Square Definition and 1000 Threads

Homework Statement Homework Equations V= a21/3 h The Attempt at a Solution I may be wrong or right I don't know. I'm pretty sure I did it right.

$\Large{S6.7.R.19}$ $$\displaystyle I=\int\frac{x+1}{9{x}^{2}+6x+5}\, dx =\frac{1}{18}\ln\left({9{x}^{2}+6x+5}\right) +\frac{1}{9}\arctan\left[{\frac{1}{2}\left(3x+1\right)}\right]+C $$ $\text{from the given I thought completing the square would be the way to solve this} \\$ $\text{but I...

How to find if a quadratic expression of the form 4x2 + 4.n.x - P ......(x,n and P are natural number) is a perfect square. For example, 4x2 + 64x - 31 Thanks.

Good afternoon, I'm glad I've joined this forum. Here's my doubt: I have a serie of values in a table like this: Case 1 34 55 Case 2 23 10 Case 3 55 40 etc... the 34 means the observed value, and the 55 the control group, and so on. It's easy to do the test of course if... The problem is: if...

The problem $$ \lim_{x \rightarrow \infty} \left( \sqrt{x+1} - \sqrt{x} \right) $$ The attempt ## \left( \sqrt{x+1} - \sqrt{x} \right) = \frac{\left( \sqrt{x+1} - \sqrt{x} \right)\left( \sqrt{x+1} + \sqrt{x} \right) }{\left( \sqrt{x+1} + \sqrt{x} \right) } = \frac{x+1 - x }{\left(...

Homework Statement Hi everybody! Our experiments teacher asked us to perform a reduced chi square test in order to estimate how good a model fits to our measured data. The experiment was the melde's experiment (vibration of a string) and we measured the frequency ##f_n## for ##n=1## to ##9##...

I read this statement from Lenard Audio. "When a large signal spike is created by un-plugging or plugging in signal leads, or when a pre-amp valve is driven hard into distortion (guitar amps), a large non-symmetrical square wave may cause a temporary DC Voltage to appear across a coupling...

I am interested in mini magnetospheres. How do i calculate the intensity of the field at a certain distance if i already know theits intensity at the source?

How ##4(x + \frac{1}{2})^2 + 1## can be ##(2x + 1)^2 + 1##?

I have this expression: $$\sqrt{ 1 - \frac{16}{\sqrt{x^2 + 16}}}$$ And the textbook simplifies it to $$\frac{x}{\sqrt{x^2 + 16}}$$ But I'm not sure how it does this.

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

Root of (-2-3) ^2 = -5 ( because root of squared number is the number itself) but alsoo square of (-2-3) is 25 and its root is (+5) /(-5). Therefore what is the correct answer and reason . I think it is -5(google answer is Also -5) but I don't have any reason. Please help me

Homework Statement 1. How did they complete the square for these equations in the picture below? What was their thought process? 2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out? When you divide, how does it cancel out to give you a...

How how can we calculate the future evolution of a particle after the infinite square well potential is (somehow) turned off, releasing it into a free state? Assuming that it was in the ground state before.

I am faced with the following question: Two point charges X and Y, exert a force F on each other when they are at a distance d apart (x and y are opposite charges). When the distance between them is 20mm, the force exerted on each other is 0.5F. What is the distance d? I know that, e.g...

Hi i am fatih from turkey.i am high school student.question is "how many squares are in an rectangle subdivided into unit squares?"(a<=b) My theorem about this question.Please write your comments.Thanks For your time, thanks all mathematicians !:)

Homework Statement F = k(Q2*Q1)/(r^2) Homework EquationsThe Attempt at a Solution I asked my teacher and he said that this is an inverse square law. Didn't say anything else. He also mentioned k is constant. I assume i can plug in random values and see if there is a pattern... k=1 for all Set...

Homework Statement there is a square on the XoY plane, centered at the origin (just outlines of the square) it has a charge Q (Q>0) and side 2L, i must evaluate the electric field along the z axis. see attached image Homework Equations E=k*q/r^2 The Attempt at a Solution So first i divided...

Homework Statement Suppose that ##Y \sim N_n\left(X\beta,\sigma^2I\right)##, where the density function of ##Y## is $$\frac{1}{\left(2\pi\sigma^2\right)^{\frac{n}{2}}}e^{-\frac{1}{2\sigma^2}(Y-X\beta)^T(Y-X\beta)},$$ and ##X## is an ##n\times p## matrix of rank ##p##. Let ##\hat{\beta}## be the...

Homework Statement In one of my revision guides, there is an experiment for calculating the acceleration of free fall using the electromagnet and trap door arrangement. The biggest error is in the measurement of the height over which the ball falls. The guide says: "You could reduce the error...

Homework Statement Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two Fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) >...

This property is given in my book. The square of any determinant is a symmetric determinant. Well it works when I take a determinant say 3x3 and multiply it by itself using row to row multiplication. But it fails if I multiply using row to column. Thanks

Hi there, I'm working on a problem right now that relates to least squares error estimate for polynomial fitting. I'm aware of techniques (iterative formulas) for finding the coefficients of a polynomial that minimizes the square error from a data set. So for example, for a data set that I...

Hello! Is there a way to extract the square root of this expression without expanding? Please teach me how to go about it. $4\left((a^2-b^2)cd+ab(c^2-b^2)\right)^2+\left((a^2-b^2)(c^2-b^2)-4abcd\right)^2$ I tried expanding it and it was very laborious and I end up not getting the correct answer.

Homework Statement Calculate the magnitude of the electric field at the center of a square 42.5cm on a side if one corner is occupied by a −38.2μC charge and the other three are occupied by −26.9μC charges. (This part done) Choose the correct direction of the electric field at the center of...

If I have something like: $$\lvert \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle \rvert ^2=c$$. where ##c## is any old real number. If I undid the modulus square to find: $$ \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle=\pm \sqrt{c} $$ Would I not have to consider...

Homework Statement Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur at...

Homework Statement √[/B] A particle in an infinite square well has the initial wave function: Ψ(x, 0) = A x ( a - x ) a) Normalize Ψ(x, 0) b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)Homework...

I've been trying to wrap my head around the relationship between temperature increase of an object at a distance and temperature of a heat source. From what I've found, the temperature increase of an object from thermal radiation is affected by the inverse square law...

I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...

I had a question similar to Σ0∞ (-1)^n (x)^(n/2) and attempted to solve it using the root test getting abs(√x)<1, but I've also seen some places answer it as √abs(x)<1 so am I skipping a step.

It is well known that a circular loop of steady current does not radiate, even though each individual charge is undergoing centripetal acceleration. How about a loop of steady current that is shaped in a square? Does this structure radiate?

Hello, I have the solution of a problem but there's something I don't understand Homework Statement Find the harmonic function in the square {0<x<1, 0<y<1} with the boundary conditions u(x,0)=x u(x,1)=0 ux(0,y)=0 ux(1,y)=y²tHomework EquationsThe Attempt at a Solution Part1:[/B] We first solve...

I Am Wanting to Find out who Created the inverse square law.

Homework Statement Consider a one-dimensional, non-relativistic particle of mass ##m## which can move in the three regions defined by points ##A##, ##B##, ##C##, and ##D##. The potential from ##A## to ##B## is zero; the potential from ##B## to ##C## is ##\frac{10}{m}\bigg(\frac{h}{\Delta...

Homework Statement Find the work done by the three-dimensional inverse-square field ## F(r) = \frac {1} {||r||^3} r ## on a particle that moves along the line segment from P(6, 2, 3) to Q(4,2,4) Homework Equations ## \int_C F \bullet dr = \int_a^b f(h(t), g(t)) \sqrt {(\frac {dx} {dt})^2 +...

Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...

I understand that this determines a probability, but of what exactly for a single photon? The probability that the photon will be detected on a surface where the photon is pumped, e.g. where on the surface the laser is aimed?

I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained? I found this below from here, but could not really...

I'm trying to visualize the effect of the inverse square law, not on a direct source of light, but on scattered light carrying visual data, such as that responsible for our everyday sight of things as well as our images of Earth from satellites. It seems to me that it should be true that, while...

Homework Statement A square of wire with side length 1.4 m rotates about an axis through one corner that is perpendicular to the plane of the square with an angular speed of 3 rev/s. There is a uniform magnetic field of 1.2 T perpendicular to the square. Calculate the EMF induced in the...

This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some...

What is the root mean squad (RMS) of a signal (or wave) and why is it important for electrical engineering? How do you Find it? What is it used for? Thank You All

Homework Statement Hello, I am using CasaXPS to model synthetic peak models for X-ray photoelectron spectroscopy data. I am fitting. The software has a lot of manuals online but they do not explain how they yield a Residual Standard Deviation, after each fit iteration. Most software use...

Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...

Homework Statement An electron in a finite square well has 6 distinct energy levels. If the finite square well is 10nm long determine: a) Approximate the possible values for the depth of the finite square well ##V_0##. b) Using a well depth value in the middle of the results obtained from part...

Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...

Find 5-digit number whose half is a perfect cube and one-third is a perfect square

Homework Statement For an upcoming lab I've been asked to build a circuit to convert a square wave (vi(t))e into a sine wave (v0(t)) by selecting appropriate resistor/capacitor values for the circuit below (from what I know, it's impossible to produce an accurate sine wave with just this, I...

Hi, I was wondering about the meniscus we get in a round tube, like a test tube or a boiling tube, or even a classic measuring cylinder. If we have a square transparent rectangle with water in - would this at all reduce the effect of the meniscus? How else is the effect of the meniscus reduced...