Points Definition and 1000 Threads

I'm trying to understand the concept of vectors. Vectors have magnitude and a direction. When I read vector with some values \textbf{x} = \left(\begin{array}{c}x_1\\x_2\\x_3\end{array}\right) = \left(\begin{array}{c}1\\2\\3\end{array}\right) I'm not sure what these values are. Are the values...

Homework Statement isn't that p1 and [2 at the same point ? why shouldn't the P1 = P2 , which is ρg(h1 +h2 +h3) ? Homework EquationsThe Attempt at a Solution

Hi, Suppose I have a data structure that models a polygon, by storing all the nodes of the given polygon, and their connections (i.e. edges). I understand that sorting a set of nodes that may form a concave hull is ill-defined, as there could be many polygons that can be formed with those. But...

Hi, I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are...

Homework Statement "Determine the set of points at which the function is continuous" ƒ(x,y,z) = √y/(√(x2-y2-z2)) Homework Equations ƒ(x,y,z) = √y/(√(x2-y2-z2)) The Attempt at a Solution If y is zero this function would be discontinuous or if the denominator became zero. As much detail as you...

Homework Statement A dipole is centered at the origin, with its axis along the y axis, so that at locations on the y axis, the electric field due to the dipole is given by E vector = 0, 1/4πε0 * 2qs/y^3, 0 V/m The charges making up the dipole are q1 = +6 nC and q2 = -6 nC and the dipole...

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?

Homework Statement A strip of invisible tape 0.13 m long by 0.019 m wide is charged uniformly with a total net charge of 5 nC (nano = 1 ✕ 10−9) and is suspended horizontally, so it lies along thex axis, with its center at the origin, as shown in the figure below. Calculate the approximate...

Homework Statement Given A = [2, 9, 8], B = [6, 4, −2] and C = [7, 15, 7], show that AB and AC are perpendicular, then find D so that ABCD forms a rectangle. Homework Equations Dot Product The Attempt at a Solution The vector AB = B - A = [4,-5,-10] The vector AC = C - A = [5,6,-1] AB⋅AC...

Homework Statement Problem that was gone over in class, but I missed part of the lecture Describe all points (x,y) satisfying | p - s | + | p - t | = Q where, Vector p = <x,y> Vector s = <a,b> Vector t = <c,d> a,b,c,d and Q are constants and Q is greater than | s - t | The Attempt at a...

Is it possible to derive the standard normal distribution from using polar form p = r*e^(i*v) to distribute uniform points along the contour of a circle? I've read that it is possible to randomize points like that using X and Y values with normal distribution by normalizing each point, but I...

Looking for a Book on the LaGrangian Points solution in an Eigen System calculation for all the Planets.

Homework Statement Find the potential difference ##V_A– V_B## for the circuit shown in the figure. Homework Equations Kirchhoff's laws. The Attempt at a Solution If we assign potentials to junctions starting by setting ##A=0## Current ##i_1## flow through each vertical resistances and ##i_2...

Hey, all. I've decided to go back and work on some old K&K problems that I didn't finish last time. Here's a neat one that's been giving me trouble. I hadn't attempted problem a yet (I admittedly completely overlooked it by accident!). For b, I had a difficult time finding a good starting...

A sphere with radius "r" has three points on its surface, the points are A, B, and C and are labelled (xa, ya, za) and so on. What is the general formula to calculate the area on the surface of the sphere defined by these points?

Hi! I am trying to build a better understanding of quadratic functions. So I had this idea of trying to fit a quadratic function to two arbitrary points, but I am not sure how this really works. Given the points (-4,1) and (12,1) on a Cartesian plane, how can a quadratic function be defined...

I think this should be my last question :D It's a question i missed on my last exam and have no idea how to do it and I wanted to quickly go over because my final is in a few hours so if anyone could help that would be awesome View image: 20151215 092327

identify the type of critical point as spiral, center, saddle, proper node or improper node. in addition, identify the stability of the critical point as stable, unstable, or attractive and stable. View image: 20151215 084536 1 In order: proper node, saddle point, improper node, center But I...

Spacetime shrinks in a gravitational field. As I understand it, objects falling into a black hole will appear to contract in size and run slower as they approach the horizon. This is similar to how things contract and slow down when traveling close to the speed of light because they are...

Hi Community, I have this question. When I graph it I get: When I answer the first sets of questions a, Intercepts: x=(-6), x=0, x=6 Stationary points: (0,0) , (-3\sqrt{2}, -324) , (3\sqrt{2}, -324) Points of inflection: x=0 This is where I was wrong. (It's a turning point isn't...

I have a hammock that is rated to 400 lbs. I want to use two neodymium magnets to suspend the hammock from two steel posts. Do I need two magnets rated 400 lbs each?

Homework Statement A +4.0 μC-point charge and a -4.0 μC point charge are placed as shown in the figure. What is the potential difference, V_A - V_B, between points A and B? (k = 1/4πε_0 = 8.99 × 10^9 N · m^2/C^2)...

Homework Statement The question is: What's the voltage drop between point A and B ?? (Suppose that E2 > E1)2. The attempt at a solution First, I need to solve the current flowing in this circuit, which can be done using KVL. The current flowing is ##\frac{E_2-E_1}{R_1+R_2+R_3+R_4}## (which...

Homework Statement X'=x-y^2 Y'=x^2 -xy -2xHomework Equations Find the critical point of this system. The Attempt at a Solution I know one point is (0,0). When I tried it I got sqrt(x)= 2 and sqrt(x)= 1 but the point (1,1) doesn't fit later parts of the question. I'm also aware that since a...

I was reading this: http://www.creatis.insa-lyon.fr/~dsarrut/bib/Archive/others/phys/www.mas.ncl.ac.uk/%257Esbrooks/book/nish.mit.edu/2006/Textbook/Nodes/chap06/node29.html Under the first figure it states "Figure 6.20: The boundary layer at a stagnation point on an airfoil has a constant...

I am planning on transferring to a 4 year university to major in physics. I am currently overseas and must take classes online. After an almost endless grueling search I was able to find a school that offered an associates program online that I feel is in the right direction for what I intend to...

Homework Statement $$\dot{x_1}=x_2-x_2^3,~~~~~~\dot{x_2}=-x_1-3x_2^2+x_1^2x_2+x_2$$ I need help in determining the type and stability of the fixed points in this system. Homework Equations The Jordan Normal Form[/B] Let A be a 2x2 matrix, then there exists a real and non singular matrix M...

A couple questions, please: I know that the Lagrangian points 1, 2 and 3 are unstable and special Lissajous orbits plus some station-keeping are required to place a spacecraft around them. But I was wondering if they are so totally unstable that they can't temporarily "capture" a passing...

Why are tangent spaces on a general manifold associated to single points on the manifold? I've heard that it has to do with not being able to subtract/ add one point from/to another on a manifold (ignoring the concept of a connection at the moment), but I'm not sure I fully understand this - is...

Homework Statement http://imgur.com/bCTKUIs What is the voltage between P and Q? Homework EquationsThe Attempt at a Solution Don't know how to begin. I thought maybe I could walk around the circuit to se how the potential changes. Is that a good idea?

Homework Statement Find all stationary points of the function G(x, y) = (x^3)*e^(−x^2−y^2) Homework Equations fx=0 and fy=0 The Attempt at a Solution Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4) Gx = 0 implies 3x^2-2x^4=0 x^2(3-2x^2)=0 hence x =0 ,+or-...

I am a bit confused. Why ##\frac{1}{\sqrt{z}}## is branch point and ##\frac{1}{z}## is pole. And why we cannot use Cauchy integral theorem when we have branch point? Why we need to cut off branch point when we integrate? Thanks a lot for the answer.

Homework Statement In the circuit the battery is ##10V## and each resistor is ##4\Omega## find the voltage on AB Homework Equations 1.KVL and KCL 2. ##V=IR## The Attempt at a Solution ##I_{1}=I_{2}+I_{3}## ##10-4I_{1}-4I_{1}-4I_{2}-4I_{1}=0\rightarrow 10-12I_{1}-4I_{2}=0##...

Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...

Homework Statement find all critical points and identify the locations of local maximums, minimums and saddle points of the function f(x,y)=4xy-\frac{x^4}{2}-y^2 Homework EquationsThe Attempt at a Solution setting Partial derivative respect to x = 0 : 4y-\frac{4x^3}{2}=0 setting partial...

Homework Statement So I have the following hyperbola x^2/4 - y^2/4 = -1 I need to find the focus points of this hyperbola. What is some analytical way to do this ? Thank yoU! Homework Equations I don't know... The Attempt at a Solution I need some analytical way to be able to do this. Can...

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!

Hello! I've encountered a problem of find all points (x,y) on $f(x)=\frac{x-\sqrt{\pi}}{x+1}$ where there are tangent lines perpendicular to $y=-(1+\sqrt{\pi}x+7\pi e^{e^{{\pi}^{110}}})$ So I first found derivative and ended up with $f'(x)=\frac{1(x+1)-(x-\sqrt{\pi})(1)}{x^2+2x+1}$ and then...

Hi all, I have a vacuum chamber which is consistently pumped out by a mechanical pump at the downstream end and is fed nitrogen at the upstream end. The path of the nitrogen is as follows: A mass flow controller regulates 150 SCCM flowing at all times. The N2 flows through several feet of 1/4...

Homework Statement Homework Equations n/a The Attempt at a Solution How was A+B = 0 derived? Is this a general definition?

I'm looking at an ungounded 3-phase system here for starters. In a perfectly ungrounded system, grabbing a phase seems safe in theory, but in practice (because perfect ungrounded doesn't exist), this is a bad idea. I'm trying to determine exactly WHY. If I have a perfect ungrounded system...

Homework Statement Homework EquationsThe Attempt at a Solution we know the electric field at A is 0, so the force is 0. V = work / charge = U / q = F⋅D / q the electric field at B is 4 times 3.6N/C = 14.4 N/C since E = F/q, F = Eq force, F = 14.4q at point b V = 14.4q⋅d/q the...

Hi there everyone, wonder if anyone can help as I'm a bit confused. Ive been asked to find the global extreme point of f(x)=e^(x-1) - x. I have checked my answer against the solution and am correct and my working is as follows: f'(x) = e^(x-1) - 1 = 0. Therefore (x-1)=ln1 (which = 0) therefore x...

Homework Statement Evaluate the Work Integral, ## I = \int_\Gamma [ (\frac{y} {x^2 + y^2} + 1) dx - \frac{x} {x^2+y^2}dy]## between the points (5, 30/pi) and (2,8/pi), using the potential function. Pesent your answer in exact form. Homework Equations ##W = \int F . dr## ##\int_\Gamma...

Homework Statement 1.) Let g(x) = x − (5/x^2) find all critical numbers (if any) of g. Give answers in increasing order (smallest first). Enter DNE in any unused space. x = x = and 2.) Let g(x) = x |x + 5| The Attempt at a Solution [/b] I know I must first take the derivative and then...

Homework Statement Find a function of a decaying logarithmic trend that passes through a set of 3 points (at x=1,2,3) whose sum is S, where S>0. Homework EquationsThe Attempt at a Solution starting point: i assumed the equation had the form: $$y= -kln(x+1)+S$$ with the condition that must...

A function ##f(x)## is continuous in the interval ##[0,2]##. It is known that ##f(0)=f(2)=−1## and ##f(1)=1##. Which one of the following statements must be true? (A) There exists a ##y## in the interval ##(0,1)## such that ##f(y)=f(y+1)## (B) For every ##y## in the interval ##(0,1),f(y) =...

Homework Statement An Arrow is shot from an initial velocity of 45 m/s 52 degrees above the horizontal. It lands on a 5 m high roof of a house. The arrow is shot from a height of 1.5 m. (v) Would it be able to pass over a 50 m high tree located 75 m away? (vi) What is its' total time of...

Hello, This question might seem silly, but I've tried some approaches and none of them seemed to work. Here's my problem: I need some sort of transform that maps points from any quad to an rectangle. I will be using this on a computer graphics software, so you can think of this rectangle as my...

Hi guys, new here. Thank you for reading my post. I'm posting today because although I'm an engineer, I have some brain tumors that have impeded my ability to process most math above basic algebra (despite the fact that prior I'd gone all the way through stats in college). It didn't really start...