Points Definition and 1000 Threads

Homework Statement Infinitely long cylinder of radius R with uniform charge ρ. Calculate the electric potential at all points in space. Homework Equations V(a)-V(b)=-∫ba\vec{E}(\vec{r}')°dr'\hat{r} The Attempt at a Solution Generally potential is calculated with a reference...

The problem is: Let A, B and C be fixed points, and α,β,γ and κ are given constants, then the locus of a point P that satisfies the equation α(AP)2+β(BP)2+γ(CP)2=K, is a circunference. Prove it. I need at least some hint to answer it, I tried using the distance between two points formula but I...

I am trying to remember how to define a branch point and cut. Given the following functions: \[ f(z) = \sqrt{\frac{z}{1 - z}} \] The branch points are then \(z = 0\) and \(z = 1\) and the branch cut is the line from \((0, 1)\), correct? \[ f(z) = (z^2 - 4)^{1/3} \] Here the branch points are...

Homework Statement Consider a solid box with dimensions L,W, and H. Let S be the set of all points whose distance is at most 1 from the nearest point inside or on the box. What is the volume of S? Homework Equations Not sure if there are any? The Attempt at a Solution My initial...

Homework Statement Total Weight of System = 3301 kg Length, Width of Sytem = (4670mm, 1931mm) Calculated Center of Mass = (2261mm, 1065mm) Find weight at the following points: Point I (104, 1046) Point II (3182, 1867) Point III (3182, 225) Homework Equations Center of...

I just completed a brief introduction to branch points in complex analysis, and I find it difficult to imagine/come up with functions with nonzero branch points. My difficulty is this: for the point to be considered a branch point, f(r,θ) and f(r,θ+2π) must be different for ANY closed path...

Homework Statement Let a particle of mass m moving in 2d space in a potential V (x, y) = -1/2 kx2 + 1/2 λ0 x2y2 + 1/4λ1x where k,λ0,λ1 > 0.At what point (x0, y0) is the particle in stable equilibrium? 2 marks Homework Equations ∂V/∂x=0 ∂V/∂y=0; ∂2V/∂x2 > 0;∂2V/ ∂y2 > 0 The...

Dear all, I was reading "Nature of space and time" By Penrose and Hawking pg.13, > If $$\rho=\rho_0$$ at $$\nu=\nu_0$$, then the RNP equation > > $$\frac{d\rho}{d\nu} = \rho^2 + \sigma^{ij}\sigma_{ij} + \frac{1}{n} R_{\mu\nu} l^\mu l^\nu$$ implies that the convergence $$\rho$$ will become...

I am not sure if this is the right forum for this question, but I arrived at the question while studying the principle of stationary action so here it is: Consider the problem of finding the shortest path between two non-antipodal points on a sphere. Usually one solves this by using calculus of...

Recently, I learned that, in a probability density function, the probability of the occurrence of any specific x-value is in fact zero, for the relevant interval on the function is a point, which has zero width and therefore has zero area associated with it under the probability curve. This...

while drawing the dc load line , , we take VCE = 0 and mark it as saturation point but but in saturation state VCE is very small but not zero..! I actually want to make clear that whether its a fact or is it just an assumption to find out saturation point..?? similarly for the cutoff point we...

Find the points of intersection of $\rho=\cos\left({2\theta}\right)$ and $\rho=\cos\left({\theta}\right)$ By setting $\cos\left({2\theta}\right)=\cos\left({\theta}\right)$, we get the solutions $\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$. My question is how come that doesn't give us all the...

Homework Statement I'm having trouble understanding a concept. Given a conducting box with point a located outside the box, point b located within the (thick) wall of the box and point c located within the cavity of the box, I have to calculate the electric field at each of these...

I'm trying to work out the equation of a curve through 5 very specific points... these points are (47.5, 46.3) (45,48.1) (43, 38.1) (40, 32.8) (37, 26.5) Thought of having general equation ax^4+bx^3+cx^2+dx+e and subbing all the points in and solving but that would take way too long... If...

excuse my TERRIBLE drawing but roughly, is this drawing a good representation of the points? A(-4,0,-1) B(3,1,-5) C(2,4,6) in my drawing i have the axis as 2, 4, 6 etc

how would i plot points in 3D on the ti nspire cx cas? like these 3 for example: (-4,0,-1), (3,1,-5), (2,4,6)

I know it's long but I really need help. I'm terrible at math. Anyway, given only a start and end point, I'm trying to draw a line by creating a number of points at regular intervals between those start and end points. This is what I have so far (it's from C# code so I hope it's not too hard to...

Homework Statement (2; 0; 1); (-1; 2; 3); (3; 2; 2) and (3;-6;-3) Homework Equations PS→⋅(PR→×PQ→)=0 The Attempt at a Solution Hi all, I am just wondering if my calculations are correct, and in fact these points do not lie on a plane. My answer is = 50 and i am not confident. Can...

Hey guys, I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question. I'm only asking about two. Please ignore question one. f'(x) = 2(x^ 1/3) - 1. Moreover, I proceeded to find f'(x)=0 and f'(x) = DNE, which gave me f(2^1/3)=4.74...

Hey guys, I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question: This thread is only for question one. Please ignore number two. So I used the quotient rule to differentiate, giving me: f'(x) = [2x(x-2)-2(x^2)]/(x-2)^3...

Imagine points in a plane with a uniform density. To use a simple model, consider just a finite region such as the unit circle and randomly place M points into that unit circle. By uniform density, I mean that any infinitesimal area anywhere in the unit circle has the same probability of...

(I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in the length restrictions.) A recurring theme in a problem I am exploring is counting the number of subsets of size n in Z^{d}_{3} that have at least m mutually cohyperplanar...

Hey guys, Need some more help again. I'll keep it brief. This thread is only for question one. Please ignore 2ab. I started off by computing f'(x) via the product rule and calculating the zeros, at which point I got: x= 1/√ 5 and x=√(3) However, I'm at a loss as to what I should do...

Hey guys, I'm doubting some of my answers and I'd appreciate some help. I'm only asking about 2abc, ignore 1ab please: For 1a, I simply took the derivative (as I did with all three of these questions) and calculated global and local extrema and critical points. Ultimately, I found that...

Definition/Summary In the plane with coordinate system (O, \vec{i}, \vec{j}) are given the points A(x_1,y_1) and B(x_2,y_2) (see the picture). We want to determine the distance d between the points A and B. Equations distance between two points (x_1,y_1) and (x_2,y_2)...

So I have several problems that ask me to find all points of intersection algebraically, but I haven't been able to make much headway on most of them. The first problem Homework Statement Find all the points of intersection algebraically of the graphs of ... on the interval [0, 4π]...

I am looking at a reflection of an object that is on the floor in a plane mirror. If the object is a certain distance away from the mirror, how would I use the properties of similar triangles to calculate the positions of the points on the mirror that each ray (one to top of eye and other to...

Homework Statement Find an equation of the plane that passes through the points (4,2,1) and (-2, 9, 6), and is parallel to the z axis. Homework Equations a(X-Xo) + b(Y-Yo) + c(Z-Zo) = 0 The Attempt at a Solution Okay so for this one, I first tried to make a vector out of the...

Homework Statement here's the question , ans any my hand written working. which one is correct ? my ans or the model answer? Homework Equations The Attempt at a Solution

Hello, I want to find out the 'average distance' between many points on a 2D plain. That is, if you were standing on a point, what would be the average distance to all other points? For example, if there are three points A, B and C. AB = 5, AC = 10 and BC = 15, adding these up and dividing by...

Homework Statement Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0) +q1 at x = 0 -q2 at dist from origin x = a +q3 at dist from origin x = -2a where q1, q2 and q3 are magnitudes of the charges. Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on...

Hi guys & girls, I'm using Google maps coordinates to draw a line and want to divide the line by its length, giving segments where the length of each segment is equal to 1. EG: P1 p1.lat = 54.97435323116719 p1.lng = 54.9742647135445 P2 p2.lat = -1.6116368025541306 p2.lng =...

Say I have an N X N array of points, I would like a formula to give the mean distance between the points. There are lots of short distances but only two long ones (diagonal). There are plenty of algorithms to do this but I would like to work out a formula if there is one. Can someone point me in...

Hi everyone: I just started to learn special relativity but totally being confused about "velocity", "momentum" and "force". 1. The relativistic momentum is defined by "rest mass * ordinary velocity * gamma". There are 2 kind of explanations. The first one is combining "rest mass * gamma"...

Hi My FORTRAN is rusty and my brain is even more rusty. I want to populate an annulus with a randomly distributed set of points. Any hints or tips to get me thinking about this would be gratefully received. Thanks D

Suppose there is a point mass performing circular motion about an axis shown below: https://drive.google.com/file/d/0B36r-g6bshskV2hIcl91aXl4ZzA/edit?usp=sharing If the angular momentum is taken about the origin O, then the angular momentum L is not parallel to the axis of rotation. As...

Homework Statement since point P is ahead of point O, why the displacement , y , of P shouldn't be Asin(wt + 2pi/(x)) ? Homework Equations The Attempt at a Solution

Determine whether the points lie in a straight line: 1) A (2,4,2), B (3,7,-2), and C (1,3,3) 2) D (0,-5,5), E (1,-2,4), and F (3,4,2) I'm not sure what method I need to use to show that they are or are not in a straight line. I know that the three points in a are not in a line but those in...

Do you need to know power series solutions to learn laplace transforms? It is because I am having trouble learning solutions about singular and ordinary points. If yes, then I'll come back to solutions about singular and ordinary points.

Homework Statement Find the equation for a hyperbola centered at the origin with points (-10,3pi/2) and (2,pi/2) Homework Equations x^2/a^2 -y^2/b^2=1 or y^2/a^2 - x^2/b^2 = 1 * r=ke/(1±ecos(theta)) *cos can be replaced with sin and the ± is either a plus or a minus depending...

Homework Statement The problem - confirm that the amount of radiation measured from a source is related by inverse-square to the distance. Here is a graph of my data fitted to y = a1 * x^a2. Every point is an average of 3-8 measurements (as many as needed to have a statistical error of...

I have a function: f(x) = Asin2(x) + Bcos2(x) + Csin(2x) and I want to find the minimum turning point(s). To start with, I calculated: f'(x) = (A - B)sin(2x) + 2Ccos(2x) Therefore, turning points occur when f'(x)=0, or: tan(2x) = 2C / (B - A) To find the minima, I then want to...

Given a function Hn-Hn is localy lip on its domain and f(p)=0 for some p an element of D if x is a solution of the system x' =f(x) on interval I and x(s) not equal to p for some s in I. how can i show that x(t) is not equal to p for all t in I

There are two charges 2 C and 3 C and 100 cm apart from each other. Find a point where electric potential is zero? Consider 2 C charge on the origin.I have tried out but don't get it solution... 1) If you take point between two charges then 2 C----------100 cm------------------3 C...

I am working on finding the area of a solid object. I have 4 points that I need to calculate a cubic equation from. I have tried relentlessly but to no avail I always get the wrong answer. The four points are;(0,2.7) (0.5, 2.9) (1,3.2) (1.9, 3.4) Using excel, the formula should be...

I have some noisy data (x-y coordinates) containing two distinct clusters of data. Each cluster is centred at an unknown point on the unit circle. How can I estimate these two points (green points in the diagram)? We can assume the noise is Gaussian and noise power is equal in x and y...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement a) Write down the steady-state mechanical energy equation for flow from point (1) (located at the free surface of the creek) to point (2) located at the free surface of the tank. For the purposes of this problem you can assume the pressures at both points are atmospheric...

Given Vector Field: $F=2(x+y)\sin\pi za_x-(x^2+y)a_y+\left(\frac{10}{x^2+y^2}\right)a_z$ specify the locus of all points at which a.) $F_x=0$ b.) $F_y=0$ c.) $|F_x|=1$ please help me get started with this. thanks!

Can someone please help me with this? I can't for the life of me figure out how to do these points. How do I line up the x, y, and z? I just can't grasp it and can't find anything online.