Value Definition and 1000 Threads

Homework Statement My teacher made up this question, but I think there's something wrong. Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx. Homework Equations Fourier trick and...

In conjunction with diving, a mixture of helium and oxygen called heliox. It will form the background to the following model invoice. Suppose that 1 mole of He and 1 mole of O2 is compressed as fast at half the volume that no heat exchange with the environment have time to take place...

Homework Statement Under what condition on the constant ##c## and ##c'## are the boundary conditions ##f(b) = cf(a)## and ##f'(b)=c'f'(a)## self-adjoint for the operator ##L(f) = (rf')'+pf## on ##[a,b]##? (Assume that ##r,p## are real.) Homework Equations The boundary conditions are...

Homework Statement Hello everyone, I need to find K for the following differential equation to be exact. (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 Homework EquationsThe Attempt at a Solution (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 dM/dy = d/dy(y3+kxy4-2*x) = 4*k*y3*x+3*y2 dN/dx =d/dx(3xy2 +20x2y3) =...

Hi folks, I'm a new graduate student in biology. I'm interested in doing theory (either simulations of biomolecules, physical models of the brain/consciousness, or models of cellular dynamics). I have had very intriguing discussions with fellow students along the following lines: 1. There are...

Homework Statement Homework Equations Newton's 2nd Law The Attempt at a Solution I was wondering if anyone could verify that I have all the correct vectors or if I am missing any. I just wanted to check before I started trying to derive the equations. [/B]

1. Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of nHomework EquationsThe Attempt at a Solution the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9...

I'm given an operator $\mathcal{L}$ is Hermitian, and asked to show $<\mathcal{L}^2>$ is $\ge 0$ I believe $<\mathcal{L}>$ is the expectation value, $=\int_{}^{}\Psi^* \mathcal{L} \Psi \,d\tau $ (Side issue: I am not sure what $d\tau $ is, perhaps a small region of space? And the interval?) I...

Homework Statement http://imgur.com/RlIdmFh http://imgur.com/3dnLK3m Homework Equations |x| = -x? The Attempt at a Solution I'm trying to make sense of this definition in my book because they are trying to prove the triangle inequality(second link), yet it keeps saying that the absolute value...

Specifically when doing integration problems. I know the indef integral of cosx/sinx+1 is ln(sinx+1) + C, but absvalue is not required here. I think it's because the sine fn must be >= 0 or it's undefined? What about in other cases, is there a general rule to know when to use absvalue? Thanks

If ##\sqrt{x^2} = |x|##, why ##\sqrt{16} ≠ |4|## instead of 4 (please see below image)?

Homework Statement The dimension h is to be determined to that a worker can comfortably slides boxes weighing up to 106 lb up and down a frictionless incline. If the worker can apply a 50 lb horizontal force to the box, what is the largest value h should have? Hint given: Before taking any...

How does one solve an equation with two absolute value functions as below My algebra book does not show how to solve with two abs functions. 2|4x-1| = 3|4x+2| I thought this might work.. |4x-1|/|4x+2| = 3/2 then |(4x-1)/(4x+2)| = 3/2 and solve the normal way..

Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. 3x1+6x2 = −6 3x1+9x2−6x3 = −12...

Homework Statement The displacement of a machine is given by the simple harmonic motion as x(t) = 5cos(30t)+4sin(30t). Find the amplitude of motion, and the amplitude of the velocity. Homework Equations x''(t) = -4500cos(30t)-3600sin(30t) The Attempt at a Solution [/B] I should note that...

Homework Statement Derive ##\sum_{n=1}^\infty \frac{1}{n^2+b^2} = \frac{\pi}{2b}\coth b\pi - \frac{1}{2b^2}## from either ##e^{b\theta} = \frac{e^{2\pi b}-1}{2\pi} \sum_{-\infty}^\infty \frac{e^{in\theta}}{b-in}## for ##0 < \theta < 2\pi##. or ##e^{b\theta} = \frac{\sinh...

I just need a quick answer, say I have a bunch of data points on a graph, I made a trendline with a function of y = 5x + 6, and a r value of R^2 = 3, is there a way of converting the r value into a percent uncertainty in the prediction of the functions? Say I used the function to predict when x...

bcrowell submitted a new PF Insights post Why Does C Have a Particular Value, and Can It Change? Continue reading the Original PF Insights Post.

Homework Statement Markov process has probabilities p_{j,j+1} = 1-p_{j,0} = (\frac{j+1}{j+2})^k for j=0,1,2,... If T_j = min[n>1 : X_n=j] What is E[T(j)|X_0=j] for j=0,1,2,...? Homework EquationsThe Attempt at a Solution I figured that T(j)|X_0=j is j+1 but don't know how to work out the...

I have done a lot of counts but I'm sure that there will be a quicker way.. Can you suggest me? I have followed the way ##\bar{p}=-i \hbar\int \psi(x)* \cdot \frac{\partial}{\partial x} \psi(x) \ dx##... Can I follow a quicker way?

Sketch the region in the plane consisting of all points (x,y) such that |x-y|+|x|-|y|<=2

Homework Statement y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2) find its local max Homework EquationsThe Attempt at a Solution i have differentiated it and found out dy/dx, in order to find the local max, i have to find out the value t when dy/dx=0 but i can't solve this equation

Find the minimum of $a^2+b^2+c^2+d^2+(a+b+c+d)^2$ given $a+2b+3d+4d=1$ for all real $a,\,b,\,c$ and $d$.

Homework Statement If the peak values of current through inductor (L), capacitor (C) and resistor (R) in parallel AC circuit are 2mA, 3mA, and 5mA respectively, then the peak value of current delivered by the source in the same circuit will be Homework EquationsThe Attempt at a Solution i (R)...

Whats the best value of ##Ω_k## (Considering Planck 2015 results).I asked best value cause If you think our universe can be also hyperbolic so ##Ω_k## can be different then 1. I remember the relationship between ##Ω_k## and k is ##Ω_k=-k/a(t)h^2## or some sort of something like that.k is zero I...

Homework Statement What's up guys, I'm stuck on #2 of this worksheet,http://luc.edu/faculty/dslavsk/courses/phys111/homework/phys111-2015hw1.pdf The half - life of C - 14 is 5730 years. Determine the value of its decay constant (and express the answer in appropriate MKS units). 2.The attempt...

I have joined to ask a question of : is f(x) a function or a value?

Is infinity divided by infinity equal to 1? 6 divided by 6 is equal to 1 however as infinity resembles 0 in the sense that 0 dived by 0 is equal to 0, I am uncertain whether infinity divided by infinity would equal 1 or instead, infinity.

Homework Statement In my notes I keep stumbling upon this equation: Equation 1: E(X-bar^2) = (σ^2)/n + μ^2 I was wondering why the above equation is true and how it is derived.The Attempt at a Solution E(X-bar^2) ##Summations are from i/j=1 to n = E[(Σx_i/n)^2)] = E[(Σx_i/n)(Σx_j/n)]...

Homework Statement Say, I was given a list, i.e. [1, 3, 7, 9, 12, 15, 24] Now I'd like to find two values closest to an input ( say, x) so that I can produce an interval ( f(a), f(b)). This interval would be used in an IVT problem where the intervals will be be part of [a,b] and will be...

Homework Statement for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]## Homework Equations Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}## The Attempt at a Solution I got the answer for the question but I have made an assumption but I don't know if...

Suppose that ##f## is continuous on ##[a,b]## and let ##M## be any number between ##f(a)## and ##f(b)##. Then, there exists a number ##c## (at least one) such that: ##a < c < b## and ##f(c) = M## Why did the author restrict ##c## to ##(a,b)## rather than ##[a,b]##? After all, ##c ∈ [a,b] ⇒ c ∈...

Dear PF Forum, Finally I have written a simple software to plot Sin(X) It can also draw y = sin(x) + cos(x). But I don't know how to use this function in real life. This software is very simple. All you need to do is altering this short function case FDrawMode of 0...

I am using RF energy harvester circuit to charge mobile in my project.The rectification part is done by Villard Voltage multiplier circuit .I need to used a supercapacitor to store the harvested energy .As the battery rating of the mobile phone is 3.7V and 2000mAh.So can i use 0.33 Farad 5 Volt...

Homework Statement Let ###f## be double differentiable function such that ##|f''(x)|\le 1## for all ##x\in [0,1]##. If f(0)=f(1), then, A)##|f(x)|>1## B)##|f(x)|<1## C)##|f'(x)|>1## D)##|f'(x)|<1## Homework Equations MVT: $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ The Attempt at a Solution I first tried...

It seems that no matter how unrelated two subjects of mathematics appear to be, there are always ways to use techniques from one area of math and use it to prove many useful results in the other, and vice versa. However, from my (inexperienced) point of view, number theory seems to be the only...

hi, if there is a initial value problem with a ζ in it with specified values what do you do with it when taking the laplace transform?

Dear PF FOrum, I have a question about Pi. In some Youtube videos, they explain why the volume of a sphere is so,... Why the area of a sphere is so,... Why the area of a circle is so,... All are good explanations, with or without differential. But I can't find the proof why Pi is 3.14. I have...

If $x,\,y$ are positive integers with $y<2014$, show that the minimal value of $\left|\dfrac{x}{y}-\dfrac{123}{2014}\right|$ is $\dfrac{1}{3792362}$.

The problem I have the triangle ABC where ∠C is 90°. The side AC is ## \sqrt{3} \ cm ## and the side BC is 1 cm. What is ∠A (α)? The attempt $$tan(a) = \frac{1}{\sqrt{3}}$$ The problem is that I have to calculate the exact value of α without any calculator. I tried to calculate the third...

Hi, I'm confused about an explanation in Elementary Calculus, the infinitesimal approach regarding Intermediate Value Theorem. The explanation: Suppose g is a continuous function on an inverval I, and g(x) # 0 for all x in I (i) If g(c) > 0 for at least one c in I, then g(x) > 0 for all X in...

It has been my understanding when working with natural wood beams/joists, that for example, two 2x12 members over a 12' span gain significant strength when they are fastened (nailed, glued or both) together rather than just lying side by side touching one another. Is this phenomenon...

Find the values of k , if any, for which the following system of equations has i) no solutions, ii) infinitely many solutions and iii) a unique solution. Solve and find the unique solution. (k+1)*(X1) + 3*(X2) - (X3) =22 2*(X1) + K*(X2) + (X3) =14 (X1) + 4*(X2) + (X3) =20

$a>1,b>1$ find the minimum value of $\dfrac {a^2}{b-1}+\dfrac {b^2}{a-1}$

Homework Statement I wanted to ask anyone willing to check my proofs to two problems, so that I may know if I am making any mistakes or assumptions. Let the function f be continuous and strictly monotonic on the positive real axis and let g denote the inverse of f. If a_1\lt a_2\lt...\lt a_n...

Homework Statement Let f(x) = 1 - x2/3. Show that f(-1) = f(1) but there is no number c in (-1,1) such that f'(c) = 0. Why does this not contradict Rolle's Theorem? Homework EquationsThe Attempt at a Solution f(x) = 1 - x2/3. f(-1) = 1 - 1 = 0 f(1) = 1 - 1 = 0 f' = 2/3 x -1/3. I don't...

Assume that I have a light bulb with luminous emittance of 160000lux (16ev), and a gray wall with luminous emittance of 300lux (7ev). I take the photo of this bulb and this background. Is there any approximate formula to estimate the gray level or RGB value of the bulb and the background in the...

Homework Statement Solve the initial value problem Homework Equations Quadratic Formula The Attempt at a Solution My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation...

In the MVT for Integrals: ##f(c)(b-a)=\int_a^bf(x)dx##, why does ##f(x)## have to be continuous in ##[a,b]##.

Homework Statement this is problem 1.4 from purcells electricity and magnetism 2nd edition. Two volleyballs, mass 0.3 kg each, tethered by nylon strings and charged by an electrostatic generator, hang as shown in the diagram...