Points Definition and 1000 Threads

Homework Statement Find the equilibrium points of the system, determine their type and sketch the phase portrait. ##\frac{dx}{dt} = -3y + xy - 10, \frac{dy}{dt} = y^2 - x^2## The attempt at a solution Putting it together: ##\frac{dy}{dx} = \frac{y^2 - x^2}{-3y + xy - 10} \equiv...

Hallo all... I have a couple of plot values that I am trying to derive a formula from. The points are almost linear but not quite... Was hoping someone could shed some light on how to go about this... I have Matlab 7.1, would like to use it if at all possible... Any help would be...

if A is a subset of B and the frontier of B is a subset of A then A=B. I am pretty sure that this is true as I drew I diagram and I think this helped. A frontier point has a sequence in the set and a sequence in the compliment that both converge to the same limit. However I'm not really...

How would I go about proving that if A is a subset of B then the interior points of A are a subset of the interior points of B?

Background: I've derived the equation of motion of the bead shown in the picture below using the Lagrangian \omega^2Rsin(\theta)+r\ddot{\theta}=0 The equilibrium points are at θ=0 and π. I'm now to show that only one of these points is stable. Homework Statement Show that only one of the...

Hello! First of all, thank you for your time in reading my post. Secondly, I am not looking for people to freely give me the answers. With all that said... Homework Statement I have a test point randomly selected on a graph, but what I am trying to figure out is where on this graph...

3.4. Let E\in  R. Prove or disprove the following statements: (i) if a\inE and b\inE^{c} = ℝ\E and a < b then [a ,b] \cap∂E IS NOT EQUAL TO ∅. (ii) if a\inE and b\inE^{c} = ℝ\E and a < b then (a ,b) \cap∂E IS NOT EQUAL TO ∅. I am really stuck I know that the frontier of a set is when a...

How do you find the interior points of a subset? I understand that a point is an interior point if there exists an epsilon neighborhood that is in the set, but I don't know how that would work with specific sets. Any hints?

Homework Statement Find the Möbius transformation that maps 0 -> -1 1 -> infinity infinity -> 1 Homework Equations w = f(z) = \frac{az + b}{cz+d} The Attempt at a Solution My first idea was to attempt to solve it as a normal system of eq's but that quickly falls apart due to...

[FONT=arial]Definition: A subset $D$ of $\mathbb R$ is said to be discrete if for every $x\in D$ there exists $\epsilon>0$ such that $(x-\epsilon,x+\epsilon)\cap D=\{x\}$. Question: Does there exist a discrete subset $D$ of $\mathbb R$ such that the set of limit points of $D$ is an uncountable...

Hello MHB,This is an old exam I got a question, Decide all stationary points to function $$f(x,y)=x^3y^3$$ under constraint $$x^3+y^3+6xy=8$$So basicly this is how they Solved it and I did so as well but I Also have learned that there is stationary point where gardient of constraint is equal to...

Tell me if I am correct: The wave part of wave-particle duality is a probability wave. An electron, for example, is always a 0 dimensional point (as far as we know), and the wave characteristic of the electron determines the possible locations of the electron and probability of finding it in...

Hello, Suppose I have a primitive cubic cell with 8 atoms, one on each corner of the cube. I don't understand how this consists of only one lattice point? Doesn't each corner have a lattice point, thus the cell would consist of 8 lattice points??

Hi, I've seen pictures like this one: http://www.lcst-cn.org/Solid%20State%20Physics/Ch25.files/image002.gif Is there any good explanation somewhere on this subject? I'm using Kittel's book but there's nothing in there on this.

hey folks, I am making a program that uses object tracking to watch a juggling pattern and plays notes based on the peaks of the balls. I want to predict when/where(x,y) a peak will happen before it does and what i have to work with is when/where(x,y) the ball appears in each frame. I have...

Homework Statement Find the potential inside and outside a uniformly charged solid sphere of radius R and total charge q. Homework Equations V(r) = -∫E dl The Attempt at a Solution I just have a question about finding the potential inside the sphere. Why integrate from infinity...

Homework Statement f(x,y)= 3x5y2 - 30x3y2 + 60xy2 +150 How do I find the critical points where this equation equals zero? Homework Equations None? The Attempt at a Solution I found the partial derivatives, but I'm stuck now and don't know where to go from here. dx = 15x4y2...

Find all starionary points to function $$f(x,y,z)=x^2+xy^2+yz^2-2z$$ and Also decide it character. I find a point at $$(-1/2,1,1)$$ now I have to check if it is semidefinit etc.. But I only know the formula for 2 variable $$Q(h,k)$$ I try search this method in My book and can't find it.. What...

Homework Statement What are the bifurcation values for the equation: dy/dt = y^3 +ay^2 Homework Equations The Attempt at a Solution Equilibrium solutions: y^3 + ay^2 = 0 ==> y^2 (y + a) = 0 ==> y = 0 (double root), or y = -a. a = 0 is the sole bifurcation point, since...

Homework Statement Which of these three points falls on the line? l: r(t)=(i+2j)+t(6i+j-5k) P(1,2,0); Q(-5,1,5); R(-4,2,5) I have the answer, but I don't understand why P and Q fall on the line but R does not. Is it because the i and j magnitudes are different for R?Homework EquationsThe...

Homework Statement Arrange compunds in order of increasing boiling points and explain why. C2Br6,C2F6,C2I6,C2Cl6 Homework Equations The Attempt at a Solution I have C2Cl6 < C2Br6 < C2I6 < C2F6 My explanation is as follows. C2F6 is highest because it has dipole dipole forces...

Homework Statement Suppose (a,b) and (c,d) are unique points in ##\mathbb{R}^{2}## that satisfy Ax+By+C=0. Suppose also that the solutions of Ax+By+C=0 form a line. Then the line that (a,b) and (c,d) lie on is unique.Homework Equations I showed in a previous part of the problem that there...

Homework Statement Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2) Find all critical points, and identify them as maxima, minima, or saddle points. The Attempt at a Solution I took the partial of x and the partial of y, and set them equal to 0. This is what I got: fx(x,y) =...

Homework Statement Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0 Homework Equations I figured it out but I am not sure why we use the equation f(x) = a[x-(-1)](x-0)(x-2) The Attempt at a Solution Im assuming its because if u times that equation that is a...

Why Mild Steel has two Yield Points ? :confused:

Hey guys, I'm just pondering a beam problem fir a structure that I'm analysing. It appears statically indeterminate to me? The beam is bolted to a support at locations A,B & C. There are two point loads between span B-C. There are no symmetrical distances or support locations etc. Initially...

Homework Statement Find the shortest distance between two points using polar coordinates, ie, using them as a line element: ds^2 = dr^2 + r^2 dθ^2Homework Equations For an integral I = ∫f Euler-Lagrange Eq must hold df/dθ - d/dr(df/dθ') = 0 The Attempt at a Solution f = ds = √(1 + (r *...

Is there already a solution to this available somewhere? Am I not googling it right? I did come upon solutions for this with a point and plane defined by way of vectors and normals but not points. Have I stumbled upon a blank I can fill? Is there room here for a math paper? My approach is...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 1) Using a graphing utility solve the following system of linear equations. Round your answer to the nearest hundredth. y = -4x+2 x - 2y = 10 My answer: x...

What will be the electric field at the points p3 and p4 in the attached image. I think at p3 it will be zero as it is inside the conducting surface But what about p4?? Will it be zero too? Due to negative and positive charges or will it be sigma/E(sub)o(/sub).. And why?

Homework Statement Find all singular points of xy"+(1-x)y'+xy=0 and determine whether each one is regular or irregular. Homework Equations The answer is x=0, regular. The Attempt at a Solution I know that x=0 since you set whatever is in front of y" to 0 and you solve for x, right...

Help! Using 3 Points to Find Quadratic Equation in General Form I have a quadratic equation question that I have to solve, but I can't seem to understand it. The question is: "Using points (1,0);(3,0);(0,-6), find the quadratic formula in General Form (ax^2 + bx + c). My teacher says...

I'm doing this in Matlab but it's not restricted to any particular software. I have a bunch of geographical points (x,y coordinates for each) and I want to take all the points that are 50 km or closer to the reference point. I took the great-circle equation to convert geographical longitude...

Homework Statement 1. (a) Find the equation of the circle with the straight line joining A(1;-1) and C(3; 4) as diameter. (b) Hence or otherwise, derive the general formula (x - x1)(x - x2) + (y - y1)(y - y2)=0 of the equation of a circle for the points A(x1; y1) and C(x2; y2): Homework...

Homework Statement I am trying to figure out how to solve for problems that give a function and ask for the critical points. However, the ones I am having difficulty with are the ones that have multiple trigonometric functions included in them.Homework Equations Find the critical points of the...

Find the Net Resistance between A and B in attachment 1. The circuit in attachment 1 simplifies to attachment 2 from the fact that the points C and E are equipotential. Same goes for D and F. So we remove CE and F as no current passes through equipotential points. But why? How are these 2...

Hi, I am trying to simulate a tangential force acting on a point on a structure and the corresponding opposing force caused by the moment of inertia of a mass at a different position. In this image the structure rotates around point c and there is a vector out of mass m opposing the...

Greetings helpful gentlemen and gentle women! The following is a problem I ran into during my internship. The background of my problem is biological/chemical in nature, so I’ll try to bother you as little as possible with the details. Thanks in advance for any help given. Homework...

So I was reading up "Zero Moment Point -Thirty Five Years of Its Life" by Vukobratic for a presentation, and is said something like this: So if I am reading this right, it's saying the point where the GRF is acting upon will shift based on the magnitude of the force created by the...

Hello. I am new to these forums. I don't really know if this is the right place to post this, but here it goes. I was thinking, what If there were two bodies (represented by points) in space (two dimensional space to keep it simple) with known position at time zero, where the first is moving...

I'm working on a green's theorem integral and I'm given a line (0,0) to (1,2) which i parameterise as (t,2t) but the answer is actually (1-t, 2(1-t)) and if I use my parameterisation on the integral I get a different answer!

Homework Statement Find the points on the graph of x3-y3=3xy-3 where the tangent line is horizontal Homework Equations y = f(x) so implicit differentiation must be used when taking the derivative of y (xy)' = xy' + y The Attempt at a Solution So if the tangent line is...

Homework Statement Problem #1: List in order of increasing boiling points, n-pentane, neopentane, 1-chloropentane, and octane. Problem 2: List in order of increasing melting points, cyclohexane, n-hexane, trans-oct-3-ene, cis-oct-3-ene, acetanilide, and aniline. Homework Equations...

Hello, I'm new in this forum. I would like to know how to calculate to obtain the function expression of some given coordinate points(x,y). For example, if I have 6 coordinate points which are (x,y) (0.23, 4.5) (0.25, 6.5) (0.35, 8.8) (0.43, 15) (0.45, 17) (0.5, 25) The (x,y) relation...

Homework Statement Find the points on the graph of y = x3ex where the tangent line is horizontal. (Your answer should include x-values and y-values) Homework Equations Product rule fg'+gf' The Attempt at a Solution (x3)(ex)+(ex)(3x2) x3ex+3x2ex= y' x3ex+3x2ex= 0...

How could one obtain a function y=f(x) that satisfies a number of data points (x_{i},y_{i}). That is how would it be possible to get a function if some points that are to lie on it have been given? I've seen some lectures on interpolation but all I've gotten is only the way to solve problems...

Hi all, Perhaps I'm asking the wrong question but I am wondering about the relationship between different definitions of, for the sake of argument, the torus. We can define it parametrically (or as a single constraint) and from there work out the induced metric as with any surface. But...

Homework Statement f(x) = x ln(x) The attempt at a solution f'(x) = product rule, resulting in 1 + ln (x) So by way of solving the problem, set 1 + ln (x) = 0 Now idealistically, find something in x that, when added to 1, equals zero. Now here's a problem I have. How do I know when to...

I'm looking for an analytical solution to a very simple problem I've come across. Start with a circle of radius a. Now place n points at random positions inside this circle. Can you calculate the expectation value for the mean distance between the points? For the sake of argument can you...

Assume that a box is motionless and is located on the floor ground (one box's face touches the floor completely). If we apply a force to this box such that the box keeps its motionless state, what we can say about the friction directions of all contact points between the box and the floor? Are...