Circle Definition and 1000 Threads

I'm doing this in Matlab but it's not restricted to any particular software. I have a bunch of geographical points (x,y coordinates for each) and I want to take all the points that are 50 km or closer to the reference point. I took the great-circle equation to convert geographical longitude...

Homework Statement 1. (a) Find the equation of the circle with the straight line joining A(1;-1) and C(3; 4) as diameter. (b) Hence or otherwise, derive the general formula (x - x1)(x - x2) + (y - y1)(y - y2)=0 of the equation of a circle for the points A(x1; y1) and C(x2; y2): Homework...

I'm having some difficulty with this problem and any help would be appreciated. What is the radius of a circle tangent to the lines y = 3x + 7 and y = .5x - 3 and containing the point (8,1)? I've determined that the given point (8,1) is the point of tangency of the line y = .5x - 3 and the...

Hello, I am currently working on a problem to calculate the light that makes it through a half circle. For example, say I put a cylinder out in the sun, where the intensity is known to be 1030 W/m^2. I would like to compute the intensity/energy/power that makes it into this. Now, given the...

Homework Statement In the figure on the right, a 4.0 kg ball is attached to the end of a 1.6 m rope, which is fixed at O. The ball is held at A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle and arrives at B, with the...

Here is the question: I have posted a link there to this topic so the OP can see my work.

[FONT=times new roman]the following diagram shows a circle with center $$O$$ and a radius $$4cm$$ The points $$A, B,$$ and $$C$$ Lie on the circle. The point $$D$$ is outside the circle, on $$(OC)$$ Angle $$ADC=0.3$$ radians and angle $$AOC=0.8$$ radians (a) find $$AD$$ I used law of...

Is there atopological space X such that XxX (the product space) is homeomorphic to the unit circle in the plane

Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Good evening. I'd like to first start by saying I am new to this forum, and I am a physics noob. I know that very fact will help people shy away from trying to help me answer this question. This problem (which an image is posted) is 1 of 5 questions on a take home kinematic quiz. I've managed to...

1. A 55 kg airplane pilot pulls out of a dive by following, at constant speed, the arc of a circle whose radius is 320 m. At the bottom of the circle, where her speed is 230 km/h, what is the magnitude of her acceleration? Homework Equations v^2= vi^2 +2a(x-xi) The Attempt at a...

Homework Statement Hello all, I am having some trouble with answering the problem below, mostly because I do not know what the letters stand for and what kind of graph is meant to be drawn. Any help on this would be greatly appreciated. Thanks For a particle going in a circle with speed U...

Hi all, I am having an issue trying to solve the following problem Homework Statement I know that the radius of the circle is 7 and the angle of the segment is 150° Homework Equations Area of a circle: A = \pi{r}^2 Area of the sector of the circle: A = \frac{n}{360}\pi r^{2} Area...

We should all know that photons only exist in quantum mechanics. In fact, the idea that energy comes bundled in discrete units is what actually caused QM in the first place. For some reason, however, I've spent my entire life under the assumption that cosmologists make true statements about...

Hello, I have an arc with an arc length = 46.88 mm and radius = 44 mm. I have an intersecting arc with an arc length = 26.69 mm and radius = 43.4 mm. A circle with radius = 24 mm fits between the two arcs. How can I determine the contact points of the circle and the two arc lines?

Homework Statement What is the integral of e-1/z around a unit circle centered at z = 0? Homework Equations - The Attempt at a Solution The Laurent expansion of this function gives : 1 - 1/z + 1/(2 z^2) - 1/(3! z^3) + . . . . . The residue of the pole inside is -1. So the integral...

I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...

Homework Statement Hi, I am trying to find the general formula of a circle in 3D Let's consider a sphere centred at (x1,0,0),with radius x1 It's equation is (x-x1)^2 + y^2 + z^2 = (x1)^2 If there is a plane x = x1 intersects with the sphere A equation of a circle is formed,which is y^2 +...

Hi all, I have found this formula being used but I am not sure what it means. It is used to find the radius of a circle in a sector. Hope you can help me understand it. sin(π/6) = r/(6-r) r is the radius of the circle itself and 6 is the radius of the sector or the circle of the sector...

When the radius of the circle decrease the object moves faster(With the same force) I believe this is a misconception .In common sense the object revolves around more,This leads us to think that it is moving fast but actually the object moves the same distance.Am I right?

Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...

Homework Statement Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 . The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.Homework Equations x=rcosθ, y=rsinθ, dL=r*dθThe Attempt at a Solution...

Homework Statement Homework Equations I suppose Newtons third and second law. centripetal acceleration = v^2 /R The Attempt at a Solution I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration? I couldn't get the calculations to add...

How do you construct the arc of the circle as a straight line by geometry not by an equation? Thank you

I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...

Homework Statement A spring with an unstretched length of 20 cm and a force constant of 100 N/m is attached to a 2-kg mass with a charge of 3.0 C. The mass is swung in a circle in a zero gravity environment, so that the spring is perfectly horizontal and is parallel to the radius of the...

consider a pendulum. The mass 'm' is hung and now we are interested in finding the velocity so that it completes one circle. Clearly we can do it easily by conserving energy. Now my problem is with the top most point. Clearly the tension is minimum at this point so that string becomes slack...

Homework Statement A car with a horn making a frequency of 'f' Hz is driven in a circle with a radius of 'r' m. The uniform velocity of the car is v ms-1. Draw graphs showing the frequency observes by the observer who is standing on; a) Position A b) Position B (Position B is very far...

I'm having some difficulty with this question. Can anyone help me out, please? Many thanks. Homework Statement A circle of radius length \sqrt{20} contains the point (-1, 3). Its centre lies on the line x + y = 0. Find the equations of the 2 circles that satisfy these conditions...

Hi, Homework Statement A circle of radius r is as shown in the attached diagram. I am asked to first express X as a function of θ, then to compute E(X). It is also stated that θ obeys U[0,2π]. Homework Equations The Attempt at a Solution Through simple trigonometry I have found X...

Homework Statement A variable line ax+by+c=0, where a,b,c are in A.P (arithmetic progression), is normal to a circle ##(x-\alpha)^2+(y-\beta)^2=\gamma##, which is orthogonal to circle ##x^2+y^2-4x-4y-1=0##. The value of ##\alpha+\beta+\gamma## is equal to A)3 B)5 C)10 D)7 Homework...

This is a tiny part of a presentation I am giving Friday, any and all help is appreciated. Homework Statement Suppose we have a circle centered on O. We are looking for the distribution of the points generated by the following method: We choose a random radius of the circle, and then choose...

Homework Statement derive/create an equation for a "great circle" route r(t) from a given point A to a given point B along the surface of the sphere with center (0,0,0) and radius = 15 test point 1: A=(2,10,11) to B(14,5,2) test point 2: A=(10,5,10) to B(0,-12,9) Homework Equations...

Homework Statement The uniform quarter-circular sector is released from rest with one edge vertical as shown. Determine its subsequent maximum angular velocity. The distance b is 560 mm. Homework Equations The Attempt at a Solution I know that I need to use: T1 + V1 + U'1-2...

A friend's homework problem (Prove any five points in the plane determines a possibly degenerate conic section) led us to a different problem that we found more interesting. We can identify a circle with three points on the circle, or six parameters $(x_1,y_1,x_2,y_2,x_3,y_3)$ where, keeping...

Hi, I am conducting an experiment and i am displaying diffraction images of light through 2 pinholes on a DSLR camera. I get a good image with lasers but when I capture images of chromatic light i only get the top half (semi circle) image. can someone explain to me why this occurs? I think...

Points A, B, C, D are on a circle with radius R. $$|AC| = |AB| = 500$$, while the ratio between $$|DC|$$, $$|DA|$$, $$|DB|$$ is 1, 5, 7. Find R.

Homework Statement A uniform rod moves in a vertical circle .Its ends are constrained to move on the track without friction.Find the angular frequency of small oscillation .Homework Equations The Attempt at a Solution Suppose the rod of length L moves in a circle of radius R . Let the...

Homework Statement A 100g (0.1kg) rock is attatched to a 1.0m rope and spun around in a circle with a period of rotation of 1.0s. What is the Radius of the circle that it forms? Homework Equations Fc = (mV^2) / r V= (2∏r/T) LCosθ = r The Attempt at a Solution Im quite stick...

So how does the topology of R^n minus the origin relate to that of the (n-1)-dimensional sphere? I would think the topology of the former is equivalent to that of an (n-1)-dimensional sphere with finite thickness, and open edges. But I suppose that is as close as one can get to the...

The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: $$d/2.$$

Homework Statement Let A, B, C, D be distinct points on a circle with centre O. If there exists non zero real numbers x and y such that ##|x\vec{OA}+y\vec{OB}|=|x\vec{OB}+y\vec{OC}|=|x\vec{OC}+y\vec{OD}|=|x \vec{OD}+y\vec{OA}|##, then which of the following is always true? A)ABCD is a trapezium...

Okay! Earlier today I was thinking about potential energy and how it is related to an orbiting object, O, around a centre, C, from which force emanates if the object O is traveling at radius r from this centre, we conclude that the force given by the change in direction must be equal to the...

Homework Statement In a circle we can place k numbers. The numbers can range from 1 to n. One position in the circle is fixed, say by 1. We have to place the other k-1 places with numbers in the range 1 to n such that no adjacent numbers are equal. Homework Equations The Attempt at...

[SOLVED]Trig problem: max square cut from circle Since this one is homework related, ill ask this as a procession so that I can make sure that I am grasping the logic. the question is that with a round log with a diameter of 16cm, what is the strongest log that can be cut where the strength =...

I have a grid and want to determine whether a point lies within (our outside of) a circle. The grid cells simply have integer coordinates, e.g. x = 5, y = 7. The circle's radius is known, and also an integer value. I wrote a program that can place points in a (quantized) circle using...

Question A thin nonconducting rod with a uniform charge distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at...

Homework Statement Consider a random walk on a circle of N points, labeled {0,1,...,N-1}. Let the initial state be X = 0 and define T to be the first time all points have been visited at least once. Show that the distribution of X[T] (i.e. last unique position visited) is uniform over...

Homework Statement Find the Arc Length from (0,3) clockwise to (2,sqrt(5)) along the circle defined by x2 + y2 = 9 Homework Equations Arc Length formula for integrals The Attempt at a Solution I have the correct answer at 3arcsin(2/3), but I tried to do this without calculus the first time...