Points Definition and 1000 Threads

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...

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...

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...

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...

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...

Hello all, I am having trouble with a homework problem. The problem is as such: Let a = {zn = (xn,yn) be a subset of ℝ2 and zn be a sequence in ℝ2 such that xn ≠ xm and yn ≠ ym for n≠m. Let Ax and Ay be the projections onto the x and y-axis (i.e. Ax = {xn} and Ay = {yn}. Assume that the...

Homework Statement The equation 5x^2 - 6xy + 5y^2 = 16 represents an ellipse. Determine two points on the ellipse at which the tangent is horizontal. Homework Equations The Attempt at a Solution I find the derivative of the equation: (-10x + 6y) / (-6x + 10y) = 0 iff...

Hello, I had a lecture in an elementary Calculus course today, and the professor used a method for classifying critical points which I can't see in my book (Calculus, a complete course, by Adams). Basically he had the function f(x,y)=x^2+2y^2-4x+4y. He found a critical point at (2,-1) -...

Homework Statement Compare the magnitude of the electric field at position A with the magnitude of the electric field at position B. A) E-Field Magnitude at Point A > E-Field Magnitude at Point B B) E-Field Magnitude at Point A = E-Field Magnitude at Point B C) E-Field Magnitude at Point...

i know that the p.d measured across XY is the p.d. across resistor B in this picture: http://img812.imageshack.us/img812/7665/68689848.png But what if resistor B is removed like in this picture: http://img707.imageshack.us/img707/7798/41743055.png What is the p.d across XY now? Is it 0...

Homework Statement So we are given the equation of a line and asked to do a bunch of stuff with it. When I get to the following question, I just don't understand what it is asking. The line: L=(2,2,5)+t(2,-1,1), where t is an element of the reals Question: Let S be the the line...

Homework Statement Prove that a line in 3D space is imaged to a line on the image plane in a pinhole camera model. Homework Equations A 3D point give by (X,Y,Z) will be imaged on the image plane at x = f(\frac{X}{Z}) and y = f(\frac{Y}{Z}) where f is the focal point. The Attempt at...

Hi, I know that the mean curvature at an extremum point where the function vanishes must be nonpositive.can this say something about the sign of the mean curvature at the farthest point on a close surface from the origin? Thank's Hedi

If I have two strings of equalities within the same align or alignat environment, and the first one is long enough to need two lines, I would want the result to look like A+B+C=D=E =F=G=H I=J rather than A+B+C=D=E =F=G=H I=J Is there a way to do this? I suppose it can be done...

So my problem is this: I need to figure out the center of a circle given two points. At one of the points, I know the tangent angle. So I know (x1, y1, θ1) and (x2, y2) and need to find (xc, yc). I also need to do this on a computer so I need some sort of closed-form solution. The way I...

Homework Statement Find the equilibrium points for the following equation. Determine if the equilibrium points are stable and if stable,approximate the angular frequency. (i) d2y/dx2 = cosh(x). Homework Equations The Attempt at a Solution For equilibrium points, do we...

Okay so I am given a 3D figure with 5 points. Keep in mind this model has the hyperbolic parallel property and satisfies the incidence axioms. The question is to construct the dual geometry and then to prove or disprove that it is an incidence geometry. My question is how do I go about...

Apart from visualizing firstly the maximum bounds of a function on a graph (domain), what are algebraic indications that some complex function does not exist at a given point? I know that if you evaluate a function that results in dividing by zero, the point is undefined. If you end up taking a...

Homework Statement A section of a circuit XY shown below absorbs 50 W of power when a current I = 1.0 A passes through it as indicated by the arrow labeled i. (a) What is the voltage difference between X and Y? (b) What is the voltage difference across element C?Homework Equations V = IR P =...

Homework Statement For each of the following arrangements of two point charges, find all the points along the line passing through both charges for which the electric potential V is zero (take V = 0 infinitely far from the charges) and for which the electric field E is zero. (Use the...

Hello. I am new to the idea of Special Relativity. From what I have read, based on what speed something is traveling it experiences an increase in mass. Let's say I am standing on the earth. I am experiencing a gravitational force of (me(m))/r^2. Now let's say I am the same person that somehow...

Homework Statement Find the co-ordinates of all points on the curve f(x)= x3 whose tangent lines pass through the point (a,0) Homework Equations f '(x) = nxn-1 The Attempt at a Solution I am really not sure how to attack this question. My initial thoughts are to find f '(x) then...

Homework Statement We are supposed to say how many limit points the set A={sin(n)} where n is a positive integer. My teacher said to use a theorem by Kronecker to help with it. His theorem says from wiki, that an infinite cyclic subgroup of the unit circle group is a dense subset...

Homework Statement A thick lens has an index of refraction of 1.560, thickness of 3.0cm, and radii of curvature of R1= -4.50cm, R2= -3.60cm. Calculate the positions of the focal points (relative to the vertices). Homework Equations \frac{n}{s}+\frac{n'}{s'}=\frac{n'-n}{R} ffl =...

Homework Statement a)Determine at least three limit points for the set {sin(n): n a positive integer} b)How many limit points does the set {sin(n): n a positive integer} have? The Attempt at a Solution For a it seems that it wouldn't have a limit point because sin(n) would not converge to...

Hello, I'm trying to do exercise number 20 from chapter 6 of this http://www.people.vcu.edu/~rhammack/BookOfProof/index.html, it asks to show that the curve x2 + y2 - 3 = 0 has no rational points. In the answer it has this tip: first show that a2 + b2 = 3c has no solutions, other than the...

I'm interested in the proper way to give a mathematical definition of a certain geometric property exhibited by certain maps from points to sets. Consider mappings from a n-dimensional space of real numbers P into subsets of an m-dimensional space S of real numbers. For a practical...

The problem is kind of easy to understand. Given is some points, say 10 points. (I am using numbering for understanding) 0 1 2 3 4 5 6 7 8 9 Now group these such that the group size is 5 and there is no overlap so, there can be 2 groups. the groups are (0 1 2 3 4) & (5 6 7 8 9) Now...

Is there a common notation for the set of limit points of a set?

Homework Statement let f = \muex let 0 < \mu < 1/e Show that f has two fixed points q and p with q < p Homework Equations a fixed point p is a point such that f(p) = p The Attempt at a Solution solving f(x) = x: f(x) - x = 0 \muex - x = 0 Now I want to take logarithms...

I found this on a webpage: In any transition element series, the number of unpaired electrons first increases from 1 to 5 and then decreases back to the zero .The maximum five unpaired electrons occur at Cr WHY?' doesn't it occur at MN??