Circle Definition and 1000 Threads

Hi all, I have a seemingly simple linear algebra problem which I have trouble with and I would like to ask for some advice how to solve it. Here is the problem: Here are my thoughts about this: It is clear that a solution is not always defined for the whole range of \nu and that for...

Homework Statement I would like to ask how to find the mass of a circle with equation x^2+y^2=4 given its density=xy^2 by not using polar coordinate but use dxdy or dydx ( cut the circle into pieces parallel to x-axis or y-axis ) Homework Equations x^2+y^2=4 xy^2 The...

Homework Statement A circle is inscribed in a triangleHere is a picture Picture of circle inscribed in triangle, not necessarily to scaleWhich is larger: the circumference of the circle, or the perimeter of the triangle? Homework EquationsC=∏D (D=diameter of the circle, C=circumference of...

Homework Statement Show that the maximum possible area for a rectangle inscribed in a circle is 2r^2 where r is the radius of the circle.Homework Equations Pre-calc ! NO TRIG ! Doesn't matter if it's easier, it's supposed to be solved with algebra. The Attempt at a Solution I have no clue...

Hello Im wondering how to calculate the acceleration of a circle down an inclined plane (due to gravity). I am familiar with caclulating the acceleration of a body sliding down a inclined plane, but not a circle. How do you determine the acceleration of a circle (preffer rotation per second, if...

Homework Statement Find the equation of the circle whose centre lies on the x-axis and which passes through points A (6,0) and B (0,10). Homework Equations The Attempt at a Solution I drew a diagram of the circle and determined that the line AB has gradient 5/3. Its perpendicular bisector...

Homework Statement An equilateral triangle of side x is is inscribed in a circle. Express the area of the circle as a function of x. Homework Equations Anything non-trig. I suspect it's got something to do with the Pythagorean theorem. The Attempt at a Solution I tried getting the...

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s center can touch each other only at the longer axis"? Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways? Thanks! :)

This problem arose for me while working out a triple integral in spherical coordinates. Basicly I know that when we shift a parabola along the axis it is simply translated. I naturally assumed that if we shifted a circle in a similar manner that it would act the same. However when we shift...

So over the course of yesterday and the day before that I've spent a few hours thinking about these problems; 1. Given a circle, place n points arbitrarily* on the edge and connect every point to every other point with a straight line. How many intersections do you get? 2. Given the same...

Homework Statement The problem is attached Homework Equations P=F/A The Attempt at a Solution I did the question like this (got wrong answer though): Surface area of sphere=4∏r2=4×∏×0.252 Atmospheric pressure=1.01×105 Force=1.01×105×4×∏×0.252≈80000N Actual answer 20000N...

Homework Statement the figure is shown on the attachment. Find the area of the smallest part of the circle. Homework Equations area of circle, sector, segment The Attempt at a Solution I cannot use the said equations since the part of the circle is not with reference to the...

Homework Statement Find the position of the center of mass for a thin sheet and homogeneous, with sides R and 2R ,from which has been subtracted a half circle of radius R. [Xcm=(2/3)*R*(4-pi)]Homework Equations Rcm=(1/M)*∫rdm The Attempt at a Solution By symmetry we know Ycm=0. For de...

I thought this was a very interesting development in the Syrian situation: http://www.jpost.com/MiddleEast/Article.aspx?id=274828

Homework Statement Describe the locus and determine the Cartesian Equation of: \left|z-3-5i\right|= 2 Homework Equations \left|z-C\right|= r -----> formula for a circle on complex plane Where C = the centre z = the moving point (locus) (x-h)^{2}+(y-k)^{2}=r^{2} -----> Formula...

\int_{-\sqrt{r^2-x^2}}^{\sqrt{r^2-x^2}} \sqrt{r^2-x^2-y^2}dy I can calculate the above integral [part of a double integral] by the conventional way [somewhat long], however my book says that this integral equals to \frac {\pi}{2}(r^2-x^2) because the integral is actually the area of half a...

Hello again, I'm finding myself stuck on what is probably a simple question, but I believe I am taking the wrong approach. The section is "Volumes with infinite integrals," and the chapter is "Improper Integrals." The question, "Use calculus to find the circumference of a circle with radius...

Homework Statement The points P and Q divide a given interval AB internally and externally respectively in the ratio 1:λ. The point X lies on the circle with diameter PQ. Prove that AX:XB=1:λ Homework Equations None The Attempt at a Solution Basically, if we define the centre of PQ and the...

Homework Statement Find the radius of a circle inscribed in a quadrant of a circle with radius 5 Homework Equations The Attempt at a Solution I worked this but I'm not sure if its correct. I looked at the first quadrant so a quarter of a circle with radius 5. I drew the radius...

Homework Statement Hello! I need to calculate a little fraction (dA) of the area of a circle (mass m and radius R and area A) and I have no idea how to do this. Homework Equations According to my textbook dm=\frac{M.dA}{A}=\sigma .dA and dA=R.dR.d\theta. The Attempt at a Solution Well, I tried...

This is not really a homework problem, I'm just doing it as an exercise puzzle. I think I'm on the right track, but at this point I feel a little exhausted and would love a hint. Homework Statement Let C be a unit circle: x^2+y^2=1 . Let "p" be a point on the circumference and "q" be a point...

This question is about circular motion in a vertical circle Question 1: would I be correct in assuming that the magnitude for tension is dependant on (a) the weight of the object (b) the position of the object with respect to the horizontal diameter of the circle So above the...

Homework Statement This question comes out of "Introduction to Topology" by Mendelson, from the section on Identification Topologies. Let D be the closed unit disc in R^2, so that the boundary, S, is the unit circle. Let C=S\times [0,1], and A=S \times \{1\} \subset C. Prove that...

imgur.com/kBTVm Hi, I understand that work done in a conservative field when a closed loop is followed is zero. The answer to this question I am sure is B. How do I explain to my colllegue that it is not zero when he thinks that the speed is constant and there is no friction and the force...

Situation 1: completely horizontal circle Imagine a ball being whirled in a completely horizontal circle. The only forces acting are tension and weight Would I be correct in assuming that in this situation NO WORK is done on the ball because the forces are directed (at all times)...

Hello, What would be the right approach to solve for a particle's wavefunction/ energy eigenvalues inside of a 2d cicrle with a potential V(r) where r is the radial distance of a particle from the center of the circle? V(r) is known and is some sort of a well potential going to infinity at R...

The question asks to look for a surface and a circle is the only function which meets the conditions. Is this still considered a surface?

I am becoming confused when I read in Wiki that the dimension of the circle in the plane is 1! It is said that the dimension of circle is 2 (in general )! I do not get it!

Homework Statement If you twirl a ball attached to a cord in a vertical circle, there would be a critical speed at the top for which the tension in the cord is zero. This is because the force of gravity supplies all the centripetal force necessary to complete the circle. How slowly would you...

Homework Statement Going over some old tests, I am asked to find the contour of the function: T = 100 - x^2 - y^2 at T = 100, T = 0, etc. I have a question regarding the contour at T = 100 Homework Equations The Attempt at a Solution Consider T = 100 100 = 100 - x^2...

I was thinking about how planets revolve around sun. Although they subscribe a elliptical motion, my question is very similar. A heavy body exerts a force on a point mass, say with an acceleration of "a". If we take the direction of this acceleration to be X, what is the linear uniform velocity...

[SIZE="4"]As we know a circle view at an angle appears as an ellipse , as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the...

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...

[SIZE="4"]As we know a circle view at an angle appears as an ellipse, as you see in the picture, the center of the camera aim to the center of the circle , the angle between the circle axis and the camera is ө, the azimuth between mojor axis(a) and the camera is ∞, the rotation of the...

Homework Statement Consider the following parameterization of the circle: a) x1 (t) = (cost, sint) b) x2 (t) = (cos3t, sin3t) c) x3 (t) = (sint, cost) How long does it take point a particle to go from (1,0) to (0,1) for each parameterization. Homework Equations The...

Homework Statement Find the total area inside the circle r = 4 and below the line r=2csc\theta Homework Equations \int^{b}_{a} 1/2r^{2}\thetad\thetaThe Attempt at a Solution r=2/sin\theta\Rightarrowrsin\theta=2\Rightarrowy=2 r=4\Rightarrow=circle with radius 4 at center (0,0) Point of...

if a beam of light originates at point 1 aimed at point 4 will it reflect to point 2 then and point 8? as in the diagram? http://en.wikipedia.org/wiki/Enneagram_of_Personality

Imagine a circle lying on xy plane and initially at rest w.r.t. frame S. Then S' comes and gets the circle and moves it with velocity v along x axis. The radius which is along x axis,should be contracted but not other radii and this means that the circle becomes an ellipse and because its sth...

I have a few statements/questions, as stated below. Would appreciate your comments on them. 1) The system is not in translational equilibrium because of a net leftwards force. 2) The system should be in rotational equilibrium based on logic; But based on the FBD, if I take moments about the...

Homework Statement find linear fractional transformation that carries circle |z|=1 onto the line Re((1+i)w)=0 Homework Equations linear fractional transformation is of the form az+b/cz+b where ad-bc≠0 The Attempt at a Solution Re((1+i)w)=0 means that the line is just the y axis, but then I...

Homework Statement Find the image of the circle |z| = 3 in the complex plane under the mapping a) w = \frac{6}{z} b) w = \frac{6}{z} + 2i The Attempt at a Solution a) w = \frac{6}{3} = 2 So this is a circle in the w-plane of radius 2, centered on the origin? b) w =...

Homework Statement Hey guys. As you can see, there are 5 questions to answer regarding this question. I'm working through it and need some help regarding a few of the questions. I have A.) The electric potential at the center of the circle is Zero. B.) The value of the electric...

I am trying to make a game where a drone approaches a ship, that may be moving, and then orbits it at a set distance. I know that if the drone is already moving in a circle of uniform motion then I use a = \frac{v^{r}}{r} I then take that magnitude and an angle derived from atan2 with cos...

1. let C be the circle |z| = 2 traveled once in the positive sense. Computer the following integrals... a.∫c zez/(2z-3) dz Homework Equations I am confused as to a step in my solution, but i believe a relevant equation is if i am integrating over a circle and the function is analytic...

Hello everyone! I've found a physics problem that i don't know the solution of(maybe because of my limited knowledge). The problem is something like this: Let's say an object travels in a circular path from P to Q and Q to R in which P, Q and Rare not the center of the circle(because P, Q, R...

An interesting thought just struck me and I wanted to confirm if it is correct. Do all objects (of fixed mass) need a particular magnitude of force to keep them moving in a circle, e.g: a ball will ALWAYS need a force of 10N to keep it moving in a circle If the speed increases then the radius...

I intend to use the Gershgorin Circle Theorem for estimating the eigenvalues of a real symmetric (n x n) matrix. Unfortunately, I'm a bit confused with the examples one might find on the internet; What would be the mathematical formula for deriving estimates on eigenvalues? I understand that...

A ball is attached to an inextensible string of negligable mass and hangs vertically under gravity. At time t=0, it is given a horizontal velocity u and begins to move in a vertical circle of radius r. At any time t>0, the ball is at an angle θ to the vertical and has a velocity v tangential to...

I am struck in a place where i have to find length of a line(a in fig i.e between P1 and P2) in the form of r and Angle A. Refer to the figure: All information available are r,O,P2,and A.

Homework Statement Consider a triangle ABC, where angle A = 60o. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E and F be the points at which circle O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the...