Square Definition and 1000 Threads

Hello PF! I've got a strange question for you physics boffins; assuming for a moment that lasers obeyed the inverse square law, what range would a typical 1mW red laser have in the atmosphere?

The problem is: [SIZE="4"]\int\frac{1}{\sqrt{1-4x-x^2}}dx I took the expression under the radical and I completed the square, yielding: [SIZE="4"] \int\frac{1}{\sqrt{5-(x+2)^2}}dx Then I figured that I could apply the arcsin formula, where a^2=5 andu^2=(x+2)^2 But by solving for "a"...

Homework Statement What is the electric field in the middle of the square in magnitude and direction? four charges are arranged at the outer corners of the square in order from left to right , then top top to bottom respectively +q,-2q,-q,+2q.Homework Equations The Attempt at a Solution...

In my abstract algebra course we learned recently of the symmetries D4. Regarding flips/reflections, of which there are 4, it seems for the 2D object that is a square, you would have to "fold it through the 3rd dimension" to obtain a flip/reflection. Couldn't you just invert the square by...

Homework Statement Show that there is a C point to these points A(-2|2|3), B(2|10|4) and D(5|-2|7), so that the quadrangle ABCD a square is. Determine the coordinates of C. The Attempt at a Solution All I have done is measure AC, CD and BC, which are 9, 9 and 12.78. But how do I get the C...

Hi,I m thinking about,what is dimension meaning in physics.Is it any analogy with square or cube,for example?Let have for example the simplest example,distance:s=v*t.Can I draw this equation like rectangle object?Like in geometry,we have for rectangle equation a*b,now we have v*t.I know,it is...

I have two known square matrices A and B of different order. Is there any way of constructing a transformation - e.g. a transformation matrix C - that transforms A to B? And, in that case, how do I determine C? Would it be something like this? AC = B Or maybe more general, how to determine...

for a square wave function, f(x)= { -1, -∞ ≤ x ≤ 0; +1, 0 ≤ x ≤ ∞ Expanding it in Fourier series gives a function like, f(x) = (4/π) * Ʃn=0∞( (sin ((2n+1)x) / (2n+) ) Plotting a graph of the equation gives something like this, http://goo.gl/vFJhL which obviously doesn't look like a...

know I'm missing something obvious. for a momentum operator p = -iħ d/dx if I square the -iħ part I get (+1)ħ2 but I believe the correct value (as in the kinetic energy of the Hamiltonian) is -ħ/2m d2/dx2. how is the value of the term -ħ/2m where the square of -i = +1? Thanks!

Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.

I was just wondering the other day about the concept of area...Area to me is the space occupied in 2d by a bounded figure... I wanted to find out WHY the area of a square is s^2 or why area of a rectangle is lxb...Consider the dimensions of a rectangle 7x5. The area can be expressed as 5 strips...

Homework Statement Prove Square Root of 15 is Irrational The Attempt at a Solution Here's what I have. I believe it's valid, but I want confirmation. As usual, for contradiction, assume 15.5=p/q, where p,q are coprime integers and q is non-zero. Thus, 15q2 = 5*3*q2 = p2...

If I want to make a Square or Rectangle storage tank 5 feet deep and 22 feet long and 1 foot wide. The tank will be under 30 psi and also vacuum. That’s not hard to do what I want is the walls not to deflect more then .001 of an inch. The walls can be plastic, plywood with a steel sheet or...

Hey, I was thinking and I realized that this is true and I want to prove it but I have nowhere to start. If anyone knows any way to prove can you give me some advice on where to start.

Is the white region a square or rectangle? See my post below for image

Mod note: These posts are orginally from the thread: https://www.physicsforums.com/showthread.php?t=626545 The square root is not defined everywhere, at least not as a function, but as a multifunction, since every complex number has two square roots. I mean, the expression z1/2 is ambiguous...

In each situation below, electric charges are arranged at the corner of a square. Each charge Q has the same magnitude with the signs indicated in the diagrams. Rank the electric potential from most positive to most negative, and the magnitude of the electric field at the center of the square...

Homework Statement I am trying to find when the square root of the expression 25+8a^2 is rational, where the number a also needs to be rational. \sqrt{25+8a^2}=b, where a and b are both rational numbers. I am trying to get an expression for a in terms of some other number m, which would always...

Will 3"od X .250" wall ASTM A500 Grade B square tubing safely carry a single point load of 180lbs. over a 12ft span. Thanks

Let's say that the variable 'x' is definitely some negative number. So if I wanted to solve: x^2 = 4 I get: \pm \sqrt{x^2} = \pm \sqrt{4} \pm x = \pm 2 I would have to take the positive value of 'x' and the negative value of '2' to make this true...is it okay to only take a positive square...

IDK if this should be in the precalc section, but I was wondering how to reduce \sqrt{(3+\sqrt{5})} / \sqrt{(3-\sqrt{5})} to (\sqrt{5} + 1) /(\sqrt{5} - 1)

In what branches of mathematics is this proven.. I have never seen a proof, so I wonder if anyone can give me the basics of what is done to proove it or got a link to a proof.. Edit: By square root I mean the positive square root.

So there are four square roots for an elliptic curve represented by an equation something like this: y^2 = x^3 + x + 6 (mod 5) How would one go about calculating these?

Homework Statement I want to show that tr\left(\hat{\rho}_{mixed}\right)=1 tr\left(\hat{\rho}_{mixed}^{2}\right)<1 when \hat{\rho}_{mixed}=\frac{1}{2\pi}\int_{0}^{2\pi}d \alpha \hat{\rho}(\psi) Homework Equations tr\left(\psi\right)= \sum_{n}\langle n|\psi|n\rangle...

Homework Statement Lets say I have a square wave of 10Hz. I want a good sampling frequency or the Nyquist rate (minimum) to accurately capture its characteristics without aliasing. Is it enough to use 10Hz x 2 as nyquist rate, or must I break it down into harmonic frequencies? and use...

Square integrable functions -- Hilbert space and light on Dirac Notation I started off with Zettilis Quantum Mechanics ... after being half way through D.Griffiths ... Now Zettilis precisely defines what a Hibert space is and it includes the Cauchy sequence and convergence of the same ... is...

I have having dificulty in determining the torsional capacity of a square HSS section. I am designing a shaft for 9.5 cubic yard mixer powered by a 80hp drive at 6 rpm output. I have calculated the applied torque to be 70,000 ft-lbs (95 kNm). I would like to determine the size of HSS...

Homework Statement A beam has a solid square cross section of 100mm and is simply supported by two supports 3m apart. Calculate the dead load that can be safely supported when applied to the middle of the beam. Homework Equations Solid square cross section of beam: 100mm Material...

Four charges are placed at the vertices of a square, centered at the origin, as shown in the diagram. If each side of the square has a length of 0.224 m, what is the strength and direction of the net electric field at the origin? Express your answer in terms of the charge magnitude q...

Hi all, I am trying to create a square wave pulse that lasts for a relatively small amnount of time which corresponds (as close as possible) to the peak of a sin wave input of period about 1 second. The only way that I can think of doing this is via a programmable device such as an arduino...

Homework Statement First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and...

Homework Statement Consider the semi-infinite square well given by V(x) = -V0 < 0 for 0≤ x ≤ a and V(x) = 0 for x > a. There is an infinite barrier at x = 0 (hence the name "semi-infinite"). A particle with mass m is in a bound state in this potential with energy E ≤ 0. Solve the Schrodinger...

Suppose I have to solve for y: x\leq 1 (x - 1)^{2} = y So I know that (x - 1) will always be 0 or a negative, therefore I must take the negative square root of (x - 1): -\sqrt{(x - 1)^{2}} = -\sqrt{y} Am I to understand that this is the same as: -1 \cdot \sqrt{(x - 1)^{2}} = -1 \cdot...

Let $a,b \in \mathbb{Z}$, and if $a+b\sqrt{2}$ has a square root in $\mathbb{Q}(\sqrt{2})$, then the square root is actually in $\mathbb{Z}[\sqrt{2}]$. Only one approach comes to my mind. Let $r_1, r_2 \in \mathbb{Q}$ such that $a+b\sqrt{2}=(r_1+r_2\sqrt{2})^2$. This gives $a=r_1^2+2r_2^2...

HI In a square 3 x 3 using the numbers 1 to 9 once only put the numbers so that: the numbers on the top row minus the numbers in the 2nd row = the numbers on the 3rd row. trying this for about 4 hrs and am always 1 number out.

Homework Statement I'm a summer REU student tasked with building a tri-axial square helmholtz coil setup. My frame will be made of aluminum while the wire used will be copper. I've been researching for days, having actually never studied these coils before, and I'm having serious trouble...

Homework Statement Find the position of the center of mass for a thin sheet and homogeneous, with sides R and 2R ,from which has been subtracted a half circle of radius R. [Xcm=(2/3)*R*(4-pi)]Homework Equations Rcm=(1/M)*∫rdm The Attempt at a Solution By symmetry we know Ycm=0. For de...

I was playing trying to work through a proof in Apostol's Calculus and can't quite understand a step noted. This is from chapter 3, theorem 1.35. Every nonnegative real number has a unique nonnegative square root. The part where you are establishing the set S as nonempty so you can use LUB it...

How do we treat expressions under a sqaure root in inequalities ? Like for ex. x+4< Math.sqrt(-x^2-8x-12) (sorry, using m.physicsforums, so i don't know what to use for a root, so JAVA :p) I request the use of this very example.

Homework Statement A square of perimeter 20 is inscribed in a square of perimeter 28. What is the greatest distance between a vertex of the inner square and a vertex of the outer square. Homework Equations The Attempt at a Solution I have a question. Can a square be inscribed in...

Homework Statement If X^2=Sqrt(x1^2+x2^2+x3^2+...)=> X? and vice versa If X=x1+x2+x3+...=> X^2? Homework Equations The Attempt at a Solution

Sorry, this is longer than I had intended. Okay so I'm 23, I live in the south of England and, although married, we have no other commitments other than to go wherever a potential future can take us. I work full time but we're looking to move away from where we are anyway. I have never before...

If I see an expression like \sqrt{E^2c^2} I can just remove the square root sign right and replace it with Ec?

Years back i learned the digit-by-digit calcualtion of square root like this : http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit-by-digit_calculation But i don't know why this works. Wikipedia gives kind of an explanation but i don't understand it. How does this method work?

load bearing of 2" alluminum square tubing im trying to build a load bearing beam out of 2" alluminum tubing 1/8 in walls can anyone tell me the weight a length 8feet long could bear befor bending its aa6061 T6 what would it hold befor bending? keep in mind math is not my cup of tea lol

Prove that (p^m+3)(p^a-1)+4 is not a perfect square. Here the p is an odd prime and all exponents are non-negative. Given m=2n+a, for some n>0 and for some a ( where a is an integer )

Homework Statement Hi everyone, I have a physics assignment that asks: Prove that the square of relativistic four-momentum for a massive particle is a relativistic invariant under Lorentz transformations. Can anyone help me to work on the problem? I'm always lost in the class ever since my...

Homework Statement Integrate: sqrt(1/4 + t^2 + t^4)The Attempt at a Solution I'm really not sure on how to go about integrating this, it's actually integrate from -1 to 1, the solutions manual has a method I'm not familiar with. I thought of factorising it first, although doing that hasn't...

Hi guys! I thought it was intergrationintegration, i think its differentiation. Im having problems trying to figure out where to start with this question: A rectangular tank with a square base x meters and height h meters is to be made from two different materials. Material for the...

I wish to show that the sum of 9 consecutive natural numbers: n(n+1)(n+2)(n+3)...(n+8) will not be a perfect square. This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already. After some searching I found that n! is not a...