Square Definition and 1000 Threads

Homework Statement I identify the curve by finding a Cartesian equation for the curve. Homework Equations r = 3sin(θ) The Attempt at a Solution r^2 = 3r(y/r) x^2+y^2 = 3y x^2-3y+y^2 = 0 Now I'm stuck, I don't remember how to complete the square as I haven't done it in ages.

Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals? Any ideas?

Homework Statement The square loop shown below is made up of four identical wires of length scripted l = 18 cm each charged with a linear density λ = 18 nC/m. Find the magnitude of the electric field at a distance z = scripted l/2 above the center of the loop. Homework Equations...

Homework Statement A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position. Homework Equations B+A/x^2=m*a...

I am making a ramps to load logs onto a portable sawmill. I would like to know the size steel tubing I need for logs weighing 4000 lbs. the ramps would be 8' long and at the following angles; never less than 25 degrees never more than 38 degrees. 1.5 x .125 tubing is available locally, but that...

Homework Statement In this task we will show that √2 is irrational. Assume that √2 = a/b where both a and b are natural numbers. Let a = p1p2p3...pn, and b = q1q2q3...qm be the prime factors a) explain why 2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn √2=a/b b√2=a...

$x\in N$ $y=x^4+2x^3+2x^2+2x+1$ prove:$y$ is not a perfect square

Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...

The sum of three integers $x,\,y,\,z$ is zero. Show that $2x^4+2y^4+2z^4$ is the square of an integer.

Hi all looking for a bit of advice me the misses and the kids are starting a indoor flower garden and some herbs for the kids now my problems have come down to the lighting I have found out the colour spectrums needed as well as the luminous intensity required for heathly plant growth but the...

Reference to Griffith electrodynamics question:- 1.16 Compute the divergence of an inverse square vector field. Now gradient is (∂/∂r)(r cap) Hence upon taking divergence of inverse square field (r cap)/r^2...We don't get 0. In fact we get (-2)/r^3. But if we write the vector field and...

Homework Statement Consider an electron subject to the following 1-D potential: U(x) = -U_0 \left( \delta(x+a) + \delta(x-a) \right) where U_0 and a are positive reals. (a) Find the ground state of the system, its normalized spatial wavefunction and the parameter κ related to the ground...

If $x,\,y$ are positive integers such that $\dfrac{x^2+y^2}{1+xy}$ is an integer, then $\dfrac{x^2+y^2}{1+xy}$ is a perfect square.

The problem statement Form a formula to generate every value in the 10x10 square spiral shown above. Use the variables: x = the column of the cell, y = the row of the cell, s = the size of the spiral (in this case 10). The formula must work for any size of spiral, where s is the width...

Hi there I am just really confused as to how they arrived at the answer to this problem. I attached a picture of the entire question and the solution. Homework Statement Please see attached file. Homework Equations Biot Savart Law for Magnetism of a Wire where the length of wire is much...

A square tube beam, 4in x 4in x .1875in thick. Length= 36in Cross sectional Area= 2.859in^2 A36 steel How do you determine its max load capacity?

Here it is, for you to critique. This is a proof by contradiction. This is a good example of how I usually go about doing proofs, so if you give me tips on how to improve this particular proof, I'll be able to improve all my other proofs. I just learned how to do proof by contradiction...

This is problem 13 from section I 4.7 of Apostol's Calculus Volume 1: Prove that $$2(\sqrt{n+1}-\sqrt{n})<\frac{1}{\sqrt{n}}<2(\sqrt{n}-\sqrt{n-1})$$ if $$n\geq 1$$. Then use this to prove that $$2\sqrt{m}-2<\displaystyle\sum_{n=1}^m\frac{1}{\sqrt{n}}<2\sqrt{m}-1$$ if $$m\geq 2$$. I have...

Hi all, So I was recently set straight on the fact that bound state does *not* necessarily mean E<0 but rather is the statement that E<V(+/- infinity). So how do we apply this definition to the infinite square well where the potential at +/- infinity vanishes, and yet the bound states have...

Ok here's a potential I invented and am trying to solve: V = -Vo in -b<x<b and 0 in -a<x<-b , b<x<a where b<a and ∞ everywhere elseI solved it twice and I got the same nonsensical transcendental equation for the allowed energies: \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} +...

Hello everyone, I am reading about the Finite Square Well in Griffiths Quantum Mechanics Text. Right now, I am reading about the case in which the particle can be in bound states, implying that it has an energy E < 0. After some derivations, the author comes across the equation \tan z =...

Homework Statement Prove that n(n+1) is never a square for n>0 The Attempt at a Solution n and n+1 are relatively prime because if they shared common factors then it should divide their difference but (n+1)-n=1 so 1 is their only common factor. So the only possible way for n(n+1) to be a square...

Third thread same topic. Non physicist asks question-why speed of light squared? Answers Its the derivitive that makes the equation work. The speed of light is some kind of ultimate measuring device. You are too stupid to understand. I think the questioners are incorrectly phrasing what...

Homework Statement Doing a bit of QM from Griffiths intro to QM and got stuck early on on the following worked example: http://imgur.com/6aPVGIr I was under the impression that the mod square of the wave function ψ(x,t) should always be a positive, real number, but I cannot understand...

Once you know how to solve it, then explain how to solve Diophantine equation: $$X^2+Y^2=aZ^2$$ $$a$$ - integer. Write the equation when it has a solution.

The base of a solid is the region bounded by the parabola $$y^2=4x$$, and the line $$x=2$$ . Each plane section perpendicular to the x-axis is square. (I assume this means the cross-section of the solid will be square) then we are not revolving but slicing. The volume of the solid is? (the...

Three unit circles $C_1$, $C_2$ and $C_3$ in a plane have the property that each circle passes through the centres of the other two. A square $ABCD$ surrounds the three circles in such a way that each of its four sides is tangent to at least one of $C_1$,$C_2$ and $C_3$. $A=(0,0)$, $B=(a,0)$...

At home I have a series of small square fridge magnets (about 25mm by 25mm and about 1mm thick). If I select two of these fridge magnets and place them together then, as you would expect, they attract one another. However the interesting observation is that sometimes the fridge magnets are only...

I have attached a copy of a vector question which i cannot do, i do not even understand what the question is asking can someone help? On a different note i seem to have a lot of trouble with simplifying square roots for example what is the square root of 2704/ is there any way to find the...

1st: Not a specific problem, I just didn't know where else to put it. We just covered this today in class. Basically what we're doing is reducing higher level matrices to 2x2 matrices and using them to calculate the determinant. I asked my teacher where that came from, and he was really...

So I was reviewing my random process notes. In it there is an integral that they have that I can't seem to get the right derivation of when they try to simply the math for ergodic mean. Basically, you have the following: A square from (-T,T) on both the x-axis and y-axis. What they want to...

Homework Statement Find the arclength of the parametrized path x(t) = (t^2)/2 , y(t) = (t^3)/3 for 1<t<3. Homework Equations Arc Length Formula The Attempt at a Solution x'=t and y'=t^2. Putting them into the arc length formula, I get sqrt(t^2 + t^4) inside. I'm confused...

Hi everyone, :) An interesting question I thought about recently. Is it true that a Latin Square of integers (or real numbers) treated as a matrix is always invertible? If not can anybody give a counterexample. I think latin squares are invertible but I am unable to prove it. Hope you can help...

Hello, This is the thread I originally wanted to respond to, but it's closed: https://www.physicsforums.com/showthread.php?t=650126 I also found this on Wiki-talk page, which seems to be the same argument...

Homework Statement This was in my test paper today: A transformer is cut into half so that one half contains the primary coil and the other half contains the secondary coil. They are moved 30cm apart. Explain why the transformer would not work The Attempt at a Solution My answer: The magnetic...

Homework Statement Problem One: Two kilometres away from a point source of infrared waves, the intensity is 4 Mw−2. Calculate the intensity 1m away from the source. Problem two: Light from a candle has an intensity of 20.0 units when a meter is placed 3.0m away. What is the reading on the...

Homework Statement i need to solve the laplace equation in square with length side 1 i tried to solve by superposition and i got infinite sum enen thouth i know that the answer should be finite Homework Equations 1.ψ(x=0,0≤y≤1)=0 2.ψ(y=0,0≤x≤1)=0 3.ψ(x=1,0≤y≤1)=10sin(∏*y)+3x...

Homework Statement Homework Equations The Attempt at a Solution I have managed to do the first 3 parts of the questions. The last two 4 markers are the ones I am having difficulties with. I have tried using the expansion postulate which states the wavefunction is equal to the...

What are three different ways that i can produce a hole with a square cross section in a plate with a thickness of at least 1"?

I have the following problem: $$\lim_{x\rightarrow 4}\frac{\sqrt{2x+1}-3}{\sqrt{x-2}-\sqrt{2}}$$ If I multiply by the conjugate of the denominator I get $$\lim_{x\rightarrow 4}\frac{\sqrt{(2x+1)(x-2)}+\sqrt{2(2x+1)}-3\sqrt{x-2}-3\sqrt{2}}{x-4}$$ but am not sure where to go from here. Any...

My textbook says that at the center of a square conducting wire of length ω, the magnetic field is: B=\sqrt{2}μ_{0}I/(\piR) I am not sure how to calculate this...? Because the Biot Savart law has a closed loop integral, we do not use piecewise addition of line integrals to find the...

Hello, I watched a lecture by Leonard Susskind, in which he said that a differential is so short that when you square it, you get zero. What exactly could he mean by this? Thank you for your time. Kind regards, Marius

Homework Statement Expand ##(1+x)^(1/3)## in ascending powers of x as far as the term ##x^3##, simplifying the terms as much as possible. By substituting 0.08 for x in your result, obtain an approximate value of the cube root of 5, giving your answer to four places of decimals. Homework...

Homework Statement Show that the energy levels of a double square well V_{S}(x)= \begin{cases} \infty, & \left|x\right|>b\\ 0, & a<\left|x\right|<b\\ \infty, & \left|x\right|<a \end{cases} are doubly degenerate. (Done) Now suppose that the barrier between -a and a is very high, but finite...

I'm interested in the use/application of the trace of a square matrix? I am trying to get an intuitive feel for what it 'means' . . . Along the lines of: for a 2x2 matrix, the determinant represents the area of the parallelogram. I know it is the sum of the entries of the diagonal of a...

So, this is probably really simple...but I keep getting the wrong answer when trying to simplify this: $$3\sqrt{\frac{(10x^3)^2}{(10x^6)^{-1}}}$$Could someone show the steps to simplifying it? Thanks so much. (:

Homework Statement A user on math.se wanted to prove that any Mersenne number m = 2^n - 1 has an irrational square root for n > 1. So, it can be proved rather easily that any non-perfect square has an irrational root, and that all of the numbers to be considered are not perfect squares...

Homework Statement A particle is in a bound state of the infinite square well. It is in a state represented by the following wavefunction, written here at t=0: ψ(x)= -√(2/3)√(2/L) * sin (3πx/L) + i*√(1/3)√(2/L) * sin (2πx/L) (a)Write the full time-dependent wavefunction for this state...

Homework Statement A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0. Homework Equations 1-D time independent Schrodinger equation. The Attempt at a Solution I have...

Homework Statement The intensity (I) of sunlight (the received power per unit area) drops with distance (d) from the sun according to the inverse square law - i.e I2/I1 is proportional to (d1/d2)^2 What is the total power received at Earth (above the atmosphere) per unit of surface area...