Points Definition and 1000 Threads

Homework Statement Suppose that n points are independently chosen at random on the circumference of a circle and we want the probability that they all lie in some semicircle. Let ##P_1...P_n## denote the n points. Let A denote the event that all the points are contained in some semicircle and...

If you have a function with countable discontinuities on an interval, I know that the Fourier series will converge to that function without those discontinuities. But how could you explain that formally? If the basis of the Fourier series span the space L^2[a,b], that would include functions...

Homework Statement Trying to figure out how to model the relationship between two 3D points, A and B. Both points have visibility to 2 common reference points, C and D. Bearing and angle readings are available from both A and B to the reference points C and D. The reference points C and D are...

Homework Statement Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Round the answers to two decimal places.) tan(x) ≈ x Homework Equations derivative...

Probably can't teach about this in the Bible belt... http://www.google.com/hostednews/afp/article/ALeqM5hISS_RrQOpDbJ9sk84ActLvv-6ZA?docId=CNG.9484301c0f281a31e8383bf96341f10b.471

Hello - I need help finding collinear points: Given: Equations of 2 lines, L1 and L2 1 points, P3 Want to find points P1 and P2 that lie on L1 and L2 respectively that are collinear to P3. I know that there can be multiple combinations of points P1 and P2 so to narrow down the list...

I'm creating a computer program and I need to see what's most efficient. I need another program [lol] that I can input 3d points in and have it create the function. the points are this v e t 100 500 3...

Homework Statement This problem is on how to identify the branch points and the branch cuts of a multivalued function. Consider the following function f(z)=Log(1+z^\alpha) where \alpha is a rational number and z\in \mathcal{C}.Homework Equations Obviously, for the function z^\alpha, it has...

Homework Statement What are the critical points of function f(x) = 2 (x^2 + 4)^(1/2) - 4x + 24 ?Homework Equations When f'(x) equals 0 or is undefined, x is a critical number.The Attempt at a Solution The original function is f(x) = 2 (x^2 + 4)^(1/2) - 4x + 24 . I got the derivative as f'(x) =...

Homework Statement Prove that if a Polynomial P(x) of degree n, shares n points with xn, then P(x)=xn. (a more general proof would be almost the same but for two polynomials, but I think I've proved this if this is proved)Homework Equations (FTA) Fundamental Theorem of Algebra - Every P(x) of...

I was wondering how they got all the different combinations of points? Why can't they just put (+-√2,+-1,+-√(2/3)) ?

Homework Statement Find the plane through the points P = (1, 1, −1) and Q = (2, 1, 1) and parallel to a line r {(1, 0, 2) + t(1, 0, 2), t ∈ R} with distance 1 to the plane Homework Equations A=(a1,a2,a3),B(b1,b2,b3),A and B are vectors. AxB= det[i j k;a1 a2 a3;b1 b2 b3] ";" means change of...

Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by x1=x+a(x-y) Given that a is positive number, how can it be shown that the distance x1 to y is larger than distance x to y. I'm mainly interested in a vector interpretation of the above update...

Homework Statement y= (x^2 -7) e^xThe Attempt at a Solution I'm trying to find inflection points by setting the second derivative=0 I found that the derivative is: ##2xe^{x}+x^{2}e^{x}-7e^{x}=0## ##e^{x}[2x+x^{2}-7]=0## Then, the 2nd derivative: ##e^{x}[(x-1)(x+5)]=0##, then the inflection...

Homework Statement Homework Equations KE= 1/2 m v2 PE = mgy The Attempt at a Solution I'm not sure how to start this because there is no given mass. If I use a kinematics equation I don't have an acceleration.

Homework Statement Prove that \int_0^{\infty} \frac{x^{1/\alpha}}{x^2-a^2} dx = \frac{\pi}{2a}\frac{a^{1/\alpha}}{\sin(\pi/a)}\left(1-\cos(\pi/\alpha)\right) where a>0 and -1<1/\alpha<1 Homework Equations It is apparent that there are two first order singular points at x=a and x=-a...

How can one create a uniform solid-angular distribution of vectors in 3D space from a common origin, or in other words a grid of points on the surface of a sphere wherein the points are equidistant from each other? Spherical polar coordinates/the latitude-longitude scheme is obviously not the...

Homework Statement Points (4,4) and (2,0) Minimise 3x1+6x2 s.t. 6x1-3x2=12 x1,x2>=0 Homework Equations The Attempt at a Solution I tried solving this the way LP questions are solved in general, graphically. So I drew a graph plotting the objective and the constraint...

Are inflection points critical points? and what about at the value that f(x) undefined? Is that critical point too?

Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ? *The centres of these circles are all (0,0) *

PROBLEM STATEMENT: I'm looking for a somewhat general method to find the expression for the distance (in \R^2 mortal, euclidean space) between a point in a certain curve and some point outside the line. ATTEMPTS TO SOLVE THE PROBLEM: In the case of the distance between the origin and some...

Classify the equlibrium points of the system-Pls help me, its urgent! Hi , I have my maths exam tomorow and I am not able to understand the concept to classify the equilibrium points of a system.. I will be grateful if anyone could help me with this problem Classify the equilibrium points...

Homework Statement Use implicit differentiation to find y' if (x-y)/(x+y)=(x/y)+1. Now show that there are, in fact, no points on that curve, so the derivative you calculated is meaningless. Homework Equations The Attempt at a Solution I managed to get it into the form: dy/dx =...

Homework Statement Hi guys, I'm having real difficulty with understanding accumulation points. I don' really know why that is since others seem to understand the concept fine but I'm very lost. For example, I'm practicing some questions and one of the is : If S is the set of rational...

Hello everyone, I'm an optometry student who is currently doing Optics 1, and I have a general question about focal points. I can do the math regarding F1, F2, and the nodal ray, and I am decent at drawing the ray traces, but I would like to know more about the actual real world applications...

Is there a clean may to get the fixed points for \begin{alignat*}{9} F - 2B' - cB - \frac{3}{4}AB^2 - \frac{3}{4}A^3 & = & 0 & \quad & \Rightarrow & \quad & B' & = & \frac{1}{2}F - \frac{c}{2}B - \frac{3}{8}AB^2 - \frac{3}{8}A^3\\ 2A' + cA - \frac{3}{4}A^2B - \frac{3}{4}B^3 & = & 0 & \quad &...

Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a weighted barycenter x_o=(o_i*x_i)/(o_1+o_2+...+o_k) also belongs to that line (assume o_i are arbitrary weights)? Does the choice of weights restrict the solutions (ie, a...

Does anyone know where I can find an algorithm for the points of intersection of two ellipses existing with arbitrary center points and rotations and having 0, 1, 2, 3 or 4 points of intersection?

Homework Statement Find the points on the graph y=x^3/2 - x^1/2 at which the tangent line is parallel to y-x=3. Homework Equations The Attempt at a Solution First I found that the derivative of y=x^3/2 - x^1/2 is 1x. I then rewrote the other line as y = 3+x and found the...

Hi all, If a,b,c,d are position vectors of four points A,B,C,D.The points will be coplanar if xa+yb+zc+td=0,x+y+z+t=0,provided x,y,z,t are not all 0,and they are scalars.Is this test needed to show 4 points are coplanar? If we consider two lines joining A,B and C,D then this will give us two...

y=x^5 x=y(y-1)^2 find points of intersect correct to 1 decimal point

So I know that the Lebesgue outer measure of a set of only countably many points is 0. An example of this is the rationals as a subset of the reals.I want to make sure my intuition behind this is correct. The process: Now, if we are going to take the Lebesgue outer measure of the rationals, we...

Hi I used plot digitizer software to pull data points off a picture of a graph and i need to fit a line to the points (and get an equation for the line). I know the data points fit to an s-curve from the picture. I'm thinking excel doesn't do this, or maybe I missed it? I have access to maple...

Homework Statement f(x,y) = xy(9x^2 + 3y^2 -16) Find the critical points of the function and their nature (local maximum, local minimum or saddle) Homework Equations The Attempt at a Solution I have partially differentiated the equation into: fx = 27yx^2* + 3y^3 -16y fy =...

Tricky problem worth 2 points on my final grade :) Homework Statement Homework Equations I honestly don't know how to tackle this. I think it's going to contain ƩF=mg, and some basic kinematic equations. The Attempt at a Solution Where do is start?

Hello everyone! I'm trying to prove that the closure of $A = [-\infty,0)$ is $[-\infty,0]$. So far, I have proved that all points in $[-\infty, 0)$ are limit points of A, then I have proved that $\sup A = 0$, so it is in the closure, so $[-\infty, 0]$ subsets the closure. But how do I know...

Homework Statement What is the minimum number of points a sample space must contain in order that there exists n independent events A_1, ..., A_n , none of which has probability zero or one? Homework Equations None at this time The Attempt at a Solution I was thinking that if each A_i...

The equation for the number of possible connections between n points on a 2D plane is (n-1)*(n/2). What is the equation for the number of possible connections between n points on a 3D plane? Is it the intregal of (n-1)*(n/2)?

Homework Statement Let A,B,C be three sets of complex numbers as defined below A = {z:|z+1|\leq2+Re(z)}, B = {z:|z-1|\geq1} and C=\left\{z: \frac{|z-1|}{|z+1|}\geq 1 \right\} The number of point(s) having integral coordinates in the region A \cap B \cap C is Homework Equations...

I am trying to use Mathematica to fit a curve to these data points ListPlot[{{2*Pi/(1 - 0^2/16), 5 (3 - Log[2])}, {2*Pi/(1 - .05^2/16), 10 (3 - Log[2])}, {2*Pi/(1 - .1^2/16), 15 (3 - Log[2])}, {2*Pi/(1 - .15^2/16), 20 (3 - Log[2])}, {2*Pi/(1 - .2^2/16), 25 (3 - Log[2])}...

Hello everyone! I'm asked to find a set that is bounded and that has exactly two limit points, now this is how I am thinking. Consider the set $A_n = [0,\frac{1}{n}) \cup(2-\frac{1}{n},2]$, if $A_1 = [0,1)\cup(1,2]$, $A_2=[0,1/2)\cup (3/2,2]$. If I let $n$ grow indefinitely, I will have only...

Homework Statement Find the local max/min or saddle points of f(x,y) = (x-y)(1-xy) Homework Equations The Attempt at a Solution I expanded the equation to f(x,y) = x-y-(x^2)y+xy^2. Then I found the partial derivatives of the function. fx = 1-2xy +y^2 fy = -x^2-2xy I'm...

Homework Statement Let's say that we have a second order polynomial function, and we know all of the points where it intersects with the x and y axis. Ex: (-2; 0), (0; 2), (1; 0) How does on determine the ax^2+bx+c polynomial form based on that? Homework Equations - The Attempt at...

Find the points of discontinuity: f(x) = x + 1 , for x < 1 and 1/x for x ≥ 1? ^ supposed to be a piece-wise function. State whether f is left- or right-continuous at each point of discontinuity. I'm having difficulty figuring this out... please help?

Homework Statement I have to prove that the supremum and infimum of a set of limit points of a a sequence {an} are themselves limit points. Homework Equations The Attempt at a Solution I have been messing around with definitions but have not made any progress. Please help...

Problem: I'm trying to make sure i understand the following proof: Suppose we have the metric spaces (X, d) and (Y, d) with Y < X. Then A is open in Y \Leftrightarrow A = B \bigcap Y where B is an open set in X. Here is the proof I have written down: (\Rightarrow) - Assume A...

Homework Statement Here is the question along with part of the solution. I am online concerned about finding the force at C. The Attempt at a Solution For my solution I decided I would sum the moments about point B. However I ended up getting the wrong answer for the force at...

Homework Statement Find the points nearest and furthest from the origin on the intersection of a plane with a paraboloid. Plane: x+y+2z=30 Paraboloid: z=x^{2}+y^{2} Homework Equations The Attempt at a Solution Obviously the first step is to find the equation of the...

Homework Statement A projectile is fired with velocity v0 and passes through two points, both a distance h above the horizontal. The angle of the barrel of the gun is adjusted for the maximum range, find the horizontal separation of the two points. Homework Equations Max range for projectile...

Hey everyone! Recently got a question in maths which asks: "Use integral calculus to find the equation of the quartic that has stationary points of inflection at (1, 23) and (3, 15) and a y-intercept of 24" This means that the second derivative has the form (as inflection points are...