statements...

My working: S3 = A S2 = B S1 = C' S0 = D' F = Sum-Minterm(0, 1, 2, 4, 5, 8) (Basically i find when is X smaller then Y) Used Kmap to arrive at A'C' + B'C'D' + A'B'D' Am i correct?

Hello! (Wave) I am writing a text in LATEX and I wrote this: \begin{align*} \epsilon_p(a+b)&=((a+b)\pmod p, (a+b)\pmod{p^2}, (a+b)\pmod{p^3}, \dots )\\ &=(a\pmod p+b\pmod p, a\pmod{p^2}+b\pmod{p^2}, a\pmod{p^3}+ b \pmod{p^3}, \dots) \\ &=(a\pmod p, a\pmod{p^2},a\pmod{p^3}, \dots)+(b\pmod...

May there exist an integral domain R, with fraction field K, that fulfills the following condition: there exists x\in K, x\not \in R and a maximal ideal \frak m of R{[}x{]}, such that \frak m does not contain x-a for any a\in R ? Motivation : I am trying to prove a difficult result. A way to...

Homework Statement A particle with charge q moves with velocity v near a long, straight wire which has a current I flowing through it which generates magnetic field B. Give an expression for the magnitude of the force on this particle in terms of q, v = | v | and the magnitude of the magnetic...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] (A+B)&(C+D) + (A+B)&(C+D)' + C (A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans (A+B)&[(C+D)+(C'&D')] + C by Distributive I'm just wondering if I did anything wrong in this simplification or...

Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...

How can one compute and/or tell if a given expression is a traveling wave? I thought of using the characteristic wave equation δ^(2)ψ/δt^(2)=v^(2)δ^(2)ψ/δx^(2). An example of an expression would be ψ(x,t)=A(x-t). Should I partially derive this expression twice with respect to x and then to t...

I just wanted to post a solution for anyone interested. Any notes on how to solve would be nice for others. 1. Homework Statement Mastering Physics (3rd edition) Problem 26.40 The figure (Figure 1) shows a thin rod of length L with total charge Q. Part A) Find an expression for the...

This comes from one of the research papers that I'm reading. The authors decompose Eq. 1 and obtain Eq. 2. After several attempts, I have been fairly unsuccessful at obtaining Eq. 2 from Eq. 1. I have tried using partial fractions decomposition without much success. Any help would be greatly...

ds2=guvdxudxv Why is the invariance of ds2 as shown above? Why can't it be something like ds2=guudxudxu or ds2=dxudxu ? Isnt it based on Pythagoras theorem? Why must it have 1 u and 1 v instead of just 2 u or 2 v? Forgive me for such dumb question as I just started.

If $x,\,y,\,z>0$ and $x+y+z=1$, find the minimum of $\left(x+\dfrac{1}{x}\right)^{10}+\left(y+\dfrac{1}{y}\right)^{10}+\left(z+\dfrac{1}{z}\right)^{10}$.

(tg 570* sin 1469) / (ctg 495 * cos 781) = Its in degrees

Evaluate the expression $(2^{2^{2014}}+1)(2^{2^{2013}}+1)\cdots(2^{2^2}+1)(2^{2^1}+1)(2^{2^0}+1)+1$

I encountered this expression while trying o express $f(x)=\ln\left({\frac{1+x}{1-x}}\right)$ in terms of a power series: $$\int \left[ \sum_{n=0}^{\infty}(-1)^n x^n + \sum_{n=0}^{\infty}x^n\right] \,dx$$ The book simplifies this expression as $\int \sum_{n=0}^{\infty}2x^{2n} \,dx$ by expanding...

Take for example a fetus of 2 weeks old and a baby of 2 years old. The fetus doesn't show any limbs, skull. How do I know that is a human fetus ? :nb)

Homework Statement A voltage source given by ##v_s(t)=25cos(2\pi\times10^3t-30^\circ)## is connected to a series RC load. If R = 1MOhm and C = 200pF, obtain an expression for ##v_c(t)##, the voltage across the capacitor. Answer known to be: ##v_c(t)=15.57cos(2\pi\times10^3t-81.5^\circ)##...

i couldn't find the definition of Minterms and maxterms of boolean's expression on the internet nor my book. Can someone explain it? I was given only this in my book, without any explanation.

Hello I'm working through the see-saw mechanism. This is currently from the one-generation section. (I haven't got to the three generation workings yet... although I'm guessing I'll come across something very similar in the three generation model) Could someone please tell me if it is correct...

Hi guys i need your help! How can i reduce this equation: (Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)] into this: (B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)? I'm totally depressed, I'm always stocked in sqrt part of the equation: if there's a techniques in dealing this kind...

Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to...

If $k^{101}=1$ and $k\ne1$, evaluate $\dfrac{k^2}{k-1}+\dfrac{k^4}{k^2-1}+\dfrac{k^6}{k^3-1}+\cdots+\dfrac{k^{200}}{k^{100}-1}$.

Homework Statement Find a closed form expression for the function f(x) which the power series Σn=0..∞ n(-1)nxn+1 converges to and determine the values of x for which f(x) equals the given power series. Homework Equations N/A The Attempt at a Solution I'm actually not sure how to start. First...

Homework Statement [/B] I need to differentiate the exponential function i = 12.5 (1-e^-t/CR) and I need to plot a table so that I can do a graph of i against t but I'm not sure how. (CR is the equivelant of Capacitance 20 Micro Fards and Resistance 300 Kilo Ohms)Homework Equations [/B] How do...

Mind-controlled transgene expression by a wireless-powered optogenetic designer cell implant. Kind of a sensationalized title, since it's really just interpreting brain waves through a BCI, but neat anyway. http://www.nature.com/ncomms/2014/141111/ncomms6392/full/ncomms6392.html

Homework Statement Between two metal plates a metal strip is inserted as shown on the figure. a) Calculate the electric potential anywhere inside the capacitor. b) Simplifly ##U(x,y)## for ##x>>a##. c) Calculate the electric field in the middle of the capactior. Homework EquationsThe Attempt...

Homework Statement Q. How to find Remainder of the following expression ##32^{32^{32}}\mod{}6=?## Homework Equations The Attempt at a Solution ##32^{32}\mod{}2=0 \implies 32^{32}=2x## ##32^{32}\mod{}3=1 \implies 32^{32}=3y+1## would it help to find the remainder of ##32^{32^{32}}\mod{}6##

Hi, I'm trying to covert a NFA to a regular expression and I've manged to come up with an answer but I don't think that it is right. Here's the question - http://i.imgur.com/NUHxTXY.png And here's my workings -...

PROBLEM SOLVED - the worked example I was referring too was wrong :/ ---------------------------- Hello, I've been stuck on a question in one of my SR problem sets for some time now, and managed to find a worked solution to a similar problem online. I've attached an image of the problem (the...

I have heard different things and want to get a "professional" opinion on this. It seems like the words "term" and "expression" are technical terms with specific definitions in math and I want to know what they technically refer to (not just the personal slang or informal definitions someone...

transform the first member to the second member $\sqrt{\frac{\sec^{2}(\phi)-1}{\sec^{2}(\phi)(1+\cot^{2}(\phi))}}+\frac{\csc^{2}(\phi)}{\csc(\phi)}\sqrt{\frac{\csc^{2}(\phi)-1}{\csc^{2}(\phi)}} = (1+\cot(\phi))(1-\sin(\phi)\cos(\phi))$this is what I tried so far...

Find the coordinates of the expression (cos x + sin x)^3 in the basis {1, sin x, cos x, sin 2x, cos 2x, sin3x, cos3x}. I don't understand where to start since I am dealing with cos and sin now. :confused:

Please, I'm stuck. How to get the rhs from the lhs? X^{\alpha}_{\ \ \alpha^{\ \prime}}X^{\beta}_{\ \ \beta^{\ \prime}}\epsilon^{\alpha^{\ \prime}\beta^{\ \prime}}=det X\epsilon^{\alpha\beta}

Homework Statement If a car has p litres of petrol in the tank it can travel a kilometres. With v litres of petrol in the tank it can travel b kilometres. Find an expression in terms of v in terms of p, b and a. 2. The attempt at a solution I just cross-multiplied how I was shown in class...

Homework Statement Evaluate the following: A XOR (B XOR C) = A XOR (BC' + B'C). Using Boolean expressions. [This question came up in my test today (as part of a review of 'Digital Logic Design') for my 'Computer Architecture' course. It was worth 6 marks. The total test was marked out of 15.]...

Homework Statement Assume you have a fully charged capacitor with initial condition V(0) = V_0 connected in series to two resistors R_1 and R_2. Derive an expression for the voltage over the capacitor with respect to time. Homework Equations 1. Kirchhoff's voltage law \sum_n V_n = 0 2. Ohm's...