Circle Definition and 1000 Threads

A. Write the equation of radius 1 centered at (0,0). x^2 + y^2 = 1 B. Does the point (3/5, 4/5) lie on the circle? (3/5)^2 + (4/5)^2 = 1 (9/25) + (16/25) = 1 25/25 = 1 1 = 1 Yes, the point (3/5, 4/5) lies on the circle. Correct?

Hey, not sure if this is the right place to post this, but here it goes. how do you calculate the moment of inertia for a circle that is not at its center of gravity. I am trying to find the moment of inertia for a complex shape made of many circles, and this seems like a good place to start...

Homework Statement Prove that any chord perpendicular to the diameter of a circle is bisected by the diameter. Homework EquationsThe Attempt at a Solution I was thinking that maybe I could form two triangles, show that these triangles are congruent, and then conclude that the two lengths of...

Homework Statement Homework EquationsThe Attempt at a Solution At distance s, the speed of the car is v. $$ v^2 = 2wτs$$ $$\frac { mv^2} R ≤ kmg$$ Let's denote the maximum distance covered without sliding is smax. $$\frac { m2wτsmax} R = kmg$$ $$ smax = \frac {kgR} {2wτ}$$ Is this correct...

This may be a basic question, but why does the Sun rise at the same sideral time between December 22 and June 22 on the Arctic Circle? And how can I prove it?

Homework Statement Hello I have this circle with the equation : [/B] (x-a)^2+(y-b)^2=r^2 I want to find dy/dx for it 2. Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...

Homework Statement Homework EquationsThe Attempt at a Solution this is the answer https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1038060.html but why the c1 = 0, c2 = 1, c3 = 3, c4 = 6 etc why not c2 = 2? c4 = 4?

Maintaining R as the constant hypotenuse in the triangle formed by x and y coordinates in a 'perfect' circle, r2=x2+y2 r2=x2+y2 So knowing that in 9.8 metres above ground it will take 1 second for an object to fall, I tried to find how many metres in the X direction an object must cover in 1...

Homework Statement A line charge has the total charge Q evenly distributed over a circle boat with radius a and sector 2β, placed according to the figure Find the Electric field E and the potential V in the origin. Homework Equations I know for this case that E(r) = (1/4πε) ∫ (λ(r')/R2)R...

Homework Statement Homework Equations d(y)/d(x) --> max area area of triangle = 1/2 . base . height The Attempt at a Solution for number (2) [/B] x^2 + y^2 = r^2 --> circle equation base = 2R, height = y Area = 1/2 . 2R . y area = 1/2 . 4. √ (r^2 - x^2) area now is half of max = 2, so...

some formula related I tried to draw the problem can anyone give me clue how to solve it?

The answer to the question of the thread title is yes, according to what I found on web. Now a manifold is by definition a topological space that (aside from other conditions) is locally Euclidean. What does such condition means? Is it the same as saying that each of its points must have a...

Homework Statement [/B] imgur.com/a/bsAKl [I didn't know how else to upload an image from my iPad] In this problem: -Center of the circle=Point F -Arc AB= 110 degrees -Arc CD= 40 degrees Find the measure of angle E. Homework Equations I know of some equations, but I don't know if they...

Determine the equation of the circle that satisfies the given conditions. Write the equation in standard form. The circle passes through (-4, 1) and its center is the midpoint of the line segment joining the centers of the two circles x^2 + y^2 - 6x - 4y + 12 = 0 and x^2 + y^2 - 14x + 47 = 0...

Find the equation of the circle passing through the origin with center (3, 5). Can someone get me started? Must I use the point (0, 0) here?

Find the equation of the circle tangent to the x-axis and with center (3, 5). (x - h)^2 + (y - k)^2 = r^2 h = 3, k = 5 r = 5 (x - 3)^2 + (y - 5)^2 = 5^2 (x - 3)^2 + (y - 5)^2 = 25 Yes?

The unit closed disk minus the point ##(0,0)## ##\mathbb{D}^1 \setminus (0,0): \bigg[(x,y) \in \mathbb{R}^2 | 0 < x^2 + y^2 \leq 1 \bigg]## is homeomorphic to the unit circle ##\mathbb{S}^1: \bigg[(x,y) \in \mathbb{R}^2 | x^2 + y^2 = 1 \bigg]## Since ##\mathbb{D}^1 = \big(\mathbb{D}^1 \setminus...

1. Sketch the circle of radius 1 centered at (0, 0). (A) Write the equation of this circle. I must use x^2 + y^2 = r^2. The radius is 1. This means r = 1. The equation is x^2 + y^2 = 1. Correct? B. Does the point (3/5, 4/5) lie on this circle? (3/5)^2 + (4/5)^2 = 1^2 (9/25) + (16/25) = 1...

What I would like to be able to calculate is the following: Suppose a hoop or ring is held up perpendicular to the ground and you stood in front of it, it would look perfectly circular and knowing the radius you could calculate the area of this circle. Now if this hoop was tilted over backwards...

Can anyone help me with the following scenario: A hopping circuit is painted on a school playground. It consists of 25 small circles, with the numbers 0 ( at the 12 o' clock place) to 24, arranged as a big circle. Each student jumps either 3 or 4 spaces clockwise(so a student can end up either...

If a circle has 6 segments, how many maximum parts which can be formed? I know that 1 segment makes 2 parts, 2 segments make 4 parts, and 3 segments makes 7 parts. Judging by the pattern, is the answer 22? What will the exact picture of the circle be? Thank you very much.

Hi , just curious about the F.B.D of a pebble moving in a vertical circle, which component that balances the weight of the pebble at the horizontal position , as tension is providing the required centripetal force , weight is acting downwards , which component balances it ?

I want to create a plate of distinct circles on Matlab where their radii are generated by randn(1,p) and centers are random. I am currently doing the circles using viscircles, but some of them are overlapping, and since I want approximately 100 ones, this problem only gets worse. How can I make...

I need help in solving this problem. Below shows all the measurements of the diagram, I need to find x:

Hi everyone. I was looking at complex numbers, eulers formula and the unit circle in the complex plane. Unfortunately I can't figure out what the unit circle is used for. As far as I have understood: All complex numbers with an absolut value of 1 are lying on the circle. But what about...

Hi, i have this problem..., giving two circle (example radius 1 = 500 units, radius 2 = 200 units, distance between centers = 275.73 units) find Euler Spiral (aka Cornu spiral, aka Clothoid https://en.wikipedia.org/wiki/Euler_spiral) tangent giving circle (unknown tangent points). For this...

Homework Statement A box is sliding with constant acceleration a to the right. Inside the box there is a quarter of a circle upon which a frictionless ring can slide. Find the angle theta in terms of the other given variables. Picture in solution Homework Equations F=ma, etc. basic stuff...

Homework Statement Two charges placed at circumference of a circle of radius ##a## at ##\pi/2## from each other. Find the relative magnitude of third charge kept on the circumference such that the system is at equilibrium.Homework Equations Coulombs law. The Attempt at a Solution Let ##Q##...

Yes, one more reason to be humble, I know. This is the simplest problem I couldn't solve so far. Assume we have a circle of center O, a ruler of arbitrary size and a pencil. We use the ruler and the pencil to choose 4 points on the circle - the extremities of two diametral/diagonal segments...

I am putting in a new flue for a Pot Belly stove. The ceiling through which the flue goes slopes at 12.5º. I want to cut a hole in a metal plate that will be fixed to the ceiling, and through which the flue passes. So, a vertical circular flue, radius R, passing through a ceiling sloped at...

(mentor note: posted in a non-homework forum hence no template) Hello! I have a problem I'm trying to solve. I'm transforming a circle with known radius. Knowing it's radius i can calculate the circumference. I transform it by squeezing one side, leveling it, creating a circle segment with a...

Determine the center and the radius of circle. x^2 + y^2 - 10x + 2y + 17 = 0 Can this be done using completing the square?

Homework Statement A child is swinging a .325 kg ball at the end of a .74 m long string in a vertical circle. string can withstand a tension of 12 N before breaking. What is the tension in the string when the ball is at the top of the circle if its speed at that point is 3.4 m/s? Homework...

The radius of a circle is r units. By how many units should the radius be increased so that the area increases by b square units? I don't know where to begin. A = πr^2 Does this question involve the area of a circle formula? If so, in what way?

(cos(s), sin(s)) gives an arc-length parameterization of the unit circle so that the speed is constantly 1, but the second derivative doesn't give zero acceleration which should be the case with constant speed?

Do the lunar poles have something like and Artic circle where the Sun and/or Earth are fully visible in the sky for very long periods of time?

$\triangle ABC$ with its incircle $I$ (radius $r$) and circumscribed circle $O$ (radius $R$) the distance between points $O$(circumcenter) and $I$(incenter) is $d$ prove:$d=\sqrt {R(R-2r)}$

Hi PF! If we have flow around a curved object that is sufficiently thin, I Have seen many texts assume the surface is linear rather than curved. Can someone help me with what "sufficiently thin" is quantitatively and how this allows us to neglect surface curvature? As a simple toy problem...

Homework Statement Equation: x^2+y^2-6x-2y+8=0 Find the center and the radius. (Help) : Find the equation of the tangent to the circle above that passes through the beginning of axis O (0,0)The Attempt at a Solution I found the center and radius and i believe the values are : C (3,1) and R...

Homework Statement A small car with mass .800 kg travels at a constant speed of 12m/s on the inside of a track that is a vertical circle with radius 5.0m. If the normal force exerted by the track on the car when it is at the top of the track is 6.00N, what is the normal force at the bottom of...

Homework Statement An object with mass of m traveling in a circle rail ,when reached point A the object derailed and moved in a parabola path to point B and so on find the length of AB in term of R and theta. given that B is on the same horizontal level as A Homework EquationsThe...

Homework Statement Solve 2D wave eq. ##u_tt=c^2 \nabla^2u## in a circle of radius ##r=a## subject to $$u(t=0)=0\\ u_t(t=0)=\beta(r,\theta)\\u_r(r=a)=0\\$$and then symmetry for ##u_\theta(\theta=\pi)=u_\theta(\theta=-\pi)## and ##u(\theta=\pi)u(\theta=-\pi)##. Homework Equations Lot's I'm sure...

Homework Statement in circular motion (e.g. a pendulum) is the kinetic energy still 1/2 m v ^2 or is it a different equation? Homework Equations 1/2 m v ^2 The Attempt at a Solution

Homework Statement Let γ : I → ℝ2 be a smooth regular planar curve and assume 0 ∈ I. Take t ≠ 0 in I such that also −t ∈ I and consider the unique circle C(t) (which could also be a line) containing the 3 points γ(0), γ(−t), γ(t). Show that the curvature of C(t) converges to the curvature κ(0)...

I need to calculate the force or moment required to bend a thin strip into a circle

Find the equation of the circle tangent to the y-axis and with center (3, 5). Can someone provide the steps needed to solve this problem?

Find the equation of the circle tangent to the x-axis and with center (3, 5). Can someone provide the steps needed to solve this problem?

Homework Statement The streamlines of a certain flow are concentric circles about the origin, and the absoute value of the velocity varies according to the law |V|=k*r^(n) Show that the angular speed of any fluid element in flow is described by: εz=(1/2)*k*(n+1)*r^(n-1) Homework Equations...

Homework Statement In the drawing you can see a circumference inscribed in the triangle ABC (See the picture in the following link). Calculate the value of X https://goo.gl/photos/CAacV2dJbUrywfXv92. The attempt at a solution It seems I found a solution for this exercise with the help of a...

Homework Statement The problem is from D'Inverno's book on GR, problem 5.6. We're using the Jacobian/transformation matrix to convert the tangent to a circle centered at the origin of radius A from Cartesian to polar coordinates. I can do the problem and get the book answer, that's okay...