Circle Definition and 1000 Threads

http://gyazo.com/bc7f6da4d4c4aca300bb5efb2410fc8d.png The problem, and my solution are in the image. I need help on finding the equation of the osculating circle, I found radius but I don't know where to go from there. Also if you could just check if my math seems correct that would help me...

(I am not sure if this is the right place to post it but since my solution involves some Calculus, I decided to post it here.) (Also, I am not well versed with the correct words and terms to be used while doing geometrical probability problems, I am sorry if I write something wrong. :o )...

Homework Statement For what values of a do the points (4,3),(-3,1),(1,a), and (1,5) lie on a circle? The Attempt at a Solution So my solution came down to getting the equation a(x^2+y^2)+bx+cy+d=0 Making a matrix with the first three points, doing R1-R4, R2-R4, R3-R4, then reducing the matrix...

Hello, I was working problems from a very old trigonometry book, Loney's Trigonometry from 1895. There appears here a problem stating: The value of the divisions on the outer rim of a graduated circle is 5' and the distance between successive graduations is .1 inch. Find the radius of the...

As the title inquires, I am curious as to how or why the Sin function represents y coordinate on the unit circle.

From A circular sheet of RADIUS "R" a sector tie is cuts so that the coil Gets a funnel. Calculate the angle of the circular sector to cut back so of funnel has the maximum capacity. Answer tha angle is 2sqrt(6)pi/3

Homework Statement A sphere of radius ## R ## carries charge density ## \rho = ar^5 ## where ## a ## is a constant. Find the flux ## \Phi ## of its electric field through a surface of a circle with radius ## R ## if the circle lies in a plane tangent to the sphere and its center touches the...

Hi, I have an involute gear and measured co-ordinates of two arbitrarily chosen points (on the involute portion) of a tooth. Can I find out the base circle with this information? Thanks.

Let P(x,y) be a point on a unit circle that is centered at (0,0). How to compute exactly the function \frac{\partial^2 x}{\partial s^2} where x is the x-coordinate of the point P(x,y) and s is the tangent at point P(x,y) . Clearly, \frac{\partial x}{\partial s} =...

The circle seems to be of great importance in topology where it forms the basis for many other surfaces (the cylinder ##\mathbb{R}\times S^1##, torus ##S^1 \times S^1## etc.). But how does one define the circle in point set topology? Is it any set homeomorphic to the set ##\left\{(x,y) \in...

Homework Statement A light spring has unstressed length 15.5cm.It is described by Hooke's law with spring constant 4.30N/m.One end of the horizontal spring is held on a fixed vertical axle,and the other end is attached to a punk of mass that can move without friction over a horizontal...

Here is the question: I have posted a link there to this thread so the Op can view my work.

Homework Statement Is it true that the if you slice a circle into two segments, you can think of one of the pieces as being half an ellipse? Homework Equations The Attempt at a Solution Not sure, I was just thinking about this! Not really any idea how to proceed to a solution, or how I can...

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

Homework Statement DIAGRAM ATTACHED AT BOTTOM Q. The following statements are true for an element in plane stress state. (this is 2D) (1) one of the principle stresses is 40Mpa; (2) σx= -2τxy; (the algebraic values) (3) in x'oy' with θ=30°, the two normal stresses σx'=σy' Determine...

In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area...

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

One rule of circle theorems is,a line drawn from center to the mid-point of a chord cuts the cord at 90°. What's the proof? It's true that two radius and a chord creates an isosceles triangle. So, How can I prove that in an isosceles triangle,a line drawn from the vertex angle to the mid-point...

Homework Statement The ellipse has equations x = 2cos(t) and y = 3sin(t) where 0 <= t <= 2*pi The problem asked me to calculate the curvature at points (2,0) and (0,3). I did that, but now the problem asks what the equation of the osculating circle is at each of those points. I know the...

find the radius of the small circle O_2:

Ok so when I try to get the centroid of a semicircle using ∫rdm/∫dm, ∫dm = ρ∫dxdy for x^2, but now that the area is (0.5)∏(x^2 + y^2) what would ∫dm be? If I did use ρ∫dxdy I have to do some weird integration of sqrt(30^2 - x^2) which we haven't learned yet. If I do have to ρ∫dxdy how would I go...

Homework Statement If n things are arranged in circular order, then show that the number of ways of selecting four of the things no two of which are consecutive is $$\frac{n(n-5)(n-6)(n-7)}{4!}$$Homework Equations The Attempt at a Solution My approach to the problem is that I first select the...

Homework Statement Find the equation of the tangent drawn from the point(-5,4) to the circle x^2+y^2-2x-4y+1=0 Homework Equations y-y1=m(x-x1) x^2+y^2+2gx+2fy+c=0 The Attempt at a Solution The equation of the tangent using the point is as follows y-4=m(x+5). Now, if I substitute...

Homework Statement Consider the bivariate density of X and Y, f(x, y) = pi/2 for x^2 + y^2 ≤1 and y > x and = 0 otherwise. (a) Verify that this is a bivariate density (that is, the total volume ∫∫ f(x,y)dxdy = 1) Homework Equations The Attempt at a Solution The problem I'm having is...

Homework Statement Find the length of the chord which the circle 3x^2+3y^2-29x-19y+56=0 cuts off from the straight line x-y+2+=0. Find the equation of the circle with this chord as diameter Homework Equations x^2+y^2+2gx+2fy+c=0 The Attempt at a Solution I can solve the second part...

Homework Statement Find the equation of the circle which intersects the x-axis at two points at 2 unit distance from the origin and the radius is 5 Homework Equations x^2 + y^2 + 2gx + 2fy + c=0 r=(g^2+f^2-c)^1/2 The Attempt at a Solution I first tried to solve it by assuming...

Hi -- Thinking about the problem, where I have three circles in a closest possible packing inside an equilateral triangle. So two circles on the floor, adjacent to each other touching and a third circle placed on top so that the distances off their centers from each other are all 2R, R=Radius...

I considered the question of whether three tangents to the circle could meet at a common point and only came up with a contradiction by lengthy constructive means. Circles are "nice", so there must be some clever ways of showing this fact that given a point outside the circle there are two...

Homework Statement Use vectors to demonstrate that on a circle any two diametrically opposed points along with an arbitrary third point(on the circle) form a right triangle Homework Equations Hint: assume without a loss of generality that the circle is centered at the origin and let v...

Homework Statement How many necklace with 5 white beads and 5 black beads can be constructed? Homework Equations Circular Permutation problem The Attempt at a Solution] I did 10!/5!5!=252 but from there I didn't get anywhere. I know this includes repeats from rotational...

http://www.natuurkunde.nl/servlet/supportBinaryFiles?referenceId=1&supportId=606217 Hello everyone, I was wondering if anyone could shed some light on the following problem: While composing a practise test for a chapter about conservation of energy, I made a problem like the one in the...

Homework Statement A 400g steel block rotates on a steel table while attached to a 1.20m -long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 4.71N perpendicular to the tube. The maximum tension the tube can...

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

Hi Guys can you please help me out for the following question: Show that the equation of the circle $$\gamma(a;r)$$ centered at $$a\in\mathbb{C}$$ and radius $$r$$ can be written in the form: $$|z|^2 - 2Re(\bar{a}z) + |a|^2 = r^2 $$

Both statements 1 and 2 are given as an explanation of why the original statement is true, but I don't understand why you can use statement 2 (since in the original vector equation you do not have Sin2(t), -Cos2(t)) Show why r(t) = <e-t, Sin(t), -Cos(t)> approaches a circle as t →∞. 1. As...

I was thinking about this when I was trying to work out a simpler way of finding the volume of a sphere. Suppose we cover a hemisphere with a piece of pliable thin cover. Stretching the cover flat would make a circle. The circumference of the sphere is 2*pi*r. The distance along the surface of...

A particle is moving in a circle of radius R in the xy plane. During the motion, neither the x- nor y-component of the particle's velocity exceeds v. Find the minimum possible time for the particle to complete one circle. (I.e., find the minimum possible period of revolution.) Hint 1: I...

Homework Statement Find the curve whose curvature is 2, passes through the point (1,0) and whose tangent vector at (1,0) is [1/2 , (√3)/2 ]. The Attempt at a Solution I know I must use the Fundamental theorem of plane curves but I don't know how to apply it correctly here. Another...

Homework Statement r=7sin(∅) find the center of the circle in Cartesian coordinates and the radius of the circle The Attempt at a Solution My math teacher is impossible to understand >.< and then the stupid homework is online and crap blah this class but I REALLY want to understand the material...

Homework Statement Approximate uncertainty in the area of a circle of radius 5.5×10^4 cm? Homework Equations πr^2 The Attempt at a Solution

Homework Statement Derive the formula for surface area of a sphere using integration of circlesHomework Equations Need to get : S = 4πr2The Attempt at a Solution Consider a sphere of radius r centred on the origin of a 3D space. Let y be an axis thru the origin. The sphere can be sliced into...

Homework Statement I am after finding general geometric expressions for a quarter-circle that is split into two segments along either its domain or range (they are equal). I.e. Taking the circle shown in Figure 1 and concentrating on the upper right quadrant, I am after expressions for the...

Hello I have a problem where a wire is pulled around a half circle (disc) and then both ends pulled. The force in both ends are equal (F1 + F2). The disc must in total put up a force (F3) equal to F1 + F2 to not be pulled along by the wire. My question is how does the force of the...

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

Homework Statement An object of mass 'm' if revolving in a circular path of radius 'R', this is analogous to a gravitational motion except that the force is applied from a point on the circle itself, it is required to find the force law Homework Equations from the point of application...

(a) if $r=6$ and $\displaystyle \pmatrix { 6 \\ 0 } $ then $A$ is $6$ from $0,0$ on the $x$ axis and if $\displaystyle \pmatrix { -6 \\ 0 }$ then $B$ is $-6$ from $0,0$ on the $x$ axis and if $\displaystyle \pmatrix { 5 \\ \sqrt{11} }$ implies $\sqrt{5^2 + 11}=6 = OC$ (b) I presume...

Thanks again to those who participated in last week's POTW! Here's this week's problem! ----- Background Info: A string is wound around a circle and then unwound while being held taut. The curve traced by the point $P$ at the end of the string is called the involute of the circle. If the...

1. Homework Statement Let S be the set of complex numbers z such that |z|=1. Is S a cyclic group? 3. The Attempt at a Solution I think this group isn't cyclic but I don't know how to prove it. My only idea is: If G is a cyclic group, then there is an element x in G such that...