Points Definition and 1000 Threads

Homework Statement Find all critical points of u(x,y)=(x-y)(x^2+y^2-1) Homework Equations - The Attempt at a Solution Partial differentials: ux=3x^2+y^2-1-2xy=0 uy=-x^2-3y^2+2xy+1=0 I know the critical points are the solutions to the above two equations. But how do...

Homework Statement Locate and classify the critical points of f(x,y) = (x-y)(xy-1). Homework Equations The Attempt at a Solution I found the partial derivatives with respect to x and y and I got: ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1 After setting them both equal to zero I can't...

Homework Statement Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vectors llACll= 2 llBCll Homework Equations Not sure. The Attempt at a Solution I found the equation of the line for vector AB: (1,2,-1) +t(2,0,1) Then found the scalar equation...

The point P(4t^2, 8t) lies on the parabola C with equation y^2 = 16x. The point P also lies on the rectangular hyperbola H with equation xy = 4 a) Find the value of t, and hence find the co-ords of P. working: so x = 4t^2 and y = 8t i sub these into xy = 4 and get t = 1/2 and can then...

Homework Statement I am confused here . Each wire is of resistance R How in this image E G and D are at the same potential and in this image How A and F and Dand G are equivalent? Homework Equations I don't think any equations will be used in solving this but I guess V =IR might be...

Homework Statement The question is to find Equivalent resistance between opposite ends of a cubical resistor network . each resistor of resistance R . I am referring to this website here http://mathforum.org/library/drmath/view/65234.html I am halfway through it but I am stuck at a...

By Peano's space-filling curve, there exists a continuous map f: I -> I^2 whos image fills up the entire square I^2 (where I=[0, 1]). This can also be represented by gluing points of I together. Which points of I get glued together? I was looking at the proof of Peano's space-filling curve...

Homework Statement Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3). Homework Equations Center of a triangle: x = ax+bx+cx /3 y = ay+by+cy / 3 Magnitude = <a,b> , √(a^2+b^2) The Attempt at...

There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...

Hi, I really need some help here. Right now I am plotting points on a 3D Scatter plot chart in Mathematica. I want to assign each of these points with a value which will be the label. Basically each point has 4 variable in the parameter. Its x,y,z cartesian coordinate position and the last...

Hi, i have three points A',B',C' and want to find a vector passing through B' and parallel to the other two points in the plane containing these 3 points. So this how i started, A'=(9,27,-0.6) B'=(12,27,-6) C'=(19,25,-8) I found the vector AB' and AC' first. A'B'= A'-B' A'C'=A'-C'...

Hey, how do I determine whether or not points lie in a straight line? Is there a symbolic approach to determining so? Or do I need to spatially visualize it? For instance, A(0,-5,5), B(1,-2,4), C(3,4,2) does lie in a straight line according to my book. Thanks!

Homework Statement I am trying to find the critical points of the following hyperbolic function: f(x) = a / (b + x) Homework Equations Critical points--> where f '(x) = 0 One of the points on the graph is a/2b The Attempt at a Solution I am not sure how to proceed with this...

Homework Statement f(x,y)= 16(y^2) +(x^4) y + 4(x^2) + 4 My problem is recognizing which critical points to consider valuables. Homework Equations fxx, fyy, fxy, and second partials test. D=fxx(fyy)- (fxy)^2 The Attempt at a Solution I found: fx=0 4(x^3)y +8x=0 (x^2) y= -2...

Hello, I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory. I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam. However I cannot apply the beam theory...

The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN. I'm not quite sure where to start. Could someone please help me?

Homework Statement For each part, find the cartesian equation of the plane through the given points. (1,0,3), (2,-4,3),(4,-1,2) The Attempt at a Solution No attempt. Dunno how to do :(

Hi I have a set of data points in units of (time, voltage), and they have the form of a Gaussian when I plot it. I would like to normalize my data set, i.e. find a factor C that I multiply on to the voltage-data such that the area is 1. However, is there a way to numerically integrate data...

Homework Statement http://img444.imageshack.us/img444/9288/51927159.jpg The Attempt at a Solution (a) I'm mostly stuck on this part because I keep getting a complex number: 3x+y = 0 so x=-y/3 Substituting this in the second equation: \frac{y^2}{9} +1 = 0 \therefore \ y = \sqrt{-9}...

Critical Points, intervals, local max/min help! Calculus. 1. I need help with a homework problem that I just cannot get right. It asks: Answer the following questions about the functions whos derivative is given below. f'(x) = (sinx +1)(2cosx +\sqrt{3} ), 0\leqx\leq2∏ a. what are the...

How do we prove that the gradient points in the direction of the maximum increase? Would it be enough to simply state that the gradient is just the derivates of a function w.r.t all the variables a function depends upon. Since the derivative of a term w.r.t a certain variable gives the maximum...

Q.In which of the answers below are the substances listed in order of increasing melting point? a) Cl2 < CHF3 < H2O < CHCl3 < SiO2 b) Cl2 < CHCl3 < CHF3 < H2O < SiO2 c) Cl2 < CHF3 < CHCl3 < H2O < SiO2 d) Cl2 < H2O < CHF3 < CHCl3 < SiO2 e) SiO2 < H2O < CHCl3 < CHF3 < Cl2 How can we tell...

Homework Statement We are given the curve y = (1+x)/(1+x^2) Homework Equations y' and y'' The Attempt at a Solution I know the inflection points of y are the local minimum and maximum of y'; this can also be restated as the critical points of y''. My attempt is to find the...

Homework Statement Use the Cauchy Riemann equations to those points whose functions are analytic ##f(z)=x^2-y^2-x+iy(2x+1)## Homework Equations C-R eqn's ##u_x=v_y, u_y=-v_x, z(x,y)=x+i y## The Attempt at a Solution ##u(x,y)=x^2-y^2-x## ##v(x,y)=y(2x+1)##...

Hi, I am in honors track Complex Analysis, and I think I've reached my limit. We got this proof, and I don't know where to start. "We saw in class that a mobius transformation can have at most one fixed point (or else is the identity map), extend this idea to all analytic functions mapping...

Homework Statement Find the points x^2 + xy + y^2 = 2 that are closest to the origin.Homework Equations Distance FormulaThe Attempt at a Solution I have to first solve this without using Lagrange Multipliers. This is essentially an ellipse. So I first completed the square: 3/4\,{x}^{2}+...

Homework Statement Find the equation of a circle if the circumference is 18∏ and contains the point (2, 8) The Attempt at a Solution I know I can find the radius by setting 18∏=2∏r. r=9. the equation of a circle is (x-h)2+(y-k)2=r2 So I have 92= (2-h)2+(8-k)2 which becomes...

Is there a theorem that states that n distinct points in R^n-1 or higher one can be separated in an equal distance as the distance is greater than 0? We know that 4 distinct points in R^2 cannot be positioned in an equal distance>0 but in R^3 it is possible as a pyramid shape. If there is...

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...

[FONT=Times New Roman]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...

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 [FONT=CMR12]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...