Square Definition and 1000 Threads

Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$

I don't know what to say. sqrt(4) = +/- 2, but constants are fixed. When written sqrt(4), it seems sqrt(4) is a constant, but not in the latter case. Help!

$$x^{2}+1 \neq n! $$since $$x^{2}+1=(x+i)(x-i) $$so ,$$ x^{2}+1$$ has only prime of the form of (4k+1) , where n! has prime of the form( 4k-1) and (4k+1) . :oldbiggrin:

I recently came across the following interesting problem. Suppose A = BC where A,B, and C are matrices. We know a ton of A's and their corresponding C's. We want the least square estimator of B. When A and C are vectors the solution is well known. But what is the solution when they are...

$\int\frac{1}{\sqrt{16+4x-2{x}^{2}}}dx$ factored out 2 then completed the square $\int\frac{1}{\sqrt{2\left[9-{(x-1)}^{2}\right]}}dx$ next?

I found that the series represented by An = n∗(n+1)/2 - k never includes a perfect square if and only if the prime factorization of 8∗k+1 includes a prime factor, p, to the ith power where p = +/−3 mod 8 and i is odd and that this can be proved mod p(i + 1) For instance, 8* 4 + 1 = 3^1 * 11^1...

Homework Statement A particle of mass m is confined to a space 0<x<a in one dimension by infinitely high walls at x=0 and x=a. At t=0, the particle is initially in the left half of the well with a wavefunction given by, $$\Psi(x,0)=\sqrt{\dfrac{2}{a}}$$ for 0<x<a/2 and, $$\Psi(x,0)=0$$ for a/2...

Homework Statement Show that if a square matrix A satisfies A3 + 4A2 -2A + 7I = 0 Mod note: It took me a little while to realize that the last term on the left is 7I, seven times the identity matrix. The italicized I character without serifs appeared to me to be the slash character /. then so...

hi! when I send a square wave to a digital oscilloscope it detects the signal + dc signal. I wanted to know why. I was thinking about internal resistance of coaxial cable i was using. signal got out of an oscilloscope/wave generator and in channel A of the same oscilloscope/wg. It was +-1...

Homework Statement Integrate f(z) = Re(z) = \frac{z+\bar{z}}{2} along the contour of the square {z = x + iy | |x| ≤ 1, |y| ≤ 1} with counterclockwise rotation. Homework Equations Cj: φj(t) = z0 + (z1 - z0)t C1: 1 -i + 2it C2: 1 +i - 2t C3: -1 +i - 2it C4: -1 -i + 2t The Attempt at a...

I recently posted a suggested proof to a theorem and wish to mark the finish of the proof with a filled-in or shaded/black square as some texts do ... I typed in \square as a guess and got an unshaded square ... how to do get a shaded or black square? Hope someone can help ... Peter

I have just begun studying electrostatic and I'm trying to do this exercize: We have a square with charges +q , -2q, +2q, -q1)Compute the electrostatic field \vec{E}at the center of the square. I did this way : I find \vec{E_A}=\frac{q}{2 \pi \epsilon_0} \vec{u} {E_B}=\frac{-q}{ \pi...

Homework Statement Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2. The Attempt at a Solution I honestly have no idea where to begin with this problem. Any ideas?

Homework Statement The expectation value of <P^2>= -ħ∫ψ* ∂^2ψ/∂x^2 dx For the Guassian wave-packet ψ(x)=(1/(π^1/4)(√d))e^-((x^2)/(2d^2)) Limits on all integrals are ∞ to -∞. Homework Equations <P^2>= -ħ∫ψ* ∂^2ψ/∂x^2 dx ψ(x)=(1/(π^1/4)(√d))e^(iKx)-((x^2)/(2d^2)) The Attempt at a Solution Ok...

Hello, in Griffith's section on the Finite Square Well, ##\psi(x)## (what is the name of this anyway?, I know ##\Psi(x,t)## is called the wave function but how do I call just ##\psi(x)##?) Anyways, The solution is For x < a and x > a, the terms that are infinite as x approaches infinity are...

Homework Statement Problem 2.4 from Griffiths Intro to Electro[/B] Find the electric field a height z above the centre of a square loop with sides a and linear charge density λ. height is given to be z and sides given to be a, ∴ distance from origin to side is given by a/2 Homework Equations...

The integers $x$ and $y$ have the property that for every non-negative integer $n$, the number $2^nx+y$ is a perfect square. Show that $x=0$.

Why do the sound waves reflect and form standing wave when they travel along a string with sinusoidal waveform? But they do not reflect back when they are in square waveform ?

Homework Statement Homework EquationsThe Attempt at a Solution (a) $$ \int_{0}^{a} \mid \Psi (x,0) \mid^{2} \hspace {0.02 in} dx = 1 $$ $$ \int_{0}^{a} \mid A[ \psi_{1}(x) + \psi_{2}(x) ] \mid^{2} \hspace {0.02 in} dx = 1 $$ Since the ##\psi_{1}## and ##\psi_{2}## are orthonormal (I don't...

hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective...

hi all... i have problem about square roots for fast calculation, like below sample : is there fast calculation method not commonly/usually ways. it's possible? please, see my picture? thanks in advance.. susanto

Hello everyone, This is probably going to come off as a very silly question. However, I have not had calculus in several years. I was angry that my physics textbook did not have a derivation of Electric Potential Energy. So, I finally came across it, and I see that the integration of the...

For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...

I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...

I am wondering if anyone has used AD8333 to demodulate a square wave input (Not the LO, but the RF input).

I understand how to solve these equations when the square is on this side of the equal sign: x2 + 8x + 7 = 27 But when the square is on the other side, I am thrown. Like this one... x2 = 14x - 33 The solutions manual shows the next step as the following, but what do you do to get to this...

Hey guys, It is stated that a 100% perfect square shaped wave have infinite odd harmonics and it is impossible to produced theoretically. But, assuming if a perfect square wave is produced, what would it sound like? I remember someone said it in Youtube it would actually sound like a clarinet...

say i have the matrix (4,2,5,6,3,1) and on top I have (1,2,3,4,5,6) i.e. a 2x6 permutation matrix. Let's call it sigma. how would I calculate (sigma)^2? I can break it down into cycles: sigma = <1,4,6>compose<3,5> thanks.

I'm going through an explanation in a number theory book about Tonelli's algorithm to find the square roots of a quadratic residue modulo ##p## where ##p## is prime, i.e. I want to solve ##x^2 \equiv a \pmod{p}## with ##(\frac{a}{p}) = 1##. The book goes as follows: Let ##p - 1 = 2^s t##, where...

Hello This is not exactly a homework problem. I was browsing through an old book, "Elementary Algebra for Schools" by Hall and Knight, first published in England in 1885. The book can be found online at https://archive.org/details/elementaryalgeb00kniggoog . I was studying the process of...

I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...

Homework Statement A long squared rod with sides ##l##, thermal conductivity ##\lambda ##, specific heat ##c_p## and density ##\rho ## is cooled with water with constant temperature. Inside our squared rod we have a long square heater with sides ##l/2## and is completely centered inside the...

In the renaissance Leonardo DaVinci discovered that the perfect square is 1:1:618. I would like to know if there is a perfect square measure, then is there a perfect measure for a triangle or a circle? If so, could Pi be measured by a new and other calculation system which is similar to...

Homework Statement A square coil rotates around an axis passing through the center. It is inside a magnetic field of B= 0.6T uniform and constant. The side of the coil is a = 2cm, the resistance R is 0.1 ohm. The coil is powered by a generator that gives an emf = 0.2 + 0.24sin(ωt). The current...

Homework Statement Consider a square of side length 1. Two points are chosen independently at random such that one is on the perimeter while the other is inside the square. Find the probability that the straight-line distance between the two points is at most 0.5. 2. The attempt at a solution...

Homework Statement Consider a square hill barrier produced by a 10V potential. Incident upon this barrier is a steady stream of 5eV electrons. (a) If half the electrons are transmitted, how thick is the barrier? (Please derive the transmission probability rather than merely quoting it.)...

$$\int_{}^{} \frac{1}{\sqrt{16+4x-2x^2}}\,dx$$ $$\frac{\sqrt{2}} {2}\int_{}^{} \cos\left(\frac{x-1}{3}\right)\,dx$$ So far ? Not sure

Hi! :o I'm stuck :confused: I was thinking I need to use the equation $f=kw^2$ but I'm really not sure.

Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...

A perfect square inside a circle (so the inner square's corners touch the circle) and a perfect square surrounds the circle (so the circle touches the sides of the outer square. Are the extra bits between the inner square and the circle equal to the extra bits between the circle and the outer...

Show that for any square matrix, the matrix A + ( A )^t is symmetric. My attempt. I know that A square matrix has the property that asub (ij). Where i=1,..., m and j=1,..,n. M=n(same number of rows and columns). I know that a transpose of a matrix means to interchange the rows with columns...

I have come across a bit of conflict in wording of some physics and chemistry textbooks about the probability of finding particles in certain places. To be more specific, I have come across 3 different statements: 1. $$\int_a^b {| \psi(x) |^2 dx}$$ The above integral is said to give the...

Homework Statement What are the fundamental frequencies for a 50 kHz square waveform of 50% duty cycle and a 25 kHz sinusoidal waveform, respectively? (The duty cycle of a square waveform is the ratio between the pulse duration and the pulse period.) Homework Equations My teacher then gave...

I don't recall ever doing this but maybe I have. z2 = a = p [cos Ψ + i sin Ψ] = √3 + i*√3 p = √6 Ψ = π/4 Using the formula in the notes, z = 61/4 * exp[i*(π/4 + 2π*k)/2], k = 0, 1.

Homework Statement In the figure, four charges, given in multiples of 5.00×10-6 C form the corners of a square and four more charges lie at the midpoints of the sides of the square. The distance between adjacent charges on the perimeter of the square is d = 1.30×10-2 m. What are the magnitude...

Hi, I'm doing a fit using Chi-square distribution. I have a data set and their errors, I found the best estimate minimizing Chi square, as usual, and I like to found the error bars of my best estimates but I don't know how to do that. Which is the standard form to do it?

Homework Statement Prove that the X^2 distribution is stochastically increasing in its degrees of freedom; that is if p>q, then for any a, P(X^2_{p} > a) \geq P(X^2_{q} > a), with strict inequality for some a. Homework Equations 1.(n-1)S^2/\sigma^2 \sim X^2_{n-1} 2.The Chi squared(p) pdf is...

Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? Homework Equations I know that the equation for this is 10 (log R2/R1) The Attempt at a...

Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? & If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I...

Homework Statement Let m be the number of numbers fromantic the set {1,2,3,...,2014} which can be expressed as difference of squares of two non negative integers. The sum of the digits of m is ... Homework EquationsThe Attempt at a Solution I got a solution from a magazine but I didn't under...