Points Definition and 1000 Threads

Homework Statement a particle of mass m is contrained to lie on along a frictionless,horizontal plane subject to a force given by the expression F(x)=-kx. It is projected from x=0 to the right along the positive x direction with initial kinetic energy T(o)=1/2kA^2, k and A are positive...

Homework Statement attached Homework Equations The Attempt at a Solution The first two were pretty simple, but I'm having trouble grasping why my guess for #3 was actually correct. Why are we ignoring the parallel battery/resistor combo up top and just adding the voltages of the...

Homework Statement I have four questions based on this principal that I'm struggling with. 1. The Potential at the surface of a sphere of radius R is given by V = kcos(3θ). K is a constant. (Assume no charge inside or outside the sphere). a) Find the potential inside and outside the...

Consider the equation dy/dt = alpha - y^2 a) Find all of the critical points. How does it change as alpha < 0, alpha = 0 or alpha > 0? b) In each case of different alphas, consider the graph of f(y) vs y and determine whether each critical point is asympototically stable, semistable, or...

Can an ellipse's focal points be outside the ellipse? I have tried googling this, but without any good explanations or answers. According to my calculations, the focal points of the ellipse defined by x^{2} + \frac{y^{2}}{4} = 1 are (-\sqrt{3},0) (\sqrt{3},0)) . I maybe wrong of course...

This isn't really hw, just me being confused over some examples. I have 'learned' the basic definitions of neighborhood, limit point, closed, and closure but have some trouble accepting the following examples. 1. For Q in R, Q is not closed. The set of all limit points of Q is R, so its...

I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which represent the circle diameter and another point (P3) NOT on the circle but on its plane. Also known the length of the line from P2 to X, for example d. Another thing that may help, the...

Homework Statement Let X be a metric space and let E be a subset of X. Prove that E' is closed and that E and E-closure have the same set of limit points. Homework Equations The Attempt at a Solution I have proven that E' is closed. Now, from the definition of a closed subset of a metric...

Hi there, I require some advice on how to interpolate more data points on a bump profile. Basically i have a curve defined be twentyfive (x,y) data points. The bump is meant to accurately represent half of an aerofoil. I would like to accurately interpolate more data points (lets say up to...

Let F : \mathbb{R}^2 \rightarrow \mathbb{R}^2 be the map given by F(x, y) := (x^3 - xy, y^3 - xy). What are some singular points? Well, I know that for an algebraic curve, a point p_0 = (x_0, y_0) is a singular point if F_x(x_0, y_0) = 0 and F_y(x_0, y_0) = 0. However, this curve is not...

So suppose you have a nice simple linear system dx/dt = a1x + b1y + c1 dy/dt = a2x + b2y + c2 and a critical point (x0, y0) ≠ (0,0). If you want to analyze the stability in the usual linear method, then I assume there should be some transformation to have the critical point at the origin. So is...

Homework Statement Prove that if E \subset X and if p is a limit point of E, then there is a sequence \{p_{n}\} in E such that p=\lim_{n\to\infty}\{p_{n}\} (I presume that there is an invisible "p_{n} \rightarrow p implies that" at the beginning of the sentence). Homework Equations -...

All complex numbers of the form $(1/n) + (i/m)$, $n,m\in\mathbb{Z}^+$.Complex numbers aren't well ordered so how is this treated?

All numbers of the form $(-1)^n + (1/m)$, $n,m\in\mathbb{Z}^+$. Is this true $(-1)^n + (1/m) = (-1,1)$? If so, the accumulation points are $x\in [-1,1]$ and the set is open.

Accumulation points of rationals and open or closed. I know the accumulation points are all real but I don't understand why. The set is neither open nor closed to but I don't truly see it. Can someone explain both?

All numbers of the form $1/n$, $(n = 1,2,3,\ldots)$.$1/n = (0,1)$ The accumulation points are $x\in [0,1]$. This set is open.

Homework Statement Homework Equations F=Keq1q2/r2 The Attempt at a Solution Using Coulomb's Law, here's what I've worked out: FAB=0.593N FAC=0.309N Fx=0.309 - 0.593cos60°= 0.0125 Fy=0.593sin60° =0.514 √(0.01252 + 0.5142) = 0.514 N/C and θ = tan-1(0.514/0.0125) = 88.6° I'm not sure why...

Homework Statement Find equation of plane containing points: (1,1,5),(3,5,3),(8,8,1),(10,2,2),(18,6,-1),(-1,-3,6) Homework Equations Find 2 vectors given 3 points, using a common point. The cross product of these 2 vectors will be the normal vector of the plane. Use normal vector...

I was trying to compare some solubilities (in water) and some boiling points, and I could not explain it for some molucules. Also, I have some doubts in the theory itself. Why is 2-pentanone more soluble than pentanoic acid? Why is a ketone more soluble than the respective aldeyde...

Homework Statement Find and characterise the stationary points for F(x,y,z) = x2 + xy + y2 - 2z2 +3x -2y +z The Attempt at a Solution I found fx, fy, fz and let them equal to 0. Solving gives me the critical point (-8/3,7/3,14). From here I'm not sure how to determine the nature...

Homework Statement How to find instantaneous acceleration when the velocity final is 4 m/s, the velocity initial is 1 m/s, the time final is 5 seconds, and the time initial is 2 seconds? Homework Equations The Attempt at a Solution I have no idea how to do the second derivative...

Hello all, I'm thinking about the following exercise from Intro to stoch. analysis: Let V be a continuous, nondecreasing function on \mathbb{R} and \Lambda its Lebesgue-Stieltjes measure. Say t is a point of strict increase for V if V(s) < V(t) < V(u) for all s<t and all u>t. Let I be the...

This is something that interested me after reading about time dilation. For the point of making it simpler, ignore relativity relating to gravitational fields Lets say for example, that the Earth does not orbit the sun, and the solar system doesn't orbit within the galaxy etc (makes it easier...

Homework Statement This doesn't seem like much more than a kinematics problem but it's for an upper division mechanics course so I chose to post it here. Feel free to move to intro if necessary. Homework Equations kinematics equations The Attempt at a Solution I focused...

Homework Statement Find the Cartesian Eqationn of the plane containing the points (0,-2,6), (1,8,-2) and (2,0,5). Homework Equations The Attempt at a Solution → OA = 0,-2,6 → AB = 1,10,8 → AC = 2,2,-1 Cross product of AB AC = 6,-15,-18 X - 0 * 6 Y - (-2)...

Say we take N random points in a volume V and connect the points pairwise with line-segments. I would like to estimate the number of segments that intersect some small volume v, and where N is large enough so that any small random sample volume v will have many intersections. Little volume v may...

Hi guys I'm helping my girlfriend with her Calc 1 homework and we seem to be stuck on this one problem. Am I missing something obvious? Homework Statement Homework Equations P = P_0 a^t \frac{5}{20} = \frac{P_0 a^1}{P_0 a^{-1}} \frac{1}{4} = a^2 a =...

A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this about its two end points, you get a sphere. What about for something less than 180 degrees (e.g. 90)?: I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to...

Hey guys, new here and this is my first post. Wondering if anyone could help me. So I've encountered a problem on Lagrange's undetermined multiplier. Usually i have no problem with these, but this one caught me off a little. g(x,y) = x^2 + y^2 - 4xy - 6 = 0 Find the points closest to the...

Homework Statement Just doing some review, and I keep getting the wrong answer. Can someone explain this for me please? The equation of the straight line through the points (-€2; 1) and (2; 3) is Book says the correct answer is 2y = x + 4 What are the steps to get 2y = x + 4 ...

Homework Statement 2. A solid copper sphere of radius 15.0 cm carries a charge of 40 nC. Find the electric field (i) 12.0 cm, (ii) 17.0 cm and (iii) 75 cm from the centre of the sphere. (iv) Explain how your answers would change if the sphere were hollow. Homework Equations...

I was reading a textbook on real analysis and came across this definition:Given a real sequence we say x is an accumulation point if given any \in greater than 0 we can find infinitely many natural numbers n such that |xn-x| is less than \in. I also found a theorem that stated if a real...

Why there is no interior points in a Cantor set? Please explain me in detail.

I wish to take up a discussion between Elroch and DrStupid in RossiUK’s topic “First Post – a question about Black Holes and Gravity”. My post is essentially an exposition of Elroch’s view, which I have shared for many years. Elroch’s exposition was very sedate, and I feel it needs to be shouted...

Homework Statement What is the potential difference between points a and b in the diagram? http://imgur.com/Ubr4A Homework Equations The Attempt at a Solution I have calculated the currents to be: I1=0.30A I2=0.65A I3=0.35A What I tried doing was (0.30*5) - 0.35= 1.15 V but...

I have a lattice plane in 3 dimensional space. Now, I want to cut it in a unit cell, but I have to write some code the make things get easier. As you can see from my figure, I can know the four coordinates of the highlighted atoms which form the boundaries of the top plane. My problem is if...

Homework Statement Find the inflection points and use second derivative test to determine where the function is concave up or down Homework Equations f(x) = (x - 1)/(x2 - 4) The Attempt at a Solution f'(x) = (-x2 + 2x - 4) / (x2 - 4)2 f''(x) = 2x3 - 6x2 +24x -8 / (x2-4)4...

Homework Statement Find the electric field strength at point P, which is located midway between charges A and B. The charges are separated by 20 cm. The first charge has a charge of 20 micro coulombs. The second charge has a charge of -30 micro coulombs. Homework Equations Electric...

I'm at a loss on this question...my troubles seem to be algebraic or that I'm simply missing something.x' = \mu - x2 +4x4 my method for these questions has basically been to do everything required to draw bifurcation diagram bar drawing the actual diagram itself (ie, find equilibria, what...

Homework Statement The problem as attached in the picture.The Attempt at a Solution So here's the problem that I was facing: G(t) has stationary points at t = 0, t = -1/2, t = -4 They correspond to (0,0), (a/4, -a) and (16a,-8a) in the function G(t). However, only (0,0) is a suitable...

I am struggling to find a way to count the number of irrational points defined recursively which satisfies specific conditions. This is the only hurdle I need to overcome, but the problem is proving itself extremely difficult. Here is my construction of a recursion. My goal is to...

I would like to find a way to get the intersection points of a circle and a sphere in 3d. The center of each and their radii are known. This needs to be a general solution so that I can move the center of the sphere in steps and find the intersection at each step. I am curious if this can be...

Hi, there are two material points with unitary mass that can move on a stright line. They are subject to a potential of mutual interaction V which depends on x and y and it's not symmetric, where x and y are the coordinates of the two points. I can choose in the istant 0 v1,v2,x and y. How...

Homework Statement Given a parametric eqn for the x,y coordinates , x(t),y(t) , how can i find the control points? Homework Equations de Casteljau's algorithm is used to compute the value for a given t given the control points. The Attempt at a Solution Control Points 0,3 are given...

Hello, I'm new here and I am not a physicist so please excuse any ignorance on my part. I am wondering if there are any ideas or theories involving the possibility of connecting two points within our universe and being able to see through or move between the two points. I am familiar with the...

I am trying to find out a method of determining the area below a curve. The end points of the curve are known in cartesian space, and the curvature of the curve is known. A diagram of the curve is here, shown in the images belowthis webpage ß must be in radians Where; MD =...

Hello all, I am having an issue with the splot command in gnuplot. The format of the data I am trying to plot is shown below: 3.09411 71.75663 -2.17624 3.09238 67.64099 -1.94456 3.10106 73.70542 -2.85122 3.09494 75.71568 -3.49932 3.09846 75.29150 -1.14593 My...

Hello everyone! I just finishexd reading Death By Black Hole and I was interested in the Lagrange points. Neil talks about how if you placed objects inside of them you could use the points as place holders for objects while building in space. I couldn't seem to find anything about the width of...

How to Find the points on curve which are nearest to origin

I have two circles with the same radius and I want to calculate the points of tangency. For example, in the picture below, I want to calculate (x3,y3) and (x4,y4). I have the radius and the distance between the two circles as shown below: