Square Definition and 1000 Threads

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or 100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted



◻


{\displaystyle \square }
ABCD.

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  1. R

    MHB Solution To Equation Involving Square Root: Extraneous Solution?

    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:)
  2. I

    MHB What are the new formulas for x and y that will converge to $\sqrt{k}$?

    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...
  3. T

    I Online sourses to learn chi square test of homogeneity

    I want to study chi square test of homogeneity from any authentic source- book / website especially problems where samples are compared for more than one attribute. What are some relevant sources? Relevant background: I was studying examples from random online sources before I saw this book...
  4. arivero

    I Bootstraping a space from its tensor square

    By space, I mean a vector space which could be a representation of a group or even have some expanded algebraic structure. So I am not sure if this question goes here or in the Algebra subforum. Consider the tensor square r\otimes r of an irreducible group representation r with itself, and...
  5. J

    I Square root of the delta function

    Is square root of delta function a delta function again? $$\int_{-\infty}^\infty f(x) \sqrt{\delta(x-a)} dx$$ How is this integral evaluated?
  6. Mr Davis 97

    B Simplifying an exponential with a square root

    I have the expression ##e^{\frac{1}{2} \log|2x-1|}##. I am tempted to just say that this is equal to ##\sqrt{2x-1}## and be done with it. However, I am not sure how to justify this, since it seems that then the domains of the two functions would be different, since the latter would be all real...
  7. J

    I Prove Ramanujan Identity: 3 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+...}}}}

    How do you prove the identity 3 = \sqrt{1 + 2\sqrt{1 + 3\sqrt{1+4\sqrt{1 + \cdots}}}} with a real proof that actually proves the convergence? I know there are "proofs" that "prove" the identity with some trickery that ignore all the convergence issues, and I'm not interested in those trickeries.
  8. Y

    MHB Solve Limit with Square Root: \[\lim_{x\rightarrow -\infty }\sqrt{x^{2}+3}+x\]

    Hello I am trying to solve this limit here: \[\lim_{x\rightarrow -\infty }\sqrt{x^{2}+3}+x\] I understand that it should be 0 since the power and square root cancel each other, while the power turned the minus into plus, and then when I add infinity I get 0. This is logic, I wish to know how...
  9. Fetchimus

    Infinite Square Well homework problem

    Homework Statement A particle of mass m, is in an infinite square well of width L, V(x)=0 for 0<x<L, and V(x)=∞, elsewhere. At time t=0,Ψ(x,0) = C[((1+i)/2)*√(2/L)*sin(πx/L) + (1/√L)*sin(2πx/L) in, 0<x<L a) Find C b) Find Ψ(x,t) c) Find <E> as a function of t. d) Find the probability as a...
  10. giokrutoi

    Helicopter flying around a square course

    Homework Statement helicopter is flying in air it goes A,B,C,D points which are distributed in square and helicopter goes one circle in 4 hours if wind is blowing in direction from A to D then the whole circle is flown in 3 hours question: how does it takes to fly from A to C if wind blows in...
  11. H Psi equal E Psi

    Two particle in a square potential well?

    Hi guys! I'm struggling with the following problem: Consider two distinguishable (not interacting) particles in a quadratic 2 dimensional potential well. So ## V(x,y)=\left\{\begin{matrix} 0,\quad\quad-\frac { L }{ 2 } \le \quad x\quad \le \quad \frac { L }{ 2 } \quad and\quad -\frac { L }{...
  12. garylau

    How to integrate the electric field of the square sheet

    Sorry i have one question to ask how to integrate the electric field of the square sheet( see the pink circle below) it looks hard for me thank you very much
  13. davidhowie34

    How to find magnetic field in a square coil next to an RC circuit

    Homework Statement 1. (35 pts) You have a coop job helping to test a capacitor energy storage system. There is a rather large capacitor with capacitance, C = 2.02F. It is charged to a potential V = 602.V with the polarity of the capacitor as shown. The large, solid line on the right of the R–C...
  14. Unteroffizier

    Algebra II, Rational Expressions & Square Roots problems

    Problem 1 Simplify/solve: 2*81/2-7*181/2+5*721/2-50 Attempt at solution: a1/2=√a ⇒ 2*√8 - 7*√18 + 5*√72 - 50 = 2√8 - 7√18 + 5√72 - 50 = ? Do not know how to proceed beyond this point. Have experimented with little luck. Problem 2 Simplify/solve: a-1(1+1/a2)-1/2 * (1+a2)1/2 Attempt at...
  15. T

    Completing the square word problem

    Homework Statement i've attached an image of the given problem. please see below Homework Equations tax revenue - maintenance cost = net revenue. net revenue can never be negative The Attempt at a Solution i've tried setting (p1)^2 for the revenue of a random city, (p2)^2 for the revenue of...
  16. M

    MHB Is this theory regarding the graph and the square root valid?

    http://mathhelpboards.com/pre-algebra-algebra-2/find-value-squareroot-3-using-graph-drawing-suitable-straight-line-19973.html I guess I found a method to obtain the square root of any number using the above graph. $x^2-2x-3$ What I did to find the square root of 3 was replace $x^2$ with the...
  17. Vitani11

    Probability of Finding a Particle in a Small Interval in an Infinite Square Well

    Homework Statement A particle is in the n=1 state in an infinite square well of size L. What is the probability of finding the particle in the interval Δx = .006L at the point x = 3L/4? Homework Equations ψ(x) =√(2/L) sin(nπx/L) The Attempt at a Solution The problem states that because Δx is...
  18. S

    Symmetric square well, wavefunction is weird

    Hi, I'm trying to work my way through some problems and am stuck on one for a symmetric infinite square well, of width 2a, so -a<x<+a. Since this is the symmetric case, the wavefunction should be a linear combination of the terms (a)-½ cos (nπx/2a) for odd n, (a)-½ sin (nπx/2a) for even n...
  19. D

    Solve Infinite Square Well Homework: Find Energy, Probability

    Homework Statement ISW walls at 0 and L, wavefunction ψ(x) = { A for x<L/2; -A for x>L/2. Find the lowest possible energy and the probability to measure it? Homework Equations Schrodinger equation ψ(x)=(√2/L)*(sin(nπx/L) cn=√(2/a)∫sin(nπx/L)dx {0<x<a} En=n2π2ħ2/2ma2 The Attempt at a...
  20. H

    Question about Inverse Square law and sound intensity

    Homework Statement For school, I have to make a task about sound intensity and the distance to the sound source. I have to prove that the relation between these two is known as the inverse square law _1/ I_2 = ( _2/_1 )². Does someone know how I can plot the inverse square law or prove that it...
  21. Captain1024

    Fourier Series Coefficients of an Even Square Wave

    Homework Statement Link: http://i.imgur.com/klFmtTH.png Homework Equations a_0=\frac{1}{T_0}\int ^{T_0}_{0}x(t)dt a_n=\frac{2}{T_0}\int ^{\frac{T_0}{2}}_{\frac{-T_0}{2}}x(t)cos(n\omega t)dt \omega =2\pi f=\frac{2\pi}{T_0} The Attempt at a Solution Firstly, x(t) is an even function because...
  22. S

    A Square of the exterior derivative

    Is ##\text{d}^{2}=\text{d}\wedge\text{d}## a definition of the exterior algebra, or can it be derived from more fundamental mathematical statements?
  23. RicardoMP

    I Square integrable wave functions vanishing at infinity

    Hi! For the probability interpretation of wave functions to work, the latter have to be square integrable and therefore, they vanish at infinity. I'm reading Gasiorowicz's Quantum Physics and, as you can see in the attached image of the page, he works his way to find the momentum operator. My...
  24. F

    Wireless, RF, inverse fourth power law vs inverse square law

    When, in wireless communications, does the inverse fourth power-law become relevant? My understanding is that is that what cause the average signal power to degrade to the forth power is cancellation from self reflections. So by my way of thinking, an LOS point to point system, like a...
  25. S

    Investigation about the inverse square law of light radiation

    Homework Statement *Main ideas in bold[/B] Investigation of the inverse square law of light radiated from a light bulb. (done method, diagram, results and graph) Independent variable = the distance from the LDR (cm) Dependent Variable = resistance (k/ohms) Brief method: using an LDR, bulb...
  26. Cimino54

    What is the Net Force on q1 in a Rectangle of Charges?

    Homework Statement Four charges, q1 = +145 µC, q2 = +55 µC, q3 = −150 µC, and q4 = +27 µC, are fixed at the corners of a 4 m by 5 m rectangle, as illustrated in the figure below. What are the magnitude (in N) and the direction (in degrees counterclockwise from the +x-axis) of the net force...
  27. Q

    Quantum mechanics HW problem on infinite square well.

    1. ##<x>= \int_{0}^{a}x\left | \psi \right |^{2}dx## ##\psi (x)=\sqrt{\frac{2}{a}}\sin\frac{n\pi x}{a}## then ##<x>= \frac{2}{a} \int_{0}^{a}x \sin\frac{n\pi x}{a}dx## 2. Homework Equations 1) ##y=\frac{n\pi x}{a}## then ##dy=\frac{n\pi}{a}dx## and 2) ##y=\frac{n\pi x}{a}## then...
  28. M

    MHB Find the factors using a complete square

    Problem First you are asked to, write this expression as a complete square $x^2+2ax+a^2$ & ii. Using that find the factors of $x^2+2ax+a^2-9$ Workings i $(a + x)^2$ Where do I need help ii. Using that find the factors of $x^2+2ax+a^2-9$ Many Thanks :)
  29. Guaicai

    How to get the results like that in Finite Square Barrier?

    [this thread was moved from the Quantum Physics subforum, hence no template] In this page : http://www.physicspages.com/2012/08/06/finite-square-barrier-scattering/ When the E<V The boundary condition tells us the equation (9) (10) and (11) (12). I tried to get the results from those equation...
  30. P

    B Why the square of the wave function equals probability?

    If the problem is just to avoid negative probabilities, then why isn't the modulus of the value of wave function equal to the probability of finding the particle? I mean, is it proved by mathematics that the integration of the square of wave function value over a particular region is equal to...
  31. P

    MHB Square metric not satisfying the SAS postulate

    I'm not sure on how to do this problem. Can someone please help and explain? Thank you! Recall (Exercise 3.2.8) that the square metric distance between two points (x1, y1) and (x2, y2) in R^2 is given by D((x1, y1), (x2, y2))= max{|x2 − x1|, |y2 − y1|}. Show by example that R^2 with the square...
  32. moenste

    RMS of square wave and alternating currents

    Homework Statement Find the value of the RMS current in the following cases: (a) a sinusoidally varying current with a peak value of 4.0 A, (b) a square wave current which has a constant value of 4.0 A for the first 3 ms and -2.4 A for the next 2 ms of each 5 ms cycle, (c) an alternating...
  33. karush

    MHB 206.8.7.58 Int 1/(x^2-6x+34) dx complete the square

    $\text{206.8.7.58}$ $\text{given and evaluation}$ $$\displaystyle I_{58}=\int \frac{dx}{{x}^{2}-6x+34} =\dfrac{\arctan\left(\frac{x-3}{5}\right)}{5} + C$$ $\text{complete the square} $ $${x}^{2}-6x+34 = \left(x-3\right)^2 + 5^2 = {u}^{2}+{a}^{2} \\ u=x-3 \\ a=5$$ $\text{standard integral} $...
  34. R

    Fermions in infinite square well in compact geometry

    Homework Statement The global topology of a ##2+1##-dimensional universe is of the form ##T^{2}\times R_{+}##, where ##T^{2}## is a two-dimensional torus and ##R_{+}## is the non-compact temporal direction. What is the Fermi energy for a system of spin-##\frac{1}{2}## particles in this...
  35. karush

    MHB 206.8.4.35 integral complete the square

    $\tiny{206.8.4.35} \\ \text{given }$ $$\displaystyle I_{35}=\int \frac{1}{\sqrt{x^2+2x+65}} \, dx = $$ $\text{complete the square} \\ x^2+2x+65 \implies x^2+2x+64+1 \implies \left[x+1\right]^2+8^2 \\$ $\text{u substitution } \\ \displaystyle x+1= 8 \tan\left({u}\right) \therefore du=8\sec{u}...
  36. P

    If A, B are n order square matrices, and AB=0, then BA=0?

    Homework Statement If A and B are square matrices of same order, prove of find a counter example that if AB = 0 then BA = 0. Homework Equations A^{-1} A = I_n, ABC = (AB)C The Attempt at a Solution AB = 0 \Rightarrow A^{-1} A B = A^{-1} 0 \Rightarrow (A^{-1} A) B = A^{-1} 0 \Rightarrow I_n...
  37. Oannes

    Finding Surface Area in square feet with Volume & Thickness

    Homework Statement How large a surface area in units of square feet will 1 gallon of paint cover if we apply a coat of paint that is 0.1cm thick? Homework Equations Since Volume is L * W * H and we can assume the object is square besides the height which in this case will be the thickness. So...
  38. ShayanJ

    Contour integration with a square root

    Homework Statement Find the value of the integral ## \int_0^\infty dx \frac{\sqrt{x}}{1+x^2} ## using calculus of residues! Homework EquationsThe Attempt at a Solution This is how I did it: ##\int_0^\infty dx \frac{\sqrt{x}}{1+x^2}=\frac 1 2 \int_{-\infty}^\infty dx \frac{\sqrt{|x|}}{1+x^2} ##...
  39. Einstein's Cat

    B Solving Square Root & Quadratic Equations

    Let's say there's an equation 0 = √x - √x I intend to make x the subject of the equation; however because it is a square root, there are numerous solutions; however can I just assume that 0= √x - -√x= 2√x Can I now just rearrange this equation to make x the subject? In other words is the...
  40. Joppy

    MHB Show that is the square of an integer

    I couldn't find this problem anywhere else on the forum so I thought I'd post it. If however, I am duplicating, mods feel free to remove the post :p. No doubt many of you know it already, but I found it quite interesting. Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^2 +...
  41. L

    Steel square tubing center strength

    Size O.D. Wall 3" x 2" x 0.1875 3" x 2" x 0.125 5ft long center 500lb how much bend will there be thank you for your time
  42. P

    Taking the square of a formula

    Homework Statement Hi sorry if the titel is wrong I want to know if i can write this ##a^2 + u^2 -2au= (a-u)^2 = (u-a)^2## I get different results when integrating ##x^{-\frac{3}{2}}## in the range ##(a-u)^2## to ##(a+u)^2##
  43. C

    B Simplifying Sqrt(y^6): Do We Need Abs Value Bars?

    I'm trying to decide if simplifying sqrt(y^6) requires use of the absolute value bars. For example, the rule "nth root(u^n) = abs(u) when n is even" can be used to simplify sqrt(y^6) as sqrt[(y^3)^2]=abs(y^3). However, the rules of rational exponents can also be used to simplify sqrt(y^6) as...
  44. karush

    MHB 242.7.5.88 1/((X+2)sqrt(x^2+4x+3)) complete the square

    $\large{242.7.5.88}$ $$\displaystyle I_{88}=\int\frac{dx}{(x+2)\sqrt{{x}^{2}+4x+3}}= -\arcsin\left(\dfrac{1}{\left|x+2\right|}\right)+C $$ complete the square of $${x}^{2}+4x+3 ={x}^{2}+4x+3+1-1=(x+2)^2-1 $$ Set $u=(x+2) \ \ du=dx$ then $$\displaystyle I_{88}=\int\frac{1}{u \sqrt{u^2-1}}...
  45. D

    Why Is There Little Helium in Earth's Atmosphere?

    Homework Statement There is almost no helium gas in the earth’s atmosphere - indeed the price of He has increased in recent times due to worries about a limited supply. (Bad news for parties and for all the scientists who use liquid He as a coolant.) we know that the “escape velocity” required...
  46. M

    MHB Find and approximate value square root of 3 using the roots of the graph.

    Using a graph of function $y=3-(x-1)^2$ which has got its negative & positive root s-0.8 and 2.7 respectively, Find an approximate value for $\sqrt{3}$. Any suggestions on how to begin? Should I be using the quadratic formula here? Many Thanks :)
  47. P

    I Gauss' theorem and inverse square law

    So, I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields? I think not because in order to not have a Flux depending on distance but a constant one we need that r^2 of the...
  48. M

    MHB How have I dropped a factor 2 on the square root of 19?

    The main problem is http://mathhelpboards.com/pre-algebra-algebra-2/find-length-dc-19355.html#post88492 In this question $15 = \dfrac{\left((x+3)+(2x-3)\right)h}{2}=\frac12 ((x+3)+(2x-3))\times((2x-3) -(x+3))=\frac12((2x-3)^2-(x+3)^2)=\frac12(3 x^2-18 x)$ So we get $30=3x^2-18x$ Now using...
  49. M

    MHB Find the value of x square + y square

    If x-y= 1 & x2y - xy2 =2, Find the value of x2+y2 Any Ideas on how to begin? Many Thanks :)
  50. M

    MHB Find the angle X inside a pentagon with a square

    If the the question is too small , Please be kind enough to read it from here Question The interior angles of a pentagon add up to 540 degrees. So thinking that this is a regular pentagon with all 5 sides equal an interior would be 108 degrees. And speaking of the square All four sides are...
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