Points Definition and 1000 Threads

Homework Statement Hi All, I have a problem in calculating the thickness of a coating material inside a tube. The tubes inside diameter is measured before and after coating. The coating thickness is calculated by substracting the diameters and dividing by two to get the thickness of the...

Homework Statement Find all the fixed points to the following Mobius transformation. Homework Equations m(z) = (2z + 5)/(3z - 1) The Attempt at a Solution Aren't all fixed points going to map to themselves? So shouldn't it be solving for m(z) = z and coming up with roots of a quadratic...

Homework Statement The following is part of a solution to a problem about finding equiblirum points of a differential equation and sketching its bifurcation diagram http://img32.imageshack.us/img32/9194/63226925.jpg How did they get y= -1 \pm \sqrt{1- \mu}? Homework Equations The...

If p(x) is a polynomial such that p(0)=5 ,p(1)=4 ,p(2)=9,p(3)=20 , the minimum degree it can have

Homework Statement Hey, stuck on this question in my hydraulics course: Question involves lubricating oil pumped around a large piece of machinery. Density of oil = 810 km/m3. Viscosity = 0.01 kg/m.s throughout the system. Flow rate is 0.140 Litres/sec Pipe diameter = 3mm Pressure...

trying to prove dual of "there are at least tree points on every line" Hi, Assuming the propositions of incidence: (1) on any two distinct points is at least one line. (2) on any two distinct points is at most one line. (3) on any two distinct lines is at least one point. and the...

Homework Statement suppose f and g are conjugate show that if p is an attractive fixed point of f(x), then h(p) is an attractive fixed point of g(x). Homework Equations f and g being conjugate means there exist continuous bijections h and h^-1 so that h(f(x)) = g(h(x)) a point p...

Hi, First time posting so be gentle :) I have a website and on the website I calculate popularity of objects over time. One of the objects is called 'Store Category' - a store has one or more categories. I.e. the store Easyjet, has categories 'Flights', 'Hotels' etc. In order to apply...

Homework Statement Twelve identical wires, each with resistance 1.0 ohms, are linked together to form a octahedron (see figure). What is the resistance between corners E and F? http://etc.usf.edu/clipart/65700/65732/65732_octahedron_md.gif Homework Equations I assume: Ohms Law...

Last week I read this article in Science Daily about BOSS and its recent most accurate measurements of the universe to date. http://www.sciencedaily.com/releases/2012/03/120330081844.htm In describing the experiment to measuring the accelerating expansion of the universe...

Homework Statement f(x,y)=5xy-7x^2+3x-6y+2 [b]2. Homework Equations (f_xx)(f_yy)-(f_xy)^2 the hessian or discriminant of f The Attempt at a Solution i arrived at a solution but i don't think its correct, and the answer isn't in the back of the book, so i just wanted to ask if i did...

Hi folks, I need to evaluate (numerically) a multi-dimensional integral of the form \int_A f(x) dx. Now in my application, I already have points inside the domain A which are distributed like \frac{f(x)}{\int_A f(x) dx}. So I hoped I could use these random points in some importance sampling...

Hi, I'm look for a program that can solve for a general function when given a set of pairs of points? Does anything like that exist? Thanks.

Homework Statement T or F, If f:ℝ→ℝ is continuous on a dense set of points in ℝ, then f is continuous on ℝ. Homework Equations definition of continuity using sequences, maybe? The Attempt at a Solution false. Take f(x)= {1 if x\in Q(rational numbers) and 0 if x\in...

Homework Statement Find the equation of the plane passing through point A(2,1,0), B(3,-1,5) and C(2,2,1) Homework Equations Um..I don't know? The Attempt at a Solution Vector AB=(3 -1 5)^T-(2 1 0)^T=(1 -2 5)^T Vector AC=(2 2 1)^T-(2 1 0)^T=(0 1 1)^T perpendicular...

Homework Statement Hi I have an equation as follows: f(x) = (2x-2.3)/(2x-5.29)^2 what i got for the derivative was: f'(x) = (-1.38-4x)/(2x-5.29)^3 Homework Equations f(x) = (2x-2.3)/(2x-5.29)^2 f'(x) = (-1.38-4x)/(2x-5.29)^3 The Attempt at a Solution what i got for the...

What is the correct way to calculate the probability of a given number of consecutive data points forming a saw-tooth pattern? The magnitudes of the rise or fall (the size of the moutain and valleys) are not material. The only requirement is that each set of three consecutive data points...

Homework Statement ## f\left( x,y\right) =x^{2}-4xy+6x-8y+2y^{2}+10 ## ## f_{x}=2x-4y+6=0 ## ## f_{y}=-4x-8+4y=0 ## ## f_{y}=-4\left( x-y+2\right) ## -2=x-y, then solving fx and using this equality ## f_{x}=0=2\left( x-2y+3\right) =0 ## 2(-2 -y+3)=0 2(1-y)=0 y=1, then pluggin...

How would one show that if there is a number c for which g'(c)=0, then every point on the level set {(x,y)|H(x,y)=c} is a degenerate critical point of f? I know that the question may seem vague, but this is the question as it was given to me by my professor. It is something to think about...

Homework Statement A right-angle is drawn on a sheet of paper. A ruler , which always remains perpendicular to the bisectrix of this angle moves over the paper with a speed 10cm/sec. The ends of the ruler intersect the sides of the angle. What are the speeds along the sides of the angle of...

I would like to know the distribution of z as the euclidean distance between 2 points which are not centred in the origin. If I assume 2 points in the 2D plane A(Xa,Ya) and B(Xb,Yb), where the Xa~N(xa,s^2), Xb~N(xb,s^2), Ya~N(ya,s^2), Yb~N(yb,s^2), then the distance between A and B, would be...

I have computed the singular points of Chebyshev equation to be x= 1, -1. What is the best way to find whether they are regular? Thanks.

Hi guys, I have questions about algebraic functions and not sure where to ask. Hope it's ok here. Given the algebraic function f(z,w)=a_0(z)+a_1(z)w+\cdots+a_n(z)w^n=0 I recall seeing a reference that stated as n increases, the critical points of the function migrate to the unit circle or...

In my textbook, it says that impurities lower the melting point and increase the boiling point. But is this only true if the boiling point of the impurity is greater than the boiling point of the solvent, and the melting point is greater than of the solvent too? So essentially, if greater...

"Show that if a>b>c>0, then the function $f(x,y,z) = (ax^{2} + by^{2} + cz^{2})e^{-x^{2}-y^{2}-z^{2}}$ has two local maxima, one local minima, and four saddle points"

Hi, Can anyone help explaining the points of action of drag and thrust forces on an aeroplane in flight and also the realtionship between Lift-Drag ration and wing configuration?! Any help would be great!

if two points have the same electric potential, is it true that no work is required to move a test charge from one point to the other? Does that mean that no force is required, as well?

Homework Statement If I just had the set containing \pi on the real line. So this is an isolated point. Is this set closed? The Attempt at a Solution I think this set is closed because it contains its limit points, because it only has one point. Am i thinking about this correctly?

Homework Statement Two coplanar lines l1 and l2 are perpendicular to each other, l1 passes through the points (-3,2,3) and (-8,10,6). Find the equation for l2 if it passes through the point (7,49,25) Homework Equations The Attempt at a Solution determine the equation of l1 and use...

If a line segment of size L, is made up of an infinite amount of points. Then divided into half, and then half again, divided into half to infinity, would this mean that the resulting line segment is a point made up of an infinite amount of points? Or would it be ∞/∞?

In SR the points in Minkowski space correspond to events. I recently read in a GR lecture note that the points on the manifold do NOT correspond to events like in SR (the author even says the points don't have a direct physical meaning). So what do they represent then? And if I continuously...

Hello everyone. I would like to hear some suggestions on minimizing a function. I have discrete 2D function (a grid, where each (x,y) point have some value), where I know only extreme points (more specifically - ridges. http://en.wikipedia.org/wiki/Ridge_detection). I want to reconstruct...

Hi, I have been working on some Mandelbrot wallpapers for some time but have so far only visualized the whole set i.e. no zooming. I think that it could be nice with wallpapers visualizing a zoomed in part of the border of the set. Does anyone know coordinates to interesting places for zooming...

Consider the curve f(x) = 1/x Consider two points on f(x): Pa and Qa, where the x-coordinate of Pa is a, and the x-coordinate of Qa is a+1. Let La be the line connecting Pa and Qa 1.) Find the equation for La 2.) Find a formula that expresses A(a) = the area between f(x) and La 3.) Determine...

Homework Statement Prove the following statement is true or not: the statement: Let (X,d) be a non-empty metric space and A is a non-empty subset of X. Then if A' is not empty, then A' is infinte. Homework Equations Definition of limit point and its negation. The Attempt at a...

Hey! I have a problem that I have no clue how to solve. So I was hoping you guys could help me. I'm not from an English speaking country so I apologize. Homework Statement A thing is made to travel in water and on land. In water it travels with 20 m/s speed but on land with 25m/s speed. The...

Homework Statement Find the critical points where \alpha = 1. dv/dt = v2 + \alphav - u + \delta [I will call this (1)] du/dt = \betav - u [call this (2)] For what values of \beta and \delta are there no critical points? Homework Equations The Attempt at a Solution So...

I need to move an object based on 100 images rotating. The object needs to move in a path that is forming an ellipse when I'm rotating the image based on my gestures. I have 4 points, 2 pairs of opposite points on X/Y axis, on the ellipse but how do I calculate the rest of the points so that...

I'm a little bewildered when reading about these Julia sets. From the definition a Julia set is the closure of all repelling periodic points of a complex map f. However I read that a Julia set always contain periodic and non-periodic points. Wasn't the definition including only periodic points...

Homework Statement In my book it specifically asks to "find the points of inflection" of f (x) = 2x^3 + 9x^2 - 24x - 10. Homework Equations f (x) = 2x^3 + 9x^2 - 24x - 10 f'(x) = 6x^2 + 18x - 24 f''(x) = 12x + 18. The Attempt at a Solution What I don't get is why it asks for pointS...

Homework Statement Show that there exists one root int (0,2) of the following function: f(x)=(1-x^2)^2-√((1-x^2)*(1-1/2*x^2)) Homework Equations The Attempt at a Solution I first found: f(0)=0 and f(2)=7.268 But, i don't know what to do now. I'm not sure if it has...

Homework Statement A wheel with a radius 50 cm is rolling along the ground at 10m/s[E]. That is, the centre point of the wheel is moving at 10 m/s [E]. - What are the velocities of the top, bottom, front, and back points of the wheel, relative to its center? - What are the velocities...

Homework Statement i have a sphere with center at origin that is partially empty inside with a non-uniform charge. i have 2 arbitrary points outside the sphere. find the difference in potential between the 2 points.Homework Equations The Attempt at a Solution 1) find total charge of sphere 2)...

Hi, Q: By investigating the stationary points of f(x)= x3+3x2+6x-30 and sketching the curve y=f(x) show that the equation f(x)=0 has only one real solution. A: Well, I don't understand how I should use both. Plotting the graph, I can clearly spot a solution: x = 1.9319548 I know how to...

I'm reading a math book and found a couple of proofs I can't do. 1. Given x \in R^n, a \in R, \sum\limits_{i=1}^n{x_i}=na, prove that \sum\limits_{i \in A}\prod\limits_{j = 1}^k {x_{i_j}} \leq \binom{k}{n}a^k where A = \{i \in \{1, 2, ... n\}^k : i_1 < i_2 < ... < i_k\} which essentially...

This thought experiment involves two people named Person-A and Person-B. Person-A fires a gun from a car which is traveling at 60mph. Imagine that the bullet travels at a constant speed of 300mph for some time, assuming that the air friction is ignored. Person-B is stationary observing the...

QUESTION: In the circular restricted 3-body problem, if we consider motion confined to the x-y plane and adopt units such that G(m1 + m2) = 1 [m1 and m2 are the masses of the two heavy bodies], the semimajor axis of the relative orbit of the massive bodies = 1, and n = 1 (n is mean motion...

This is a question that has been burning for some time, I have been wondering, instead of plotting the different points of a function onto a steady x and y axis, is it possible to have a single point (at the origin) and have the planes move instead. The space moving around the point. When I...

given the lines in space L1 : x = 2t + 1, y = 3t + 2, z = 4t + 3 L2 : x = s + 2, y = 2s + 4, z = -4s – 1 Find the point of intersection of L1 and L2. How do i solve this?

Have the following question and just wondering if my solution is correct Let g(x)= x^5+3x-1. Show that there are no distinct points x_1, x_2 in R such that g(x_1)=g(x_2). Proof by contradiction. Assume we have two solution x_1<x_2 in ℝ, i,e g(x_1)+g(x_2)=0, since g is differentiable on...