Square Definition and 1000 Threads

Suppose a square shaped object has an initial length of L1 and final length (after thermal expansion) of L2. Initial temperature is T1 and final temperature is T2. Suppose it has an area of A. So initial area is A1 and final area is A2 (after thermal expansion). Here A1 = (L1)^2 and A2 = (L2)^2...

Hi I was working on a physics problem and it was almost solved. Only the part that is mostly mathematical remains, and no matter how hard I tried, I could not solve it. I hope you can help me. This is the equation I came up with and I wanted to prove it: $$\lim_{n \rightarrow+ \infty} {...

Hi all, I have a system whereby, there are different aperture shapes which are: circle, triangle, square e.t.c. this apertures are all 300um in diameter. I will like to know if the encircled energy calculated for the different apertures after diffraction will be different due to different...

Hi all, Whats the significance/application of square fractal grid turbulence studies?

I am trying to create a two phase type setup where I have a square wave in the multi-gigahertz frequency. However, I want the second wave to start once the first one reaches 90 degrees. How can the circuit be configured to do this? Will a phase shifter do or can a square wave be phase shifted at...

Let ##A## be a matrix of size ##(n,n)##. Denote the entry in the i-th row and the j-th column of ##A## by ##a_{ij}##, for some ##i,j\in\mathbb{N}##. For brevity, we call ##a_{ij}## entry ##(i,j)## of ##A##. Define the matrix ##X## to be of size ##(n,n)##, and denote entry ##(i,j)## of ##X## as...

In https://mathworld.wolfram.com/InnerProduct.html, it states "Every inner product space is a metric space. The metric is given by g(v,w)= <v-w,v-w>." In https://en.wikipedia.org/wiki/Inner_product_space , on the other hand, "As for every normed vector space, an inner product space is a metric...

i do not seem to understand part ##ii## of this problem...mathematical induction proofs is one area in maths that has always boggled me :oldlaugh: let ##n=3, p=7, ⇒m=4## therefore, ##7=(4-3)(4+3)## ##7=1⋅7## ##1, 7## are integers...##p## is prime. i am attempting part ##iii## in a moment...

Using the equation En = (h2*n2 ) / (8*m*L2), I got that E1 = 0.06017eV but the answer is not correct.

After watching this video: which explains why the wavefunction in an infinite square well is flattened, I tried running the calculation in both, what seems, the more more traditional way of using sin and by the method of, what seems to be, adding the wavefunction and its complex conjugate...

$\tiny{mil.navy.01}$ This is on an sample entrance exam test for the Navy Academy Use "completing the square" to rewrite $x^2-4x+3=0$ in the form $\quad (x-c)^2=d$ a, $(x-1)^2=1$ b. $(x-2)^2=1$ c. $(x-3)^2=1$ d. $(x-2)^2=2$ e. $(x-4)^2=1$ ok I am not sure why they suggest the second transformation

I was looking at the Wikipedia article on mesons, which has a table of all the observed particles in which one of the columns is the quark content. For most particles, it is a simple set of 2 quarks, but sometimes is shows a more complicate formula, including division by the square-root of some...

When I was following the calculations of finding the potential energy of a spring standing on a table under gravity, I encountered the integral shown below, where ##d\xi## is the compression of a tiny segment of the spring and ##k'## is the effective spring constant of that segment. The integral...

I took the w derivative of the wave function and got the following. Also w is a function of time, I just didn't notate it for brevity: $$-\frac{\sqrt{2}n\pi x}{w^{3/2}}cos(\frac{n\pi}{w}x) - \frac{1}{\sqrt{2w^3}}sin^2(\frac{n\pi}{w}x)$$ Then I multiplied the complex conjugate of the wave...

I used the voltage of the power supply and resistance to solve for the current in the larger circuit (20V/5ohms=4 amps). I am not sure if the equation listed above is the correct one I should be using, but I tried it using the following numbers. For omega, I used 2*pi*frequency. N should...

Greetings, I am about to start experimenting with misnamed rocket stoves and rocket mass heaters. I say misnamed because I think the velocities are too slow to be rocket science. (Why would I experiment with these? Because I have cement, perlite, and reinforcement materials at hand and I just...

taking origin at the centre of the square. ##d\phi = \vec E.\vec{da}## $$d\phi = \frac {kqa}{(x^2 + y^2 + a^2)^{3/2}} da$$ $$\phi = \int_{-a/2}^{a/2}\int_{-a/2}^{a/2}\frac{kqa}{(x^2+y^2+a^2)^{3/2}}(dx)(dy)$$ on evaluating this double integral i get $$\phi = (q/\pi{\varepsilon}_0...

I want to make some beaching legs for my 30ft, 9T yacht... these are supports either side of the yacht that keep it upright when the tide goes out and it sits on its keel without falling from one side or the other. My question is this, would it be stronger to use sguare or round tube to do this...

My attempt: \begin{align} \lim\limits_{n \to \infty} \sqrt{n^2 + n} - n &= n\sqrt{1+\frac{1}{n}} -n\\ &=n - n\\ &= 0\\ \end{align} I think the issue is at (1)-(2) For comparison, here is Rudin's solution

Summary:: solution of first order derivatives we had in the class a first order derivative equation: ##\frac{dR(t)}{dt}=-\sqrt{\frac{2GM(R)}{R}}## in which R dependent of time. and I don't understand why the solution to this equation is...

I have to solve a certain numerical problem without using calculator and furthermore, there is a time limit for solving this problem. The answer I have got so far is ## \sqrt{\frac{100}{99}}## I know I can reduce the numerator to 10 but then I am stuck with square root of denominator which is...

Generator weights approximately 1000lbs. I will be removing from the trailer and mounting it to a concrete pad. The reason for the stand is simply because there is a 100 gallon fuel tank that needs to remain under it like it is mounted in the trailer. The spacer/stand is so that the fuel tank...

How do you complete the square of this?: ##x^2 - 3x - 7## I already worked on this but the result is not integer: ##(x - 1.5)^2 - (\sqrt{9.25})^2## Is my above work correct? How do you obtain the result in integer? How do you complete the square so that the result is integer? For example...

I ran into an interesting video on Youtube yesterday, about a fast way to compute the reciprocal of the square root of a number. I.e., to compute this function: ##f(x)= \frac 1 {\sqrt x}## The presenter is John Carmack. If you search for "Fast Inverse Square Root — A Quake III Algorithm" you'll...

https://drive.google.com/file/d/1g7fjWAUEpOo2NukqFqZI4Wrujud6sjbn/view?usp=sharing $\tiny{4.288.T20}$ Suppose that A is a square matrix of size n and $\alpha \in \CC$ is $\alpha$ scalar. Prove that $\det{\alpha A} = \alpha^n\det{A}$. Using $\alpha=5$ $\det{5A}=\det\left(5\left[...

I started out by rewriting the function as (f(x^2))^(1/2). I then did chain rule to get 1/2(f(x^2))^(-1/2) *(f'(x^2). - I think I need to go further because it is an x^2 in the function, but not sure.

I'll try to explain to you my thinking behind this problem... tell me if it's correct or not. In short, I have assumed the area enclosed between the wire and the left side of the coil to be ##A## in which is present a ##-\hat{z}## field, and noticed that the flux it generates must be canceled by...

I have an empirical frequency distribution as for example below: ##f_{2} = \, \, \, 21## ##f_{3} = 111## ##f_{4} = \, \, \, 24## The theoretical distribution is determined by two parameters. So for a chi-square goodness-of-fit test there are actually no degrees of freedom left. Yet the...

Prove that for any arbitrary odd x, that x^2 is also odd. By definition an odd number is an integer that can be written in the form of 2k + 1 for some integer k. This means that x = 2k + 1 where k is an integer So let x^2 = (2k + 1)^2 we then get 4k^2 + 4k + 1 = 2(2k^2 + 2k) + 1, This is where...

I'm following Griffith's Modern Physics 2nd edition chapter 5. I got to the part where we make ΨI(0) = ΨII(0) I get that αCeα(0) = QAsin(Q(0)) - QBsin(Q(0)) => C = QA/α But when I try to graph it, the region I distribution doesn't seem to equal the region II distribution at 0. The book goes...

Summary:: Why are you multiplying by 1000NM/kJ within square root? Practice problem for FE [Thread moved from the technical forums so no Homework Template is shown]

This is a quote from "Calculus", by Robert A. Adams. It's a translation from spanish: "Roots of square numbers If ##a## is a positive real number, there exist two different real numbers whose square is ##a##. They are ##\sqrt{a}\;## (the positive square root of ##a##) ##-\sqrt{a}\;## (the...

Hi all :) Can't find an online calculator to properly do this. I know basic sqft - if I have a room that is 12x12, the sqftg is 144. Easy. But... I am retiling the shower in my bathroom. Three walls, and not the ceiling nor the floor. I need to speak sqft to the tile store. Two of the walls...

For the first question, i believe that mechanical energy is conserved hence we can derive the total energy i think. In regards to the second question, I'm assuming its at room temperature, so helium is monotonic therefore it has 3 degrees of freedom, therefore its internal energy is 3/2KT. I am...

Obviously a particle inside an ISW of width L cannot have arbitrarily precise momentum because ΔP ≥ ℏ/2ΔX ≥ ℏ/2L. Therefore you cannot have a particle with arbitrarily low momentum, since that would require ΔP be arbitrarily small. I need to show that a photon inside an ISW cannot have...

I'm assuming the way to go about it is to integrate in spherical coordinates, but I have no idea what the bounds would be since the bottom edges of the square pyramid are some function of r, theta, and phi.

In special relativity, observers can disagree on the order of events - if Alice thinks events A, B and C are simultaneous, Bob can think A happened before B which happened before C, and Carlos thinks C happened before B which happened before A - provided A, B and C are not causally connected, of...

I will consider first the case of ## \left [ J \right ] = \int f(x,y,y') ##, if it is right believe is easy to generalize... $$ \Delta J $$ $$\int (f(x,y+h,y'+h'))^2 - (f(x,y,y'))^2 $$ $$\int \sim [f(x,y,y') + f_{y}(x,y,y')h + f_{y'}(x,y,y')h']^2 - [f(x,y,y')]^2$$ to first order: $$\int \sim...

Here are the results from the python code: Odd results: Even results: I tried to solve for energy using the equation: I substituted the value for a as 4, as in the code the limit goes from -a to a, rather then 0 to a, and hence in the code a = 2, but for the equation it would equal to 4...

I took a surface element dA at the surface of square at point x',y' now I took a point on x-axis and calculated the flux. But I got a very complicated integral though it should be simple and I can't interpret it

Marching Square - article In the "Linear Interpolation" section This article discusses how to interpolate the values when the lines are oblique. For example, for Case#2 it has the following calculation: I have written the following source code to implement the Marching Square algorithm...

Dear Recreational Geometry People, I recovered a thing I did very long ago from a drawing of mine that I fortunately just found again. With some effort I was able reconstruct what I did and redraw it. It is a geometric dissection. The task is to slice up a square and use those pieces to make a...

1. speed of light = 3*10^8 ms^-1 length of an Earth year=365 days*24 hours*60minutes*60seconds=3.15*1 0^7 seconds distance=speed*time 1 light year= 3*10^8 *3.15*10^7=9.46*10^15m 4.2 light years = 4.2*9.46*10^15m=3.9732*10^16m ~ 3.97*10^16m (to 3sf) 2. Intensity=power/area Power=1.4MW=1,400,000...

Obviously, a priori it is not possible tu use the Taylor series because the derivative ##\sim (x-1)^{1/n-1}## is not well defined in x=1. Is there any mathematical trick? or, other approximation?

Let $n$ be a positive integer. Show that if $2+2\sqrt{28n^2+1}$ is an integer, then it is a square.

Let $$Y(t)=tanh(ln(1+Z(t)^2))$$ where Z is the Hardy Z function; I'm trying to calculate the pedal coordinates of the curve defined by $$L = \{ (t (u), s (u)) : {Re} (Y (t (u) + i s (u)))_{} = 0 \}$$ and $$H = \{ (t (u), s (u)) : {Im} (Y (t (u) + i s (u)))_{} = 0 \}$$ , and for that I need to...

find the square root of ## a+b+√(2ab +b^2)## let ##√[a+b+√(2ab +b^2)]= ±(√x +√y)## then, ##a+b+√(2ab +b^2)= x+y+ 2√(xy)## where ##a+b=x+y##.......1 ##(b+a)^2-a^2=4xy## .....2 from 2, ##a^2=(b+a)^2-4xy## ##a=√[x+y)^2-4xy]## ##a=√[x^2-2xy+y^2]## ##a=x-y## therefore...

The radius of the circle is $\sqrt{50}$ cm, the length of $AB$ is 6 cm and that of $BC$ is 2 cm. The angle $ABC$ is a right angle. Find the square of the distance from $B$ to the center of the circle. \draw[purple,thick] (0,0) arc (70:328:3); \coordinate[label=above:A] (A) at (0,0)...

Please Help me solve it \[ \sqrt{x}+\sqrt{x+8}=8 \] thanks