Value Definition and 1000 Threads

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...

Homework Statement A wavelenght of 410.2*10^-9m is emitted by the hydrogen atom in a high voltage discharge tube. what are the initial and final values of the quantum number n for the energy lvl transition that produces this wavelength? Homework Equations 1/(lambda) = R * (1/2^2 - 1/n^2)...

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same. I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of...

Homework Statement Using J^2 \mid j,m_z \rangle = h^2 j(j+1) \mid j,m_z \rangle J_z \mid j,m_z \rangle = hm_z \mid j,m_z \rangle Derive that : \langle j,m_z \mid J_-J_+ \mid j,m_z \rangle = h^2[ j(j+1) - m_z(m_z+1)] Homework Equations J_- = J_x - iJ_y J_+ = J_x + iJ_y The...

Mean Value Theorem Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather...

Can we integrate: $$\int_a^b |x| dx$$ using an antiderivative of ##|x|##, namely ##\frac{1}{2} x |x|##, instead of splitting up the integration interval? I know this is not particularly useful for integrals such as: $$\int_{-5}^5 |t^3 - 8| dt$$ However, for absolute value functions with linear...

Hello everyone. Let us consider two fermions whose spin state wave functions are certain (normalized) ##\psi_{1}## and ##\psi_{2}##. So the overall normalized spin state wave function of this system is of the form: ##\psi = (1/\sqrt{2})(\psi_{1} \psi_{2} - \psi_{2} \psi_{1})## Is there any...

So I'm interested in calculating the Spearman correlation matrix, but I am running into some issues. All of the examples I have found only calculate rho scores between two columns. I am trying to replicate results from a white paper...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

Hey! :o Prove using Green's theorem that the boundary value problem $$\frac{\partial}{\partial{x}}\left ( (1+x^2)\frac{\partial{u}}{\partial{x}}\right )+\frac{\partial}{\partial{y}}\left ( (1+x^2+y^2)\frac{\partial{u}}{\partial{y}}\right ) -(1+x^2+y^4)u=f(x,y), x^2+y^2<1 \\ u(x, y)=g(x,y)...

Solve the boundary value problem: $\left\{ \begin{array}{lcl} y''&=&0,\hspace{1.0mm} 1<x<2\\ y(1)&=&0\\ y(3)+y'(3)&=&0 \end{array} \right. $ For the problem, I first calculate the eigenvalues and after check the roots and finally find the eigenvectors. Is correct this? Help me please :).

Homework Statement Consider the following inital states of the symmetric 2D harmonic oscillator ket (phi 1) = 1/sqrt(2) (ket(0)_x ket(1)_y + ket (1)_x ket (0)_y) ket (phi 2) = 1/sqrt(2) (ket(0)_x ket(0)_y + ket (1)_x ket (0)_y) Calculate the <p_x (t)> for each state Homework EquationsThe...

Homework Statement Table gives the rectilinear motion of a 4kg mass over a 5 s time interval. When the time was 3.8 seconds, the velocity of the mass was approximately what Homework EquationsThe Attempt at a Solution I first just tried to find the average of the velocities at 3.5 and 4.0...

Homework Statement Suppose, the following equation describes the relation between an independent and a dependent variable physical quantities(that will be measured by experiments; for example, temperature, current, voltage etc) x & y : ##y = ax^2 + bx + c## We have to find the values of the...

Homework Statement Find a power series representation for the function below & determine the radius of convergence. f (x)=(1+x)/(1-x)2 2.Relevant equation Shown in attached image below which is the solution the problem. 3.The attempt at a solution I'm trying to fathom the solution here...

What is the value of curvature which caused by earth(geodetic effect) on space-time?

Mod note: I revised the code below slightly, changing the loop control variable i to either j or k. The reason for this is that the browser mistakes the letter i in brackets for the BBCode italics tag, which causes some array expressions to partially disappear. Hello, I am trying for the first...