Expression Definition and 999 Threads

Homework Statement find the general formula to calculate the sum Homework Equations 1+11+111+1111+11111+....upto n terms The Attempt at a Solution 100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ... ==> (100+100+100+...upto n terms) + (101+101+101+...upto n-1 terms)...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement An N-turn circular coil of radius r with a total resistance of R is placed such that the normal to its plane is parallel to the +z axis. A uniform magnetic field varies with time according to B=B0sin(\omegat) where the amplitude B0 and angular frequency ω are constants...

Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...

Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...

Without the help of calculator, evaluate $\cos \dfrac{\pi}{7}\cos \dfrac{2\pi}{7}\cos \dfrac{4\pi}{7}$.

Hi Guys, I have an expression that i am struggling to manipulate into a laplace transform. This expression should fit one or a combination of the common transform pairs. I believe the transform the expression should be fitting is either a unit step 1/s a unit ramp 1/s^2 an exponential 1/s+a...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Okay, This could be the easiest math question on here... but I'm going to ask the dumb question anyway. I have several coordinate points to solve for, and in each case I subtract the same amount from the previous "x" to get the next "x" value (X2...3...4...5...). The only point where I...

Q4.) Quadratic equation: $$\frac{-2x^2-14x-49}{x^3-7x^2}$$

given : $\dfrac {x}{m}+\dfrac{y}{n} +\dfrac {z}{p}=1$ $\dfrac {m}{x}+\dfrac{n}{y} +\dfrac {p}{z}=0$ find: $\dfrac {x^2}{m^2}+\dfrac{y^2}{n^2} +\dfrac {z^2}{p^2}=?$

simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$

Hello! :) I have a question: Suppose that $\Sigma=\{0,1\}$.Is the language $\{0^{m}1^{n}:m+n \geq 2\}$ regular? I tried to find a regular expression.I checked the case $m+n=2$ and I found that the possible words are $00,01,11$ .But..how can I continue? :confused:

Homework Statement I need to obtain the minimum second order circuit of the function: Homework Equations The Attempt at a Solution I know that in order to get the minimum second order circuit, I need to use K-Map using both miniterms and maxiterm and compare them. My problem is to put the...

Hi, Homework Statement Consider the vector potential, \vec{A}(\vec{x}), below. The problem is to calculate \vec{A}(\vec{x}) explictly, and show that it has components A_{r}, A_{\theta} and A_{\phi} Homework Equations \vec{A}(\vec{x}) = \frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz'...

Homework Statement When pressure is applied to a liquid, its volume decreases. Assuming that the isothermal compressibility κ=-1/V(δV/δP) is independent of pressure, derive an expression for the volume as a function of pressure. Homework Equations The Attempt at a Solution I don't...

Hi, I've attached a screenshot in which a solution simplifies an expression given x>>a. I have been trying to simplify and express the equation as shown, but keep failing to recognize how they reached their solution. If anyone could provide a step-by-step breakdown that would be greatly...

Hello! Talking about propagation of an electro-magnetic field in a non-isotropic medium, I've got some troubles with the expression in object, used to show the Faraday rotation of the polarization of a field. Homework Statement An electro-magnetic field enters a particular medium...

Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D

P and k are four-momentum of two particles. I read in a paper which said that [\slashed{P},\slashed{k}]=\slashed{P}\slashed{k} - \slashed{k}\slashed{P} is time-reversal odd. Why?

Hello! Tchebysheff polynomials are often defined with trigonometric functions: T_m (x) = \begin{cases} \cos(m \arccos (x)) & -1 \le x \le 1\\ \mathrm{cosh} (m \mathrm{arccosh} (x)) & x > 1\\(-1)^m \mathrm{cosh} (m \mathrm{arccosh} |x|) & x < 1 \end{cases} But they are also polynomials, and...

Hi MHB, I am completely clueless about how to tackle the problem below, given I noticed $y$ increases as $x$ increases, so there is no maximum point over the entire domain for that function, that is for $x \ge 0$, isn't that so?(Tmi) For what value of $x$ is the expression in...

In the attached image, I am having trouble with point 66. I realize the notation is a bit archaic, so I'll explain as much as I can. [(x,y)∈]a means "the set of solutions of the proposition a(x,y)." For example, the set of solutions to the proposition x < y. -= means "is not equivalent to"...

how does $$\frac{5700}{\sqrt{15,300}}$$ turn into $$\frac{570}{\sqrt{153}}$$ ??

Homework Statement I did an experiment investigating what effect height has on force and now i need a theoretical value to compare it to Homework Equations f=ma but i don't think acceleration is constant here The Attempt at a Solution f=ma f=0.104x9.8 f=1.01 i got 49 N with...

I would like to get an answer or pointers to suitable material, on the following question: I know that ∫|f(x)|2dx is finite. Can we say that lim x→±∞ x*(d/dx)|f(x)|2 is zero? Are there any theorems about such limits with unknown functions that have some known properties? Basically this question...

Homework Statement A solid flywheel of radius R and mass M is mounted on a light shaft of radius r so that the axis of rotation is horizontal. A light, inelastic rope is wound around the drive shaft and is connected, via a light, frictionless pulley to a mass m, which is suspended a height h...

Homework Statement In a triangle ABC let A,B,C denote the angles of the triangle. Then maximum value of the expression sinA/A + sinB/B + sinC/C is Homework Equations The Attempt at a Solution Applying Cauchy Shwarz inequality \dfrac{sinA}{A} + \dfrac{sinB}{B} + \dfrac{sinC}{C} \leq...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

Hi, I'm reading a paper on foundations of QM where the expression below appeared \frac{1}{2}m\left(\frac{d^2 \overrightarrow{r}^2}{dt^2}\right)=m\left(\frac{d^2 \overrightarrow{r}}{dt^2}\right).\overrightarrow{r}+m\left(\frac{d \overrightarrow{r}}{dt}\right)^2 I cannot identify where it...

Hello, I have an array of length M. Some of the indices are non-negative. I need to derive a function/analytic expression (preferably linear or convex) that finds the span of indices for which the indices are non-negative. Example: Let p denote the desired vector. Let, p = [0 0 0.3 2.6...

Hello, This actually isn't a homework question, more of a curiosity, but since its a book problem I decided to post it here. Homework Statement An object is released from rest at time t=0 and falls through the air, which exerts a resistive force such that the acceleration a of the the...

Hello, using octave when I evaluate this expression (1+1/x)*x-x, with x = 10^(15) i get as result 1.125, I didn't undesrtood why, I know that octave show 15 digits in format long so when i evaluate (1+1/x)*x i get 1e15, the last digit is not visible and it is 1, so when i do substraction i get...

Homework Statement Find, using l'Hôpital's rule: lim x-> ∞ ((tan(ax)-atanx)/(sin(ax)-asinx)) Where a is a non constant greater than ± 1. Homework Equations -The Attempt at a Solution I can't work out anything from this point. I don't know how to change or factorize the expression (is there a...

Homework Statement In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx). Homework Equations The Attempt at a Solution The usual notation is: a,b,c are three sides of the...

Homework Statement So as a part of a very long question on homework for thermodynamics, I and some of my friends got into a debate about how to write an expression for entropy at a particular state. Homework Equations delS(state 1 to 2)= Cv*ln(T2/T1)+R*ln(V2/V1) (from constitutive...

Novice questions: 1. All complimentarities seems to be an expression of HUP... (for example from some of the quantum eraser experiments such as DCQE) Is that correct? I.e. Complimentarity is NOT a phenomena/mystery that is seperate/different from HUP 2. Can we derive/conclude...

Hi, Suppose I have \lim_{r\to 0} \left\{\int_0^{\pi} \frac{f(r,t)}{r^2}dt - \int_0^{\pi} \frac{g(r,t)}{r} dt\right\} and both integrals tend to infinity. So I combine them: \lim_{r\to 0} \int_0^{\pi} \frac{f(r,t)-r g(r,t)}{r^2} dt now at this point, the numerator in the...

Quantum -- Find the formal expression of the coefficient cn(t=o) Hello everyone, I'm really stuck on the first question of an exercise, so I can't start! :cry: Homework Statement ψ(x,t) a wave function normalized and solution of Shrodinger equation for a given potential. I the...

Homework Statement Draw the logic diagram for the following Boolean expression. The diagram should correspond exactly to the equation. Assume the complements of the inputs are not available. B(A'C'+AC) + D'(A+B'C) Homework Equations The Attempt at a Solution I can't find any...

Homework Statement Write the Sackur-Tetrode expression for the entropy of a monatomic ideal gas as a function of pressure, temperature, and number, S(N,T,P). Homework Equations S = Nk[ln(V/N(4πmU/3Nh2)3/2) + 5/2] PV = NkT U = (f/2)NkT The Attempt at a Solution I found that...

Homework Statement Formulate an expression that gives the focal length of a corrective lens, to be used in conjunction with a fixed lens. You may assume that both lenses are on the same plane, i.e. that they are very close together. The corrective lens should allow an object at a specified...

I have checked many textbooks and papers on SUSY and it seems that none of them mentions anything about the infinitesimal susy transformation on component fields in the case N\neq 1. So I am wondering what does it looks like, say for N=2 vector multiplet? Another related question is, do we need...

Homework Statement Simplify the expression using boolean algebra postulates, laws, theorems. (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) The Attempt at a Solution (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) 1. ((x +...

Homework Statement Build the truth tables for the boolean expressions. (x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')' The Attempt at a Solution Given that the expression is so complex I believe that I need to simplify first then proceed to build the truth table? Work so...

Hello, Is there some way to express the following integral in terms of some simpler functions? f(x,s) = \int^{\infty}_{-\infty} dk\, e^{-ks} \text{Ai}(-k) \text{Ai}(x-k) where the parameter s \in (0,1) and the coordinate x \in (-\infty,+\infty) The best I can come up with is to...

Homework Statement Why does this expression, given in cylindrical coordinates, rapresent an electrostatic field: $${\bf E(r)}=\frac{\alpha}{z^2}{\bf u_r}-2 \frac{\alpha r}{z^3}{\bf u_z} $$ Homework Equations The Attempt at a Solution I can't understand why the expression rapresent...

Homework Statement Simplify, if possible. (6w2-w-3) + (7w2-4w+5) Homework Equations The Attempt at a Solution I attempted to factor both expressions, but they don't seem to be factorable. Is this already simplified as much as possible, or am I missing something?

Matrice $$c_n$$ is a 2nxn2 matrice and is given by $$(\delta_{ij}+2\delta_{i,2n-j+1})_{ij}$$ determine the expression of $$|c_n|$$ progress: I have been drawing the matrice $$n=1,2,3$$ and calculate the determinant. As you see there is a pattern with the matrice and I would like to have tips...

I have the expression $$sin^{-1}(cosx)$$ I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help