Square Definition and 1000 Threads

The square root of any integer that is not a square number is always an irrational number. I find this fact rather spectacular, but my question is why is this true? I have seen the formal proof for the irrationality of root 2 so I could vaguely see how one could prove that all (apart from sq...

if a is a complex number then sqrt(a^2)=? Is it is similar to Real Number? Help me please

Can ##sqrt(-i)## be expressed as a complex number z = x + iy with unitary power?

Homework Statement Consider the curves: y = x^2 from 1/2 to 2 and y = \sqrt{x} from 1/4 to 4. a. Explain why the lengths should be equal. b. Set up integrals (with respect to x) that give the arc lengths of the curve segments. Use a substitution to show that one integral can be...

Homework Statement 2. Homework Equations [/B] The Attempt at a Solution I can find the length of the large square. The small square is where the trouble starts. If I look at the part of the circle where the small square is and put a center of a coordinate system at the bottom part of the...

Hi, Simple question, sort of: I see that according to the internet the mathematical description of a triangular wave is rather complex, so I'll try to stay as far away from that as I can, because I'm a bit rusty. I understand that if you integrate a square wave you get a triangular wave on the...

I'm starting with my self studying of math with Algebra I. The text I'm using is Gelfand and Shen's Algebra. I'm at the point where it talks about the Formula for the Square of the Sum, The Square of the Distance Formula, and The Difference of Squares Formula. In going over this, I understand...

Hello Sir, I would studying the theory of least square and I find that the derivative of the error summation between the predicated line points and the true data is equal zero. Why the first derivative is equal zero?

Homework Statement A particle of mass m and and velocity v collides with a square of mass M (at rest)whose movement is confined to rotation about its centet. I must now solve for the angular velocity and the velocity of the particle after the collision (elastic collision) Homework Equations...

Homework Statement Consider the arrangment of charges (fixed in place) shown in the figure. The square has side length d. (Figure 1) Now suppose the particle with charge q is released. It is "kicked" so that it's initial speed is v. After an unspecified trajectory, it is observed that the...

Hi, I working on their text this equation did not make sense to me. From equation 1 it differentiate second term , I wonder how he got second term of equation 2. What I think is, what I wrote at the bottom

Quick question: In the proof that the square root of 2 is irrational, when we are arguing by contradiction, why are we allowed to assume that ##\displaystyle \frac{p}{q}## is in lowest terms? What if we assumed that they weren't in lowest terms, or what if we assumed that ##\operatorname{gcd}...

$\tiny{206.08.04.59}$ $\textrm{Solve by completing the square}$ \begin{align*}\displaystyle I_{41}&=\int \frac{1}{\sqrt[]{x^2+2x+37}} \, dx\\ \end{align*} $\textit{from the radical we have}$ \begin{align*}\displaystyle x^2+2x+37&=x^2+2x+1 +37-1\\ &=(x+1)^2 + 36 \end{align*}...

Homework Statement The problem relates to a proof of a previous statement, so I shall present it first: "Suppose P is a self-adjoint operator on an inner product space V and ##\langle P(u),u \rangle## ≥ 0 for every u ∈ V, prove P=T2 for some self-adjoint operator T. Because P is self-adjoint...

i'm new on creating my own circuit. And I'm trying to create a digital clock, using 74ls90+74ls47 I have problem on creating 1hz square pulse part. This is my teacher's Simulation I have searched on google that i can create 1hz pulse by using NAND gate, crystal, or Ne555, but i can't find any...

What is the correct way to expand (p3-p4)2 where p3 and p4 are 4-vectors, with metric gmu nu=diag[1,-1,-1,-1], p = [wp, p], where p is 3-vector, and wp= (p2+m2)(1/2)

√(2-√(2^(2)-1))+√(4-√(4^(2)-1))+√(6-√(6^(2)-1))+...+√(80-√(80^(2)-1)) How the find it's value

Let ##(AB)_j## be the jth column of ##AB##, then ##\displaystyle (AB)_j = \sum^n_{r= 1} B_{rj} \alpha_r## where ##\alpha_r## is the rth column of ##A##. Also ##(BA)_j = B \alpha_j \implies A(BA)_j = \alpha_j## susbtituting this in the sum ##\displaystyle (AB)_j = \sum^n_{r = 1} B_{rj}A(BA)_r##...

Is the square of a Dirac delta function, ##(\delta(x))^2##, still a Dirac delta function, ##\delta(x)##? A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta...

Hi guys. I was wondering something. In my math class, we were analyzing how strong the data was, and there was an r and r^2 value. I know the significance of r, but what's the point of knowing the square of the r value? Also, what's the use of square root? Like where does it help? I saw it one...

Homework Statement How to integrate ## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}## AND ## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}## k a constant here. I'm unsure what substitution to do. Many thanks in advance. Homework EquationsThe Attempt at a Solution I can't really get started as I'm unsure...

I know that x^2 = 4 yields two answers: x = -2 or x = 2. I also know that x^3 = 8 yields x = 2. Question: Why does the square root yield both a positive and negative answer whereas the cube root yields a positive answer?

I have a problem to do with my project in college. I'm creating a hanging fire pit, basically made of 3 lengths of square steel bar connected to a plate at the top and on hinges. The 3 legs of the frame move in slots and when in the open position would be at 45 degrees. The actual fire pit is...

Homework Statement Using magnetic field over electric field Homework Equations no equation needed The Attempt at a Solution THis may not make sense but did an experiment dealing with the inverse square law and we measured the magnetic field in this case. Want to know is there some type of...

When we find solution set of an equation inside a square root why we should assume that inside of square root should be equal to or greater than zero? For example ##\sqrt{5x-4}##. How can I use here equal to or greater than zero symbol? Thank you.

Then it goes on explaining how Gauss law would fail because for a very large surface, E field would be vanish with flux through it and though we can calculate div for this field it won't depend on source density. But I don't get what makes this particular function so evil that it would break...

Hi, I'm preparing for an exam, and I'm going over past papers. I've solved parts a & b of this question without any problems, however I'm finding it hard to understand part c. I thought of shifting the boundary conditions so I'd have 0 and L in the place of ± L/2, but that would not work...

Homework Statement A particle of mass m is moving in an infinite square well of width a. It has the following normalised energy eigenfunctions: $$u_n (x) = \sqrt{\frac{2}{a}} sin(\frac{n \pi x}{a})$$ (1) a) Give an expression that relates two orthogonal eigenfunctions to each other and use it...

Homework Statement The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is: ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV. 1) What is the rest energy...

Homework Statement I have a problem with lines in analytic geometry, and I solved it in a certain way (parallel lines interceptions) which gives the correct result, and I'm happy with that. There was another method I thought I could use to solve it though, which went through the formulas of...

$\overline{abcd}=A$(four digital nmber) is a perfect square ,given $\overline{ab}=2\overline{cd}+1$ find $A=?$

I have this integral that when solved, involves squares and natural logs, where ##A\,##,##\,b\,##, and ##\,x_e\,## are constants while ##x## is a variable. ##A = \int_{x_e}^{x} \frac{x^2 - b^2}{x} dx = \int_{x_e}^{x} x \, dx -b^2 \int_{x_e}^{x} \frac{dx}{x} = \frac{x^2}{2} - \frac{x_e^2}{2} -...

Why do we get two answers when taking the square root? For example, let a = any positive number sqrt{a} = - a and a. Why is this the case? What about 0? Can we say sqrt{0} = - 0 and 0?

Homework Statement Gelfand - Algebra p.115 problem 264: Prove that a square has the minimum perimeter of all rectangles having the same area. Hint. Use the result of the preceding problem. Homework Equations Preceding problem: Prove that a square has the maximum area of all rectangles having...

Interesting project. I was going to post my question as a standalone but I'll post it here first, as you refer to square aluminum tubing. I've got a 2 foot long steel square tube, not a rod. If I were to place it on two fulcrums -- one on each end -- and hang a weight from the middle of the...

Is there any particular reason to choose a square shape antenna like http://www.globalspec.com/reference/70592/203279/2-5-4-by-4-wavelength-rectangular-microstrip-antenna instead of a circular shape?

if y = sin inverse (x square + 2x) find dy/dx

Homework Statement Four particles with equal charges q and equal masses m are placed on a plane so that they form the corners of a square with side length a. The charges are then released from rest at this configuration (shown as (i) in the figure). After the release, the particles accelerate...

Homework Statement Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K? Why 273K?

I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?

Homework Statement ##ABCD## is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from ##B## to ##D## with center ##A##. The piece of paper is folded along ##EF##, with ##E## on ##AB## and ##F## on ##AD##, so that ##A## falls on the quarter-circle. Determine the maximum...

Hello! I am trying to write a program that solves the Schrodinger Equation for a particle in an infinite square well. I did a lot of research regarding the methods that could be used to accomplish this. I am writing this program in Matlab. The method I am using is called the Shooting Method. In...

Yesterday, I was thinking about a problem I had encountered many years before, the central force problem with a ##V(r) \propto r^{-2}## potential... If we have a Hamiltonian operator ##H = -\frac{\hbar^2}{2m}\nabla^2 - \frac{A}{r^2}## and do a coordinate transformation ##\mathbf{r}...

Homework Statement At t < 0 we have an unperturbed infinite square well. At 0 < t < T, a small perturbation is added to the potential: V(x) + V'(x), where V'(x) is the perturbation. At t > T, the perturbation is removed. Suppose the system is initially in the tenth excited state if the...

Homework Statement A loop of wire in the form of a square 1.50 m on each side, its plane makes an angle of 40.0° with a uniform magnetic field of 0.95 T. What is the magnetic flux through the loop? Homework Equations Φ = BAcosθ A = s^2 The Attempt at a Solution I found the area of the square...

Hello,first time posting a thread not just here but generally so i'll try my best. So while i was in class we were learning about square roots,at first it seemed fairly easy,but when i asked my math teacher how do we find them more easily, he smiled and talled me:"The problem is,you just...

A particle is in its ground state of an infinite square well of width a <xl i>=√2/a*sin(πx/a) and since it's an eigenstate of the Hamiltonian it will evolve as <xlα(t)>=√2/a*sin(πx/a)e^(-iE1t/ħ) where E=π2ħ2/2ma2 If the well now suddenly expands to witdh 2a If the well suddenly expands to 2a...

Homework Statement Homework EquationsThe Attempt at a Solution I have the complete solutions for this problem, I just don't understand them: This is the first part. I don't understand what r' is, or how we found it. Otherwise I understand the concept of the problem just not the details...

Hi everyone, What is the solution set of the equation: sqrt{x+2}= x-4 I got 2 and 7. Is it correct or is it just 7. If so why? Thanks:)

I'm not sure which category to post this question under :) I'm not sure if any of you are familiar with "Greek Ladders" I have these two formulas: ${x}_{n+1}={x}_{n}+{y}_{n}$ ${y}_{n+1}={x}_{n+1}+{x}_{n}$ x y $\frac{y}{x}$ 1 1 1 2 3 1.5 5 7 ~1.4 12 17 ~1.4 29 41...