Square Definition and 1000 Threads

A ball is let down a ramp on top of a table with initial velocity of 0 ms-1. When it reaches the end of the ramp, it is launched horizontally. Knowing that we don’t take air resistance or friction into account, and that the height of the ramp is h1, and that of the table is h2 relative to ground...

Hi, Is there a way of representing the Laplacian ( Say for 2 variables, to start simple) ##\partial^2(f):= f_{xx}+f_{yy} ## as a "square of Jacobians" ( More precisely, as ##JJ^T ; J^T ## is the transpose of J, for dimension reasons)? I am ultimately trying to use this to show that the...

I have been debating this issue for days: I can't find a recursive function of this equation: ##\large{\sqrt{2+\pi \sqrt{3+\pi\sqrt{4+\pi\sqrt{5+\dotsb}}}}}## Starting value 2 always added with pi has been trying to find a solution this for days now, is what I have achieved so far: This...

Homework Statement I am trying to calculate the contour integral of the complex conjugate of z around a square with sides of length 2 centred on the origin in the complex plane Homework Equations ∫ f(z) dz = ∫ f(t) (dz/dt) dt . It looks like the integral signs won't appear here but...

i have heard how our broadcasts will be seen by aliens far away or whatever. but i realize those signals are going to "attenuate" by d^-2 anyway... how come in astronomy we can see light sources millions of light years away? shouldn't those signals be far too weak to detect after such a long...

Fitting data to a linear function (y=a0+a1*x) with least square gives the coefficients a0 and a1. I am having trouble with calculating the uncertainty of a0. I understand that the diagonal elements of the covariance matrix C is the square of the uncertainty of each coefficient if there are no...

Hello. The curve y = x2 is a parabola that looks like this: I have a shape Square that looks like this: What I am noticing is that if I consider the equation y = x2 and also the shape Square, I find that there is no connection between them but the equation y = x2 is pronounced as x-square...

A 10by10 square contains 100 1by1 squares (of course!). A circle is drawn inside above square, tangent to all 4 sides. How many of the 1by1 squares are fully inside the circle? I get 60...which I think is correct. Trying to devise a general case formula...

Homework Statement A square plate is of mass M and length of edge 2a. Its M.I about its centre of mass axis, perpendicular to its plane is equal to I(1). Four identical disks of diameter a are cut from the plane. The MI of leftover square about the same axis? Homework Equations 1) MI of...

Hi. I have coefficient of x2 as in an expression that looks like this * calculator shows little yellow triangle because 'x' is not defined. If I can write the coefficient of x2 as - 0.091372213746554 then why did the author write coefficient of x2 like this shown below? Thanks.

Homework Statement A square circuit of resistance R=20Ω and side ℓ = 0,2 m spins 100 times per second around an horizontal axis that splits it in two. There is an uniform magnetic field B=1T perpendicular to the position ocupied by the circuit at t=0s. Calculate (1) the magnetic flux, (2) the...

Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with...

In my classical mechanics course, the professor did a bit of algebraic wizardry in a derivation for one of Kepler's Laws where a second derivative was simplified to a first derivative by taking the square root of both sides of the relation. It basically went something like this: \frac{d^2...

<Moderator's note: Moved from a technical forum and thus no template.> Hi everyone, I have encountered a partial differential equation with square roots which I don't have a clue in solving it. After letting z=F(x)+G(y), I can't really figure out the next step. I tried squaring both sides but...

Homework Statement Three forces each of magnitude 1N act from one corner towards the other corner of a square there sum has a magnitude nearest to : Homework EquationsThe Attempt at a Solution diagonal of a square is equal to √2 , the answer should be 3√2

Homework Statement Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...

Homework Statement n(n+1)(n+2)(n+3) cannot be a square Homework Equations Uniqueness of prime factors for a given number The Attempt at a Solution I'm not sure but I think I've proved a stronger case for how product of consecutive numbers cannot be squares. I don't know whether it is right...

Homework Statement :[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions. 1) The angular velocity of system...

Homework Statement [/B] Use the Taylor remainder theorem to give an expression of ##\sqrt 2 - P_3(1)## P_3(x) - the degree 3 Taylor polynomial ##\sqrt {1+x}## in terms of c, where c is some number between 0 and 1 Find the maximum over the interval [0, 1] of the absolute value of the...

[FONT=Times New Roman]Define a Fibonacci sequence by $$\varphi_0=0,\,\varphi_1=1;\ \varphi_{n+2}=\varphi_{n+1}+\varphi_n\ \forall \,n\in\mathbb Z^+\cup\{0\}.$$ Show that $$5\varphi_n^2+4(-1)^n$$ is a perfect square for all non-negative integers $n$.

Homework Statement Figure 6.47 shows a horizontal infinite straight wire with current I1 pointing into the page, passing a height z above a square horizontal loop with side length l and current I2. Two of the sides of the square are parallel to the wire. As with a circular ring, this square...

There seem to be many kinds of examples where the behavior of a quantum particle having been constrained to move on a curve or surface is investigated. The simplest is the case of a particle on a circular path or a spherical surface, where the energy eigenstates are equal to the angular momentum...

Hi all! I am doing an experiment where we create a standing wave by attaching a string to a hanging mass at one end and to a string vibrator at the other (the string passes through a pulley). When plotting the graph, the slope is inevitably 1/(u*f^2) where u is the linear density and f the...

Dear Everybody, I am having trouble to determine the value of delta when c is strictly greater than 0. Here is the work: The Problem: Find the Limit or prove that the limit DNE. $\lim_{{x}\to{c}}\sqrt{x} for c\ge0$ Proof: Case I: if c>0. Let $\varepsilon>0$ Then there exists $\delta>0$...

Homework Statement Consider a bumpy road in which each hump has the shape ##y=\cosh(a)-\cosh(x)## for ##-a\leq x \leq a## where ##y'(a)=-1## so ##a=arcsinh(1)## L=2 ##(x_p(t), y_p(t)) = (t, \cosh(a)-\cosh(t))## ##(x_q(t), y_q(t)) = (t, \cosh(a))## We place the square wheel onto the bumpy...

Homework Statement I'm trying to compute the square amplitude ## |\mathcal{M}|^2 ## for a decay process in which a Majorana fermion, call it ## \chi_2 ##, decays into another Majorana fermion, ## \chi_1 ##, and a vector boson denoted by ## A^{\mu} ##. The model is such that the mass of the two...

Hello all, I was trying to find derivatives of two functions containing square roots. I got answers which I believe should be correct, however, the answers in the book differ significantly. The first answer of mine was checked in MAPLE and found correct. My guess that the author made some...

Hello Forum, Does topology reckon the art of turning a square into a circle? I am quite new to topology and maths in general, I have only dabbled and eyed on my collection of mathbooks. I have come to a conclusion of how to turn the Square into A Circle without cutting. I wonder if I am...

Homework Statement [/B] (a) At each corner of a square is a particle with charge q. Fixed at the center of the square is a point charge of opposite sign, of magnitude Q. What value must Q have to make the total force on each of the four particles zero? (b) With Q taking on the value you just...

Homework Statement An oscillator when undamped has a time period T0, while its time period when damped. Suppose after n oscillations the amplitude of the damped oscillator drops to 1/e of its original value (value at t = 0). (a) Assuming that n is a large number, show that...

This problem projects b = (b1,b2...,bm) onto the line through a = (1, 1, 1, ...1). We solve m equations ax = b in 1 unknown (by least squares). (a) Solve aT a ##\hat{x}## = aT b to show that ##\hat{x}## is the mean (the average) of the b’s. (b) Find e = b - a ##\hat{x}## and the variance ||e||2...

Assume that the ratio of a big screen TV is 16:9. TVs are advertised by their diagonal (sp?) length. What is the screen area in square inches of a: a) 40 inch TV b) 60 inch TV c) 65 inch TV d) 80 inch TV e) 86 inch TV Show the formula (equation) that you used. Thank you

Four identical particles, each having charge q and mass m, are accelerated from rest at the vertices of a square of side L. How fast is each particle moving when their distance from the center of the square doubles? I used the Conservation of Energy => Kf= -deltaU = Ui-Uf 4(mv^2 /2) = kq^2...

Homework Statement The circuit shown is in a uniform magnetic field that is into the page. The total current in the circuit is 0.20 A, flowing counterclockwise. At what rate is the magnitude of the magnetic field changing? Is it increasing or decreasing? Square wire loop with base and height...

Homework Statement Find the trace of a ##4\times 4## matrix ##\mathbb U=exp(\mathbb A)##, where $$\mathbb A = \begin {pmatrix} 0&0&0&{\frac {\pi}{4}}\\ 0&0&{\frac {\pi}{4}}&0\\ 0&{\frac {\pi}{4}}&0&0\\ {\frac {\pi}{4}}&0&0&0 \end {pmatrix}$$ Homework Equations $$e^{(\mathbb A)}=\mathbb P...

Dear all, Please solve this integral: I tried integral by substitution, but failed. Wolframalpha shows the result is 6, but I don't know how to proceed it. Can it be solved by elementary function?

How would I calculate the frictional torque of rotating an axle with a square cross section? The axles that I’m using to drive a gear box are rectangular instead of cylindrical like normal axles, so I’m trying to figure out how much more a motor has to work to turn a square axle than it does to...

I'm trying to fit a model curve to some data by performing a chi square minimisation wrt three parameters a,b and NN. The trouble I am having is that the variables with which I want to minimise the chi square with respect to appear in an integral. I attach the code I am working with...

I came across something that is completely counter-intuitive, and I'm wondering if I'm correct or not. If a square has a side that is .8m someone would do .8 time .8 which is .64. How can an area be smaller than a side I thought and so I looked it up and found only one site that said something...

Homework Statement Find the exact magnetic field a distance z above the center of a square loop of side w, carrying a current I. Verify that it reduces to the field of a dipole, with the appropriate dipole moment, when z >> w. Homework Equations (1) dB = μ0I/4πr2 dl × rhat (2) r =...

Homework Statement Hello, I am stuck on four equations for which I must find the coefficients A,B,I,J. I have tried using latex but the commands don't seem to work.Homework Equations Four equations: A+B = I+J \frac{\alpha}{k}(J-I) = A - B D = Ie^{ia(\alpha-k)} + Je^{-ia(\alpha + k)} D =...

Mod note: Fixed all of the radicals. The expressions inside the radical need to be surrounded with braces -- { } (This question is probably asked a lot but I could not find it so I'll just ask it myself.) Does the square root of negative numbers exist in the complex field? In other words is...

Hello all, I have posted on Physics Forums a few times in the past, but mostly for help with my old physics classes and not anything in the real world. Part of my work involves radiography, but it is generally done in a field environment where we just shut down large sections of land to safely...

If the inverse square law for gravity varies with distance or distribution of matter, might the need for “dark matter” be obviated?

St. Anne of Mcaffrey tells us that the original colonists on P.E.R.N. used some kind of disintegrator to make the rooms and such for the original holds and weyrs. I picture the corners as being razor straight and a perfect cube where walls meet floor. What I don't get is how such a machine might...

There are two square scale. That is, it has marking where there are square i.e marking at 0,1,4,9,16,25 and so on. When one scale is moved, it slide over the other. Now if one scale is moved odd number i.e say 123 , that is, it's zero is placed at 123 over the other scale, now. Now, can one...

I am reading Abbot's "Understanding Analysis," and in this text he assumes that the real numbers are complete, that is, he assumes the least upper bound property, and begins to prove everything from there. Later in the book he proves that the square root of 2 does in fact exist in...

Homework Statement [/B] 1. Using the Schematic of a 555 in astable mode from the Wikipedia entry on '555 Timer IC," resistor R1 = 8 kOhms and capacitor C = 3 micro-Farads. Determine the value of R2 so that the output duty cycle is D = 0.7. Note that D is not expressed as a percentage here for...

Homework Statement A state of a particle in the potential box of width a with infinitely high walls is described by the wave function: Ψ(x)=Ax(x-a) Find the probability distribution of various value of particle energy, mean value and mean square fluctuation of energy. Homework Equations...