Square Definition and 1000 Threads

Quoting from Wiki, bolded section mine: What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?

How do I find the volume of this shape? The bottom is a square in the xy plane where \(0\leq x,y\leq 1\). The object isn't a prism or pyramid so I am not sure what to do.

Homework Statement Let ##S = \{ (x,y) \space | \space x=\frac{1}{n}, n = 1, 2, 3,... \}## be a subset of the unit square. Prove ##S## has outer content zero. Homework Equations ##C(S) = inf\{ \sum A_i \} = inf\{Area(P)\}## The Attempt at a Solution There are no answers I can check my work...

Here's my problems: How might you "rationalize the denominator" if the expression is \frac{1}{2+7√2+5√3} or \frac{1}{\sqrt[3]{2}+1}? I know that in typical problems where we rationalize the denominator, we simply have to multiply the denominator and numerator by the conjugate of the denominator...

Hi; How to raising a square matrix to the power of a complex number? for example: [1 2;3 4]^(1+i) or mathematics software such as Scilab how solve such problems? -->[1 2;3 4]^(1+%i) ans = - 0.1482039 - 0.2030943 - 0.3046414 - 0.4528453 Thanks in advance...

Homework Statement I'm trying to test a hypothesis that sending people both an email announcement and direct mail announcement produces significantly more enrollments in a free webinar than email or direct mail alone. I'd like to do an analysis on these groups created from 400 people...

Square Pulse Train Fourier Series help?? Homework Statement problem+directions below: Homework Equations ω=2\pif β=\frac{2\pi}{\lambda} The Attempt at a Solution Since the problem asks to make all time-dependent sinusoidal functions deal with x-direction, i don't think i need to...

Homework Statement Flux: a. Calculate the flux of the vector v1 = (1, 3 5) through a 2×2 square in the x-z plane (i.e., y = 0). b. Calculate the flux of the vector v2=(z, y, -x) through this rectangle:0≤ x ≤3, 0≤ y ≤ 2, z = 0.. The Attempt at a Solution I guess flux is suppose to be...

A reading from e=mc2 by David Bodanis, The big question though is why? Why is squaring the velocity of what you measure such an accurate way to describe what happens in nature? One reason is that the very geometry of our world often produces squared numbers. When you move twice as close...

Homework Statement A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations The following equation for the transmission coefficient, T, is given: T = [1 + \frac{V_0 ^2...

Homework Statement Show that for a square matrix the (i,j) entry is equlivant to the (j,i) entry in a symmetric matrix. Homework Equations The Attempt at a Solution I just felt this question was weird. They don't give the answers so I'm looking for confirmation. I guess...

Homework Statement A cubical box whose sides are length L contains eight electrons. As a multiple of $$\frac{h^2}{2mL^2}$$ what is the energy of the ground state of the eight electrons? Assume the electrons do not interact with each other but do not neglect spin. Homework Equations...

Homework Statement A conductor (wire) is folded into a square loop with each side having a length of a. Total charge of Q is transferred onto the conductor. Describe the line charge density of the square loop in equilibrium. (If I am interpreting this correctly what is required is...

Hi, This question is killing me (please note that it's not homework, this is from self study): The shaded region inside a square of side "a" consists of all points that are closer to the centre of the square than any of its edges (emphasis on any of its edges--the resulting region is like a...

Homework Statement A uniform square plate ABCD has mass 0.8 kg and side length .8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...

This is a well-known result in complex analysis. But let's see what people come up with anyway: Challenge: Prove that there is no continuous function ##f:\mathbb{C}\rightarrow \mathbb{C}## such that ##(f(x))^2 = x## for each ##x\in \mathbb{C}##.

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

Homework Statement Particle is in an infinite square well of width ##L## on an interval ##-L/2<x<L/2##. The wavefunction which describes the state of this particle is of form: $$\psi = A_0\psi_0(x) + A_1\psi_1(x)$$ where ##A_1=1/2## and where ##\psi_0## and ##\psi_1## are ground and first...

How would you integrate it? \int \frac{d \varphi}{\sqrt{1 + \frac{a^2 b^2 \sin^2 \alpha}{(a \sin \varphi + b \sin (\alpha - \varphi))^2}}} I know that solving it numerically would probably be easier, but I would prefer a closed form solution in this case.

Homework Statement A uniform square plate ABCD has mass 2.5 kg and side length 0.8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...

Homework Statement There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm. What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?The Attempt at a...

Homework Statement A square loop of wire is made up of 50 turns of wire, 45 cm on each side. The loop is immersed in a 1.4T magnetic field perpendicular to the plane of the loop. The loop of wire has little resistance but it is connected to two resistors in parallel as shown. (a) When the loop...

Homework Statement I'm trying to demonstrate that if: $$\hat{L}_z | l, m \rangle = m \hbar | l, m \rangle$$ Then $$\hat{L}_z^2 | l, m \rangle = m^2 \hbar^2 | l, m \rangle$$Homework Equations $$\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$$ $$\hat{L}_z = -i\hbar \left [ x...

Hi, I have a very basic question that suddenly hit me regarding square roots. Why this is equal \[\sqrt[3]{(1+x^{3})^{2}}=(1+x^{3})^{^{\frac{2}{3}}}\] but this isn't \[\sqrt{(x-2)^{3}}\neq (x-2)^{\frac{3}{2}}\] (well according to Maple it isn't) I understand why the first one is correct...

Hello. This isn't a homework, but rather my own self-study of a textbook (Franklin's Classical Electromagnetism), so if this is an inappropriate place for these types of questions let me know. Homework Statement Four equal charges q are placed at the vertices of a square of side L. What is...

Homework Statement Square lamina (of side a) of uniform density. Find I about a diagonal. Homework Equations I = ∫ dm*l^2 The Attempt at a Solution So I drew a square and its diagonal and I imagine a differential mass drawn somewhere on the lamina. The distance squared to that...

0. The app does not have the template built in so ill do my best, sorry i don't have a computer right now. 1. This is a personal project, and there is a lot to it but I'm cutting out down to where i need help. Imagine a 2x2 grid of squares (2d for now). The center vector is at (0,0), and the...

Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...

Homework Statement Hello. Imagine a particle bound in a square well potential of potential energy V0 if |x| > a 0 if |x| < a The wave function of the particle is: (ignoring the time dependency) -A*exp(kx) if x<-a B*sin(3*pi*x/4a) if |x|<a A*exp(-kx) if x>a where k =...

How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it...

Homework Statement Get the value of a if \sqrt{6-\sqrt{a}}+\sqrt{6+\sqrt{a}}=\sqrt{14} The Attempt at a Solution nothing succesfull Feel free to move this thread,..I actually place it here to tap more brains

Homework Statement Homework Equations not sure The Attempt at a Solution I am not sure how to start this problem.

Hello, I've been trying to find online where I could calculate my grade based off a college curve. So the average grade on the test was a 63. The RMS is 16. I got a 86. So what will my grade curve to? This is out of 50 people. Also, the professor curves to a 70 (I think).

Homework Statement A square loop of wire of side length L lies in the xy-plane, with its center at the origin and its sides parallel to the x- and y- axes. It carries a current i, in a counterclockwise direction, as viewed looking down the z-axis from the positive direction. The loop is in...

Let $a,b,c$ be positive real numbers with sum $3$. Prove that $√a+√b+√c≥ab+bc+ca$.

I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))...

Homework Statement Consider a particle in 1D confined in an infinite square well of width a: $$ V(x) = \begin{cases} 0, & \text{if } 0 \le x \le a \\ \infty, & \text{otherwise} \end{cases} $$ The particle has mass m and at t=0 it is prepared in the state: $$ \Psi (x,t=0) = \begin{cases} A...

oops I meant "Rate of change of area of a square with respect to its side length" Ok I have to use this annoying Stewart textbook for my Calc class in college. Most of the questions require what I like to call "Monkey Math," where you just memorize a set of steps and then follow them rigidly...

Homework Statement Calculate mutual-inductance between straight line cable and square shape frame, as shown on picture. Homework Equations I am not sure which equation will be used here because as far as my knowledge goes , mutual inductance should be concerned with turns in...

I'm comparing the shear formula for a beam in english and metric. But it seems the formula or result don't match. In English, the formula is Vc=2*b*d*sqrt(Fc) Given b=11.81102 inches d=18.11024 inches fc=4000 psi Vc=2*b*d*sqrt(Fc)=27056 lbs Now converting the units in metric...

In my physics book there is an example of making a square wave by "simply" summing up a few cosine waves. The book says these first three waves are the first three Fourier components of a square wave, yet when I sum the three wave functions up, I get something way off; as does my calculator...

Here is the question: Here is a link to the question: Find the constant necessary to make a perfect square trinomal 5c^2-8c+__? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hello MHB, I got stuck on integrate this function $$\int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx$$ my first thinking was rewrite it as $$\int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx$$ then use the identity $$\cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x)$$ $$\int...

Hi, I'm a bit of a newbie to additive synthesis.. I just want to clarify that I am doing the correct calculation before continuing. If I wanted to calculate the 5th harmonic of a square wave (the fundamental freq. being 200Hz and the amplitude of the fundamental being 1) would the...

Homework Statement A particle in the infinite square well has the initial wave function ## \Psi (x, 0) = Ax(a-x), (0 \le x \le a) ##, for some constant A. Outside the well, of course, ## \Psi = 0 ##. Find ## \Psi (x,t) 2. Homework Equations : Equation [1.0]:## \displaystyle c_n =...

Hi does anyone know the "formula/process" for the least square method if the are giving several (x,y) points and asking me to find y=Ax^2 + B?

An electron in the ground state of a one-dimensional infinite square well of width 1.10 nm is illuminated with light of wavelength 600 nm. Into which quantum state is the electron excited? ok so I first calculated the engery of the electron in the first ground state of the square well...

Working on a physics lab report regarding uniform circular motion, one of the questions asks to graph the Tension Force vs. the square of the speed. Another part of the same question asks what the slope of the graph represents, which is where I'm stuck.

Homework Statement Solve for the wavefunctions and energy levels of an infinite square well potential extending between -L<x<L. Hint: It may be worth noting that for a potential symmetric in x, then the observed probability density must also be symmetric in x, i. |ψ(x)|2 = |ψ(-x)|2. Homework...

Hi everyone I have these 2 integrate that I can't solve, I have tried them with mathematica and wolfram, but they can't find an answer, maybe someone have an idea on how I could tackle these 2 bad boy! The first one is $$\int{ \sqrt{ \frac{1+( \frac{1}{10}+ \frac{s}{25})^2}{ \frac {s}{10}+...