Independent Definition and 745 Threads

Consider a simple textbook problem in two dimensional kinematics - say, a projectile motion problem. I know that the x- and y- components of motion are independent of one another but I don't understand why. I know this is true due to everyday observation - empirical evidence of this being the...

I have a load cell which must be placed onto a piece of vehicle structure. In an ideal world I would attach the load cell to the structure and calibrate both together to ensure a very accurate calibration, and that accurate loads are measured. However a problem arises if I need to replace the...

Homework Statement Consider three events A1, A2, and A3, and let pi = P(Ai), for i = 1, 2, 3. a) Express the probability that at least one of these three events occurs in terms of the pi ’s. b) Express the probability that at least two of the events occur. c) Suppose that A1, A2 and A3 are...

Hello, the TISE can be simplified $$H \psi = E \psi$$ Where ##H## is the Hamiltonian, and ##E## is the eigenvalue, but why don't the ##\psi## terms cancel, leaving ##H = E##? Also, what the heck does the eigenvalue ##E## have to do with the eigenvalue that I have previously encountered in...

Let's say we've a system which can be described by the Hamiltonian: $$H_0 = \dfrac{p^2}{2m} + V(x)$$ Now suppose we introduce a perturbation given by: $$H_1 = \lambda x^2$$ Our total hamiltonian: $$H = H_0 + H_1 = \dfrac{p^2}{2m} + V(x) + \lambda x^2 $$ Normally, the perturbation doesn't...

Let ${}\left\{X, Y, Z, W\right\}$ be an independent set in $\Bbb{R}^n$, is the following set independent? ${}\left\{X+Y, Y+Z, Z+W, W+X\right\}$ My textbook says it isn't, but I'm not sure why. Let $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ be scalars, then...

Homework Statement "The Daily Planet ran a recent story about Kryptonite poisoning in the water supply after a recent event in Metropolis. Their usual field reporter, Clark Kent, called in sick and so Lois Lane reported the stories. Researchers plan to sample 288 individuals from Metropolis...

Homework Statement The following text on the time independent perturbation theory is given in a textbook: \hat{H} = \hat{H}_0 + \alpha \hat{H'} We expand its eigenstates \mid n \rangle in the convenient basis of \mid n \rangle^{(0)} \mid n \rangle = \sum_m c_{nm} \mid m \rangle^{(0)}...

Has anyone been through independent study calculus course ( DE through a university out of Utah)? I really miss the aspect of having an instructor but I do enjoy being able to focus on the aspects that I am not great at while passing over things that I've already learned. I would really like to...

In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...

I asked my teacher, and I was told that volume is the independent variable, and that pressure is dependent. The textbook I'm using said the same thing. After looking up some graphs of the law, I found that both pressure and volume were used as independent variables. It seems counter-intuitive...

We have ##R^{1}_{212}## as the single independent Riemann tensor component, and I'm after ##R##. From symmetry properties and contracting we can attain the other non-zero components. The solution then states that ##R_{11}=R^{1}_{111} + R^{2}_{121}=R^{2}_{121}## . I thought it would have been...

Homework Statement I am supposed to give a thevenin equivalent circuit to the one posted in the picture. Homework Equations V=IR KVL: "voltage drops around a closed loop sums to zero KCL: "current into a node equals current out of a node" The Attempt at a Solution The part I'm confused...

So I have X1 and X2 are iid standard normal. Then I have Y=X1^2+ X2^2 and Z=X1/(X1^2+x2^2) I'm supposed to find the distribution of Y and Z and then determine if they are independent. Clearly Y is chi squared with degrees of freedom 2. But I have no idea how to find the distribution of Z...

Homework Statement Given that u(x,t) satisfies u_t-6uu_x+u_{xxx}=0 (*) and u, u_x, u_{xx} \to 0 as |x| \to \infty show that I_1 = \int_{-\infty}^{\infty}u^2dx is independent of time ( \frac{\partial I_1}{\partial t}=0 ). Homework Equations - The Attempt at a Solution I...

Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...

I'm a mathematics major and up until now I've taken Calc 1,2,3 (so single + multivariable) a combined course in Elementary Linear Algebra + Differential Equations and PDE's. My school doesn't offer any tensor calculus classes, but I was interested in learning some of it on my own. Do I have...

Homework Statement [/B] (i) Prove that dL/dt = 0 (ii) Find the relation between space part and 3-angular momentum vector (iii)Show that 3-angularmomentum vector is independent of pivot Homework EquationsThe Attempt at a Solution [/B] I'm not sure what part (iii) is trying to get at, but I...

Hey everyone I just had a quick thought that was bothering me. For a set to be a basis it must be linearly independent and span the vector space. I've seen cases however of only two vectors forming a basis for R4 I don't see how two vectors could span 4 space or am I missing something. Thanks!

Hello everyone, I am new to these forums, so if this question is in the wrong place, I will relocate it. Long story short, my school has no real physics department anymore, but I have an insatiable appetite for it. I was wondering what the next course in a physics sequence would be after...

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $$t=0$$ Clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is "another coordinate system" in which the corresponding metric has no singularity as we...

For two events ##A## and ##B##, where ##A∩B ≠ ∅##, is it possible to deduce from a venn diagram whether or not those two events are dependent? Or is such information unattainable from a mere venn diagram? Also, if we define ##C## as the complement of the union of ##A## and ##B##, why must ##C##...

Is calculating the determinant the Wronskian the only way to show that a set of functions is linearally independent? For example could you build a matrix where the numbers represent the coefficents to the polynomial functions and if it rref's to the identity matrix wouldn't this show it's...

http://tinypic.com/r/euht06/8 Hi everyone! It was the question given to us in today's test & I was wondering if anyone can tell me what is the correct answer. The teacher will post the answers by the end of this week but I am feeling anxious to know the answer. Thanks in advance. P.S. Sorry...

Homework Statement Three tanks are sent to shoot a certain target. Each tank is to shoot one round. The probabilities of a tank's round hitting the target are 1/2, 2/3 and 3/4 for tanks A, B, and C respectively. Assuming independence of A, B and C hitting, find the probability that: a. rounds...

Homework Statement Determine if the given set of functions is linearly independent or linearly dependent.Homework Equations $$S=x~sin~x, ~ x~cos~x$$The Attempt at a Solution My first instinct was to use the Wronskian. $$W[y_1(x), y_2(x)]=\begin{vmatrix} x~sin~x & x~cos~x\\ x~cos~x+sin~x &...

Homework Statement Hey everyone. I'm in an introductory differential equations class, and I think this homework problem has got me stumped. The functions y1(x), y2(x), ... , yn(x) are linearly independent on an interval I. c1y1(x)+c2y2(x)+...+cnyn(x)=0 for all x in I, implies that...

Well if I have a worldline given by x^{\mu}(\tau) And I want to make a Poincare transformation: x^{\mu} (\tau) \rightarrow \Lambda^{\mu}_{\nu} x^{\nu}(\tau) + a^{\mu}. I have one question,why can't a, \Lambda explicitly depend on \tau? that is to have: x^{\mu}(\tau) \rightarrow...

Homework Statement Write the KVL Equation for the outer loop Homework EquationsThe Attempt at a Solution The question above is a sample I have made for such a condition. The goal is not to find the value, but only write the correct equation. If an independent current source is connected in...

There is a Theorem that states that if G = (V, E) is a graph, then S is an independent set $\Leftarrow\Rightarrow$ V - S is a vertex cover. Suppose the vertices have positive integer weights. Does it follow from the theorem that: S is an independent set with maximum weight...

Homework Statement the expected frequency for the age of (21-30, 31-36, more than or equal to 37) for operation is less than 5 , so combination of these numbers are required for the expected frequency to be more than or equal to 5 . my question is which numbers should i combine? would my ans...

Sorry I failed to make Latex work, don't know why... 1. Homework Statement We consider for a given potential. Psi is also normalized... Homework Equations Show that expectation value of energy is independent of time. The Attempt at a Solution Well, I'm use to expecting values, but not of...

Hello! (Wave) Could you help me at the following exercise? (Thinking) Let $Z \sim N(0,1) $ , $Y \sim \chi_n^2$ and $Z,Y$ independent . Show that the random variable $T_n := \frac{Z}{ \sqrt{\frac{Y}{n}}} \sim t_n$.

Hi, I want to solve the following diffusion equation: (d/dt) C(r,z,t)=D*∇^2 C(r,z,t) where C is the concentartion and D is the coefficient of diffusivity (constant) with initial condition C(r,z,0)=C0 (constant) and boundary condition dc/dr=0 at r=0; (dc/dz) at z=-L equal to (dc/dz)...

Hi I've tried to solve the following circuit using Kirchoff's laws but i get wrong results.I know that because I've got a different solution of the same excercise.I've attached the image.My question is what are the equations of Kirchoff's laws because I try this over 2 hours and I can't figure...

"Volume of a primitive cell is independent of the choice of the cell." Why?

Hello everyone, I've been trying to figure out how i can have two different inputs that are switchable from one to another that drive a single output. However i don't want the inputs to drive each other, and also want the mechanism to be compact in size and fairly lightweight. So how can i do...

Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?

does anyone have a proof of this?

Suppose we have some partial differential equation for a scalar ##f## $$Df = \rho$$ taking values in ##\mathbb{R}^n##, and further suppose that the differential equation is completely independent of the variable ##y:=x^n## so that the differential operator ##D## only contains derivatives with...

It's known that the Density of States in 2D is given by, g_2(E)dE = \frac{a^2m}{\pi\hbar^2}dE The density of states in 1D and 3D are as follows, g_1(E)dE = \left(\frac{a}{\pi}\sqrt{\frac{2m}{\hbar^2}}\right)\frac{1}{\sqrt{E}}dE g_3(E)dE =...

i have drawn the venn diagram for the question... i am not sure it's correct or not. the question states both are independent events. i don't understand the working in part b ... for me , my ans would be p(A) +p(B).. correct me if i am wrong. thanks in advance.

why the topological term in gauge theory, ε_{\mu\nu ρσ}F^{\mu \nu} F^{ρσ} ,is scale-independent?

Homework Statement Given 2 1 1 0 0 0 1 1 0 0 0 3(i) Show that the rows of A are linearly independent. (ii) Show that the nonzero rows of any matrix in row echelon form are linearly independent.The Attempt at a Solution i) REF gives 1 0 0 | 0 0 1 0 | 0 0 0 1 | 0 0 0 0 | 0 x1 = x2 = x3 =x4 =...

Hey! :o I am facing some troubles understanding the proof of the following theorem. Let $\overrightarrow{F}$ be a vector field, $\overrightarrow{F}=M\hat{\imath}+N\hat{\jmath}+P\hat{k}$, where $M,N,P$:continuous at a region $D$ ($M,N,P \in C^0(D)$) . Then a suficient and necesary condition so...

I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...

Why are y and y' treated as independent variables, while they are not? Another slightly related question: if ' = d/dt then df'/dg' = df/dg because f' = df/dg g', but if we differentiate f' to g' we implicitly assume that df/dg is independent of g', is it?

I am thinking about acquiring some battery storage units for single residential house. What is the cheapest and efficient battery for homes and where can I buy it? Would it be bloom energy, fuel cell or solar panel( transparent)? What are some creative solutions? One idea was next to a river...

Homework Statement Say we have the plane, x+2y+4z=8 (part of a larger problem) Homework Equations The Attempt at a Solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two...

i.e., does the set of functions of the form, \{ x^{\frac{n}{m}}\}_{n=0}^{\infty} for some fixed m produce a linearly independent set? Either way, can you give a brief argument why or why not? Just curious :)