Circle Definition and 1000 Threads

Q1 Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear. Q2 AB and CD are two parallel chords of a...

Homework Statement Consider a function f that can be put in the form f(p) = g(|p|) where g : [0,+∞) -> ℝ is C1 with g(0) < 0 and g'(t) > 0 for all t ≥ 0 Assume that |∇f(p)| = 1 for all p ≠ 0 and prove that the set f(p) = 0 is a circle. Homework Equations Given above The Attempt at a...

doesn't that mean that one hemisphere would have a hotter summer than the other hemisphere and the opposite would have a colder winter? if so, which is which. I am willing to guess the northern hemisphere has the colder winter and southern has the hotter summer.

Hi I don't understand how you can take a cylinder with equation x2+y2=2x And rewrite it to (x-1)2+y2=1 And then it suddenly becomes the equation for the base circle of the cylinder. Would it not usually require that you remove some variable to transform it from 3D to 2-dimensional...

Homework Statement Here is the question with the solution from the textbook and my solution: I don't understand the textbook solution because in their Mohr's circle the max shear stress is 65 Mpa. However, as stated in the problem, the max shearing stress is 80Mpa and this occurs 45...

Homework Statement Let z \in \mathbb{C}. Prove that z^{1/n} can be expressed geometrically as n equally spaced points on the circle x^2 + y^2 = |z|^2, where |z|=|a+bi|=\sqrt{a^2 + b^2}, the modulus of z. Homework Equations // The Attempt at a Solution My problem is that I am...

Find the equations of the sides of square inscribed in the circle $3(x^2+y^2)=4$, one of whose sides is parallel to the line $x-y=7$.

Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ? *The centres of these circles are all (0,0) *

Hi guys, I would like to understand why a circle (and in general a n-sphere) as a subset of R^2 (in general R^(n+1)) with the standard topolgy is considered a closed and a bounded set. I think that this can be a closed set because its complement (the interior of the circle and the rest of...

Homework Statement A pilot, whose mass is 96.0 kg, makes a loop-the-loop in a fast jet. Assume that the jet maintains a constant speed of 225 m/s and that the radius of the loop-the-loop is 2.064 km. What is the apparent weight that the pilot feels (i.e., the force with which the pilot...

Homework Statement Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method. x^2 + (y-1)^2 = 1 Homework Equations Cylindrical method: ∫2∏xf(x)dx Slice Method: ∫A(x)dx The Attempt at a Solution x^2 + (y-1)^2 = 1 x =...

A fish looking straight up to the surface of a pond receives a cone of light filled with images. This bright field is surrounded by darkness. Explain what is happening and compute the cone angle. No given data but ##n_w=1.33## No give equations but I anticipate Snell's law and maybe the...

Consider a circle of radius 'a' and centre (h,b) then the equation of the circle is given by (x-h)2 + (y-b)2 = a2 I expressed this in terms of differential equations which is - a= {[1+(dy/dx)2]3/2}/{d2y/dx2} According to my book - this equation indicates that 'a' is a...

Homework Statement Using graphical means, determine how many positive roots exist, as a function of a, the the following equation. Homework Equations √(a2-x2) = tan(x) The Attempt at a Solution I've sketched graphs showing tan(x) and the semi circle overlapping for various radii...

I'm trying to prove the homeomorphism between the open intervals of the real line and the open sets of the circle with the induced topology of R^2. Notice that the open sets of the circle is the intersection between the open balls in R^2 and the circle itself. Anyone can help me...

Hi All, I'm looking for help in converting 2D density (objects/area) in a circle to 3D density (objects/volume) in a sphere, the circle and sphere having the same radius and distribution of objects being uniform. To make this problem more intuitive, here's a sample application: both crabs and...

1. I basicly have to find the coordinates of P. All the pink lines are know, coordinates of points A and centre of circle are know. 2. (x-a)^2 + (y-b)^2 = r^2 [b]3. I try to substitute mx+c into the equation and get (x-a)^2 + (y-mx-c)^2 + r^2= 0 but I can't work out what m and c...

Hi everyone! My primary question is below the problem. My problem: Circles The standard form of an equation for a circle is (x − h)2 + (y − k)2 = r2 where (h,k) represents the center of the circle and r is the radius. The y-value of the equation becomes zero at the point of intersection with...

The first thing that we should notice is that the leading coefficient $a_n = 1$. I was thinking about considering the factored form of p. I googled, and there is an algorithm called the "Schur-Cohn Algorithm" that is suppose to answer exactly this, but I can't find any information on it or...

I wish to write this equation: 1=√(x2+y2) as a parametric equation but WITHOUT the use of sine and cosine. Is this possible?

Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...

Hi, I'm not sure how to integrate this equation where a, r0 and γ are constants.

Triangle inscribed on circle proof...I am missing something :( Homework Statement I have provided a link to the problem below http://imageshack.us/a/img854/4143/photo1lsd.jpg I need to prove AE is an altitude on this proof Homework Equations all radii are congruent, cpctc, ASA...

Homework Statement I have a line obtained from using a slope of 1 and point (-sqrt(2),sqrt(2)): y - sqrt(2) = 1 (x+sqrt(2)) y = 2*sqrt(2) + x and a circle with radius 5 centered at origin. My thought was to solve this parametrically The line is the tangent line (blue...

Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...

Homework Statement Find an arc length parametrization of the circle in the plane z=5 with radius 6 and center (4,1,5) Homework Equations ||r'(t)||=r'(u) s=integral r'(u)du The Attempt at a Solution I get the equation of the circle to be (x-4)^2+(y-1)^2+(z-5)^2=6^2 Not sure where...

I'm getting conflicting information on the proper form of Mohr's Circle for the stress of a system at a rotation from nominal. Actually it seems that Mohr's Circle is not a tool for just stress or moment if area/stress calculation, but in general for a 2-D simple symmetric form eigenproblem...

I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which represent the circle diameter and another point (P3) NOT on the circle but on its plane. Also known the length of the line from P2 to X, for example d. Another thing that may help, the...

Homework Statement See image. Homework Equations ωx (ωx r) = anormal αx r =atangent x=rcos*theta y=-rsin*thetaThe Attempt at a Solution I solved for w=2 k rad/s and α= -1.5 k rad/s I also got the correct answer using the cross products. My problem is I am trying to do this problem in...

I don't know what category this question falls into. I have two parallel planes, on one I draw a circle and on the other I project it orthogonally. Now I incline the plane with the circle. The projection on the other plane will be an ellipse. I need to find out, the relationship between the...

Homework Statement Find the x-component of the electric field at the origin due to the full arc length for a charge of 3.8 μC and a radius of 1.9 m. The value of the Coulomb constant is 8.98755 × 109 N · m2/C2. Homework Equations E = kq/r^2 dq = q dθ λ = Q/ (R θ) The Attempt...

Homework Statement We are given a function defined by x = uv, y = 1/2 (u^2-v^2)Homework Equations I derived the line element ds^2 = (u^2+v^2) dv^2 + (u^2+v^2) du^2 However I decided this was to unwieldy to derive our circumference where C = 2*{R}\oint_{-R}^{R} ds So I decided to try to...

Homework Statement Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk Homework Equations None given.. The Attempt at a Solution Well (1-z)P(z) = 1+z+z^2+...+nz^n and to find roots I set it to 0: 1+z+z^2+...+nz^n = 0...

Sometime in the afternoon or in evening i see some leaves caught in something like air current which i feel that there some thing more. The leaves (tiny fallen leaves and some dust particles) revolve around a center. It looks like the leaves have formed the circumference of the circle and they...

When I first saw the infomercial I knew this Chinese manufactured piece of junk was worthless. http://www.washingtonpost.com/business/companies-marketing-ab-circle-pro-to-pay-up-to-25-million-in-refunds-to-settle-ads-charges/2012/08/23/77799a20-ed33-11e1-866f-60a00f604425_story.html...

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Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry: Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given.Please, check my reasoning on this one. I just want to make sure that I'm getting it right. My solution: Using a...

A textbook shows a circle with a line drawn through the centre and advises that the line represents the diameter of the circle, ok with that, but what happens if the circle was a pipe and the pipe had a hole drilled into it, so the pipe now has an outer diameter of 10 but the hole inside the...

say I have a circle with a diameter of d and there is a point at the top of the circle, p. I want to know the distance from point p to any other point on the perimeter and the angle θ from the tangent line of p. is there a function that will describe this? I will try to put up a picture to...

Homework Statement A small light is 22.0 cm below the surface of a liquid of refractive index 1.50. Viewed from above, the light appears to illuminate a circle on the surface of the water. What is the diameter of the circle? cm Homework Equations Snell's Law n1sin(θ)1 = n2sin(θ)2...

I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...

Homework Statement Sketch modulus((z+1)/(2z+3))=1 on the complex plane where z=x+iy Homework Equations The Attempt at a Solution I know it is a circle but i need help simplifying the equation into the form of a circle. i'm stuck at 0= 3x^2 + 3y^2 + 10x + 8 I usually...

Find the center and radius of the circle using the equation: x^2 + y^2 + 2√2x - 4√5y = 5 I just can't seem to solve this equation into the form (x-h)^2 + (y-k)^2 = r^2 in order to get the center and radius. Any help would be appreciated

Centroid of a "TILTED" Semi circle! Guys, could anyone help me out how to solve the centroid of these "tilted" semicircle. I really don't have any idea how to get its centroid since it's tilted..Please I really want to understand so kindly do it step by step, Thanks.. Just Find the x-bar and...

I know I should keeps this short, but I need to explain it a little. So, please have patience with me :) Given a standard ellipse, and its eccentricity and position on screen, is there some clever way of calculating how much a regular circle needs to be tilted in (angles) in a perspective...

Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this in MATLAB, using the 'pdist' and 'cmdscale' functions. My uber-complex code is the following: clc;clf;clear all; boundaryPlot=1.5; % Euclidean unit circle for i=1:360...

What is the equation of the circle with a center point of (10, -14) when the circle is tangent to x=13? D = √(13-10)^2 + (0-(14))^2 D = √(3)^2 + (14))^2 D = √9+196 D = √205 Radius = √205 (x-10)^2 + (y-(-14))^2 = √205^2 (x-10)^2 + (y+14)^2 = 205 But how am I suppose to graph this?

Homework Statement The problem is attached as TheProblem.jpg and the answer is A. Homework Equations Geometry rules. The Attempt at a Solution The triangle which has angles of 30deg and 10deg also has an angle of 180deg-30deg-10deg = 140deg and the other side of the line intersection...

I want to show that if the complex variables ζ and z and related via the relation z = (2/ζ) + ζ then the unit circle mod(ζ) = 1 in the ζ plane maps to an ellipse in the z-plane. Then if I write z as x + iy, what is the equation for this ellipse in terms of x and y? Any help would be...

Homework Statement -8\int^{3}_{0}\sqrt{9-x^2}dxHomework Equations The Attempt at a Solution am i right in thinking this the area of a circle in the first quadrant so my answer is-8(\frac{9\pi}{4}) = -18\pi Thanks for reading?