Value Definition and 1000 Threads

Homework Statement ##\left|\left(\frac{x}{2}\right)^2\right| < 1## Homework EquationsThe Attempt at a Solution The absolute value situation is throwing me off for some reason. Would it be correct to split this into two equations? ##-\left(\frac{x^2}{4}\right) > -1## and ##\frac{x^2}{4} < 1##...

Homework Statement All of the divisors of ##n## are in increasing order: ##1=d_1 < d_2 < \dots < d_t = n##. We know that ##d_6=15##. What is the smallest possible value of ##n##? Homework EquationsThe Attempt at a Solution Here is my reasoning. We have the chain ##1 < d_2 < d_3 < d_4 < d_5 <...

Greetings! Hey guys, I need help on how can I get pixel value of an image with pixels more than 100px (10x10). Here the code that I execute in order to get the pixel value try{ File f = new File ("input image location"); BufferedImage img = ImageIO.read(f)...

this has bugged me for quite a while. i was listen to chalmers talk about consciousness and making comparison consciousness to the field generated by a mass/charged particle. i know this is slightly philosophical question, but does a field with uniformly 0 value exist in the sense we mean...

I understand that the Uncertainty Principle relates the variances of Fourier conjugates. I am having trouble finding: 1) the mathematical relationship between the expectation values of Fourier conjugates generally; 2) and then specifically for a normalized Gaussian. Any suggestions or insights?

Homework Statement $$f(x+\frac{1}{x}) = x^2+\frac{1}{x^2}\\ f(1) = ?$$ Homework EquationsThe Attempt at a Solution I thought maybe I can find a ##x## that ##x+\frac{1}{x} =1## that I can substitute, but that ##x## is a imaginary number so I am not sure what should I do next.

hello my friends , i have two question about calorific value of coal why Lower heating value decrease with increase oxygen content but increase with increasing hydrogen , sulfur and carbon content ? Do this elements influence the higher heating value or not ?

Homework Statement Find Vx, as the 5A current source provides 50W to the circuit. Homework Equations ##P = V.I## ##U = R.I## The Attempt at a Solution [/B] At first, as 5A current source provides 50W, by ##p=vi## there should be 10v through it. Then, i applied KVL and found four equations...

Hello all, I was watching some random videos on YouTube and found one of Dr. Ben Goertzel (a leading expert in the field of AI) and he was wearing the t shirt you see below. It caught my attention. I tried working it out, but I had no luck as it got messy fast. I then tried throwing it into...

My text (Ian Ford - Statistical physics) describes an ideal gas system in a piston being quasistatically compressed by a piston head of area A under external force f. It assumes the system has a uniform pressure p. All good so far. Then it says: "the force pA equals the applied external force f"...

Hello. I am doing problem sets on very basic stat topics. When solving problems that require the use of chi-squared table, I stumbled upon an unexpected issue. I seem to miss something important about how to correctly choose the right critical value using the chi-squared table. Below are two...

we know a couple of approximate values of $\pi$ mostly $\frac{22}{7}$ and $\frac{355}{133}$ but one I found (from the net )interesting was sum of 2 surds $\sqrt{2} + \sqrt{3}$.if anyone is aware of other of interesting observation kindly let me know.

If I have ten dice and pick one at random, given that I don't know anything about them the probability of getting a dice of value 4 would be 1/6? Given that I know that there is two dice of value 4, the probability of getting a 4 would be 2/10 = 1/5? Which would be correct in repeated trials?

$\begin{align*}\displaystyle y'&=y-5\quad y(0)=y_0\tag{given}\\ y'-y&=-5\\ u(x)&=\exp\int-1\, dx = e^{-t}\\ (e^{-t}y)&=-5e^{-t}\\ e^{-t}y&=-5\int e^{-t} dt = -5e^{-t}+c\\ &y=-5\frac{e^{-t}}{e^{-t}}+\frac{c}{e^{-t}}\\ y&=\color{red}{5+(y_0-5)e^t}...

Hello, It is well know that the moment of a force ##F## depends on: a) the force magnitude ##|F|## b) the choice of the moment reference point ##P## c) the distance (lever arm) from the point ##P## to the point of application of the force ##Q##. That said, an object with a single force applied...

A coin had tossed three times. Let ##X##- number of tails and ##Y##- number of heads. Find the expected value and variance ##Z=XY##. My solution: We know, that ##Y=3-X##, so ##Z=(3-X)X## for ##X=0,1,2,3##. ##Z=2## for ##X=1,2## and ##Z=0## for ##X=3,0## So, ##E(Z)=E((3-X)X))= 2 \cdot ⅜ +2 \cdot...

$1.1.2c\\ \displaystyle \frac{dy}{dt}=2y-10, \qquad y(0)=y_0$ rewrite $\quad\displaystyle y'-2y=-10$ obtain u(x) $\quad\displaystyle u(t)=\exp\int -2 \, dt=e^{-2t}$ integrate using the boundaries: $\quad\displaystyle \int_{y_0}^{e^{-2t}y}\,du=-10\int_{0}^{t}e^{-2v}\,dv$...

$\displaystyle \frac{dy}{dt}=2y-5, \quad y(0)=y_0$ rewrite $$y'-2y=-5$$ obtain u(x) $$u(x)=\exp\int-2\, dx = e^{-2t}$$ then $$(e^{-2t}y')=5e^{-2t}$$ just reviewing but kinda ?

Homework Statement We have a coin with probability ##0\leqslant p \leqslant 1## of getting heads. We flip the coin until we get ##7## heads in a row. Let ##N_7## be the number of necessary flips to get the ##7## heads in a row. What is the expected value ##E(N_7)##? Homework Equations The...

Homework Statement I try to integral as picture 1. The result that is found by me, it doesn't satisfy Green's function for boundary value problem. Homework EquationsThe Attempt at a Solution show in picture 2 & picture 3.

Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...

(a) intial value (b) interval $\displaystyle y^{\prime}= \frac{x(x^2+1)}{4y^3}, \quad y(0)=-\frac{1}{\sqrt{2}}$ rewrite $$\displaystyle\d{y}{x}=\frac{x(x^2+1)}{4y^3}$$ $$\displaystyle y^3\, dy=\frac{x(x^2+1)}{4}\, dx$$ integrate $$\displaystyle\frac{y^4}{4}= \frac{1}{4}\left(\frac{x^4}{4}...

Homework Statement Let X be a random variable. It is not specified if it is continuous or discrete. Let g(x) alway positive and strictly increasing. Deduce this inequality: $$P(X\geqslant x) \leqslant \frac{Eg(X)}{g(x)} \: $$ where x is real. Homework Equations I know that if X is discrete...

2000 (a) Find the solution of the given initial value problem in explicit form. $$xdx+ye^{-x}dy=0, \quad y(0)=1$$ \begin{align*}\displaystyle xdx&=-ye^{-x}dy \\ \frac{x}{e^{-x}}\, dx&=-y\, dy\\ xe^x\, dx&=-y\, dy \end{align*} (b) Plot the graph of the solution $\quad...

The question is as follows: A particle of mass m has the wave function psi(x, t) = A * e^( -a ( ( m*x^2 / hbar) +i*t ) ) where A and a are positive real constants. i don't know how to format my stuff on this website, so it may be a bit harder to read. Generally when i write "int" i mean the...

In transforming an integral to new coordinates, we multiply the “volume” element by the absolute value of the Jacobian determinant. But in the one dimensional case (where “change of variables” is just “substitution”) we do not take the absolute value of the derivative, we just take the...

Homework Statement ##x,y,z \in \mathbb{R}##, find the minimal value for $$x^2+2y^2+z^2-6x+4y-10z+17$$ Homework Equations None The Attempt at a Solution First I try to use”complete the square” method to make the polynomial something like: $$(x-3)^2+(\sqrt2y+\sqrt2)^2+(z-5)^2-19$$ Then I am...

Homework Statement Let ##\vec{e}\in\mathbb{R}^3## be any unit vector. A spin ##1/2## particle is in state ##|\chi \rangle## for which $$\langle\vec{\sigma}\rangle =\vec{e},$$ where ##\vec{\sigma}## are the Pauli-Matrices. Find the state ##|\chi\rangle## Homework Equations :[/B] are all given...

Hello I have a problem when I dissolves NaCl in deionized water. I have a pH probe in my deionized water (lets say 1 L). Then I add 40 g of NaCl, imidiately the pH-value rises to about 9.0 (i'm logging hte pH value as a function of time). Then slowly the pH-value lowers, and after 11 hours ...

There is no absolute electric potential. Is it due to classical ignorance (because we don't know the static fields, capacitive coupling, etc. of the surrounding environment) or is it due to quantum ignorance (the potential can fluctuate to any value due to HUP)? My question is valid because...

Homework Statement For a region where the potential V=0, the wave function is given by ψ(x)=2αsin(3πx/a). Calculate the energy expectation value of this system. Note that α and a are two different constants. Homework Equations ψ(x)=2αsin(3πx/a) E=K+V=K K=p^2/2m ∫ψ*Pψdx=Expected momentum...

How do I calculate the average value of some damage values where there is say a 30% chance of critical hit and on a crit 150% damage is done? I run into this problem often, if I had to guess I'd say it's likely related to the binomial distribution because there's either a crit or not, fixed...

Hello, I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two...

Homework Statement Find the value of h'(0) if: $$h(x)+xcos(h(x))=x^2+3x+2/π$$ Homework Equations Chain Rule Product Rule The Attempt at a Solution I differentiated both sides, giving h'(x)+cos(h(x))-xh'(x)sin(h(x))=2x+3 Next I factored out and isolated h'(x) giving me...

Solve the absolute value equation. |3x - 2|/|2x - 3| = 2 Solution: |3x - 2| = 2|2x - 3| 3x - 2 = 2(2x - 3) 3x - 2 = 4x - 6 Solving for x, I get x = 4. However, the textbook has two answers for this problem. The answer is also 8/7. How do I find 8/7?

What is the value of the permeability constant in 1865, the time when Maxwell's theory was first published? What was the experimental method used to determine the constant. Who did the experiment.

Solve the absolute value equation. |(2x + 1)|/|(3x + 4)| = 1

Solve the absolute value equation. |x^2 - 2x| = |x^2 + 6x| Seeking the first step.

What is error in the picture?

I am making a circuit with arduino that will read AC voltage supplied to the mains, and based on that value, control a solid state relay. As per my theory till date, if the AC is >=205 or <= 230V, the relay will be on, otherwise it will be off. The circuits have been borrowed from here: AC...

http://www.counterbalance.org/cq-turok/etern-body.html https://ned.ipac.caltech.edu/level5/Kolb/Kolb3_1.html) http://www.astronomy.ohio-state.edu/~dhw/A873/notes7.pdf) According to QFT, if you make repeated measurements of some property of the field then you will in general measure a...

Homework Statement An ice-cream store makes 150 ice-cream balls every day. The cost of making each ice-cream ball is $3. The price of an ice-cream ball is $8. The demand distribution is as follows: 100 ice-cream balls with probability 25%, 150 ice-cream balls with probability 50%, and 200...

Homework Statement The current through a 100 microfarad is i(t) = 50 sin(120*pi*t) mA Calculate the voltage across it at t = 1 ms. Consider zero initial voltage. Homework Equations v(t) = (1/c) integral of i(t) from t = 0 to t = t The Attempt at a Solution Am getting v(t) = - 1.326 (...

Homework Statement I have a general question how I calculate the expectation value of V (potential energy) with Ehrenfest’s theorem. Do I have to integrate d<p>/dt with respect to d<x>. Also if the potential is symmetric (even) would that mean the expectation value of the potential is 0...

Hello, I would like to ask, if I am right with my computation. Let´s have a set of integers from 0 to 12. We start at 0 and we can go to 1 with the probability 1. From 1 we can go to 1 or back to 0, both with probability 0.5. When we start at zero, how many steps (exp. number of them) do we...

Homework Statement How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom. Homework Equations The Attempt at a Solution I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...

Homework Statement The problem ask for Thevenin Equivalent for the circuit attached. Homework Equations Vth = Vab Rth = Req Rth = Vth / Isc Rth = 1 / It The Attempt at a Solution Already calculated Vth = 166.67 V. I've no problem with that. Already confirmed by textbook answer. However, my...

I have a python code where it generates two 1D arrays, plots them using scatter plot and then draws colorbar using normalization range. How can I find individual values at those individual pixel points? HC = data["HC"] OC = data["OC"] sample = y widthmm, heightmm = 171, 233 ratio =...

Homework Statement Let ##r\in \mathbb{R}##. Determine whether ##\displaystyle \sum_{n=1}^{\infty}\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}## converges Homework EquationsThe Attempt at a Solution If ##r>1##, then ##|\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}| \le |\frac{1}{n^r}|##. The...

I have the expression ##|nr^n|^{1/n}##. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what...