Circle Definition and 1000 Threads

A circle L is going through the point O (0, 0) and P (6, 0). The center is in the line y=\frac{4}{3}x. The equation of the circle L is ... A. x^2+y^2+6x-8y=0 B. x^2+y^2-6x-8y=0 C. x^2+y^2-8x-6y=0 D. x^2+y^2+8x+6y=0 E. x^2+y^2-4x-3y=0 Since the equation of a circle is x^2+y^2+Ax+By+C=0, I...

Homework Statement Two equations are defined as follows: What is the value of ?Homework Equations Quadratic Format: ##ax^2+bx+c=0## ##y^-x## = ##1/y^x## The Attempt at a Solution I'm not sure In how to attempt this style of question as I know quadratic and equation of...

Homework Statement Homework EquationsThe Attempt at a Solution I know how to solve this problem . I just need help in interpreting the language of the problem as to what is given and what is required to calculate . 1) Is 30° the true dip and we are asked to calculate apparent dip OR 2) Is...

Homework Statement Two equal line sources of strength k are located at x = 3a and x = −3a, near a circular cylinder of radius a with axis normal to the x, y plane and passing through the origin. The fluid is incompressible and the flow is irrotational (and inviscid). Use the Milne-Thomson...

Homework Statement A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ##r_0## with angular velocity ##w_0##, but...

I'm requiring help on a circle geometry question I've done. The line L, has equation of y=0, and intersects the circle with (3,0) and radius of 29. Find the points of intersection. My working out: 292 = 841 It's centre is 3,0, Inserting that in circle equation gives (x-3)2+y2 = 841 Solving...

Does there exist a binary fractal tree… (reference: http://ecademy.agnesscott.edu/~lriddle/ifs/pythagorean/symbinarytree.htm ) …whose leaves (endpoints) lie on a circle and are equidistant? Consider a binary fractal tree with branches decreasing in length by a scaling factor r (0 < r < 1) for...

This isn't a problem assignment per-say, but for a lab calculation. In my mechanics of material's class, we learned that the radius of Mohr's circle is the maximum strain, but now in my application lab-based class, the video is saying the radius is equal to the maximum strain divided by 2. So...

Hello Forum, Does topology reckon the art of turning a square into a circle? I am quite new to topology and maths in general, I have only dabbled and eyed on my collection of mathbooks. I have come to a conclusion of how to turn the Square into A Circle without cutting. I wonder if I am...

Hi all - In the Near Eastern Late Bronze Age the Egyptians employed a two-man chariot with the axle placed at the rear of the vehicle; whereas the Hittites employed a three-man chariot with the axle placed in the center of the vehicle. As a result, the weight of the two-man crew in the Egyptian...

Homework Statement Find an equation of the circle passing through: A(-3,1) with radius 2 and centre on the line 2x-3y+3=0 Homework Equations x2+y2+2gx+2fy+c=0 r2=g2+f2-c The Attempt at a Solution using this equation , i have found 2 equations -6g+2f+c=-10 by putting (-3,1) -2g+3f+3=0...

Hello. Lets say I am riding a unicycle rolling along the wheels direction with some velocity v0. I know that for the unicycle to turn a curve the centripedal force must be provided by the static friction with the rode that acts against any slipping of the wheel. I am however having trouble...

Dear all, In the attached picture there is an equilateral triangle within a circumscribed circle. MW is a radius of the circle, and I wish to prove that MT = TW, i.e., that the triangle cuts the radius into equal parts. I thought perhaps to draw lines AM and AW and to try and prove that I get...

Homework Statement While a string is attached to a ball and the ball moves in a horizontal circle at a constant speed, does the force change both the direction and speed of the ball? Explain. Homework Equations No equations necessary. The Attempt at a Solution *I think* the force changes...

Homework Statement [/B]Homework Equations Substitution. The Attempt at a Solution Since the circle is of unit radius and around origin, limits are x = -1 to 1, and y = -1 to 1 I replaced x by cos t, and y by sin t. But what to put in place of ds? I thought about divergence theorem, but then...

Homework Statement [/B] In a circle with center S, DB is the diameter. The line AC goes 90 degrees from the center point M of the line SB. " What type of triangle is ACD? 2. Homework Equations The Attempt at a Solution I can see it is an equilateral triangle, but do not know how to explain...

From the entrance examinations to Ghana University ,from high school, i got the following problem: If O is the center of the inscribed circle in an ABC trigon,then prove that: AO+BO+CO\geq 6r where r is the radius of the inscribed circle.

Homework Statement A mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the tension in the string at the bottom of the circle is: a) 6 mg b) mg +...

Homework Statement a grinding wheel 0.5 m in diameter roates at a rate of 8.00 x 10^2 revolutions per minute. find the magnitude of the acceleration of a speck of metal cuaght in the outer edge of the wheel Homework Equations a=4pi^2r/T^2 [/B]The Attempt at a Solution I was wondering if i...

A mass m = 0.15 kg is attached to a massless string and rotates at constant speed v = 4 m/s in a horizontal circle of radius 2 m. The tension T (in N) in the string is: (a) 1.1 (b) 1.9 (c) 2.4 (d) 3.3 (e) 4.9 I would assume that first I calculate the centripetal acceleration by using v^2/r =...

Homework Statement Homework EquationsThe Attempt at a Solution I will try to choose the correct option using the common sense instead of solving it. As d decreases, the flux should increase. For R>>d, only option (a) and (d) satisfy this condition. Now, for choosing between (a) and (d)...

Say you (a skilled motorcycle racer) ride a motorcycle in a big empty parking lot and ride in a big circle of constant radius and slowly go faster and faster. If you are careful as you go faster will you all of a sudden go from very little power slide to a lot of power slide like the video...

Homework Statement In what position in vertical circular motion is the centripetal force the greatest? Top, Bottom, Left, or Right Homework Equations Can someone explain how Fc is greatest at the top? The Attempt at a Solution I had reasoned that since centripetal acceleration which I will...

Homework Statement Homework EquationsThe Attempt at a Solution Since the force is always directed towards C , angular momentum about C should be conserved . But that doesn't seem to help as we need the relation at any general angle . How should I proceed ?

I came across something that is completely counter-intuitive, and I'm wondering if I'm correct or not. If a square has a side that is .8m someone would do .8 time .8 which is .64. How can an area be smaller than a side I thought and so I looked it up and found only one site that said something...

Determine the equation of the circle in standard form, given the coordinate of the diameter PQ. P(-4, -2) and Q(6, 4) Midpoint is (5, 3). d = sqrt{(6-(-4))^2 + (4-(-2)) d = sqrt{(10)^2 + (6)^2} d = sqrt{100 + 36} d = r = sqrt{136} Let d = distance = radius (x - h)^2 + (y - k)^2 = r^2...

Hello. I have some problems with making Lagrangian. I need your advice. 1. Homework Statement I have this situation: Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ. Homework Equations [/B] L = U - V The Attempt at a...

Determine the equation of the circle in standard form, given the coordinate of the diameter PQ. P(1, -3) and Q(-5, -5)

Determine the center and radius of circle.

A. Determine the center and radius of circle. B. Also, find the y-coordinates of the points (if any) where the circle intersects the y-axis.

I am very confused about angular velocity ω and why its used in simple harmonic motion. ω is described as θ/τ but when it comes to masses on springs, there is no angle - it is zero. Angular velocity comes from circular motion but the motion of SHM is not circular. My confusion is even greater...

I would like to find the average chord length of a circle. And I have 2 methods, which gave different answers... [The chord is defined as the line joining 2 points on the circumference of the circle.] The general formula for a chord length is ##d=2R\sin(\delta/2)=2\sqrt{R^2-u^2}## Method 1...

Homework Statement The problem comes from S. Lang's "Basic mathematics", chapter 7, §1: "Consider the following generalization of a dilation. Let ##a > 0, b > 0##. To each point ##(x, y)## of the plane, associate the point ##(ax, by)##. Thus we stretch the x-coordinate by ##a## and the...

I have a circle with centre (-4,0) and radius 1. I need to draw the image of this object under the following mappings: a) w=e^(ipi)z b) w = 2z c) w = 2e^(ipi)z d) w = z + 2 + 2i I have managed to complete the question for a square and a rectangle as the points are easy to map as they are...

Homework Statement A small mass m is suspended from a string of length L. The body revolves in a horizontal circle of radius R with a constant speed v. Find the speed of the body and the period of the revolution. Homework Equations ΣFx = Tx = mV^2/r Period = (2πr)/V The Attempt at a...

Homework Statement I'm having trouble understanding how to find the angle of a vector. Here we are given the x and y component to help us find the direction of vector C. In this case, both x and y component is negative, so it should be in the third quadrant. I know that since we have both the x...

Question: Starting from rest, the toy plane flies around a circle of radius 2m, three times in 3 seconds. There is constant tangential acceleration, fins the magnitude of the acceleration at the end of 0.5s. My solution (most likely wrong): Circumference= 2pir= 4pi= 12.56631 Distance...

Suppose that L: ##S^1## ---> ##R## is a lift of the identity map of ##S^1##, where e is the covering map from ##R## to ##S^1##, where ##R## is the real numbers and ##S^1## is the circle. Then the equation e * L = ##Id_{S^1}## (where * is composition) means that 2*pi*L is a continuous choice of...

Let $S_n$ be the sum of lengths of all the sides and all the diagonals of a regular $n$-gon inscribed in a unit circle. (a). Find $S_n$. (b). Find $$\lim_{{n}\to{\infty}}\frac{S_n}{n^2}$$

Homework Statement Imagine a ball on a string that we swing vertically so that the hight changes. By conservation of energy the velocity of the ball must change right? Because at the highest point of the swing it will have maximum GPE but at the bottom, minimum right? Watching many videos has...

Start with a circle of radius r and center c. Inside of that circle is an arbitrary point p. Given an arbitrary normalized direction vector d, I need to find the radius and center the circle that (1) intersects p, (2) is tangent with the circle centered at c, and (3) has its center lying on the...

Homework Statement Modify the initial conditions (for the diffusion equation of a circle) to have the initial conditions ## g(\theta)= \sum_{n=-\infty}^{\infty}d_{n}e^{2\pi in\theta} ## Using the method of Green's functions, and ## S(\theta,t)= \frac{1}{\sqrt{4\pi...

I've been told that ##[0, 2 \pi )## is not homeomorphic to the unit circle in ##\mathbb{R}^2##. Why not? From intuition, it would seem that I could just bend the line segment to fit the shape of a circle.

$\displaystyle \int_{0}^{1} \int_{0}^{\sqrt{1-x^2}} \sqrt{x^2+y^2} \, dydx=\frac{\pi}{6}$ this was the W|A answer but how ? also supposed to graph this but didn't know the input for desmos

Homework Statement Using the results from problem 2.18 for the setup shown in the Figure below show that if the system is to remain at rest, then the coefficient of friction:a) between the stick and the ground must satisfy $$ μ ≥ \frac {sin(Θ)cos(Θ)} {(1+cos(Θ))(2-cos(Θ))} $$ Homework...

OK just seeing if this is setup OK before I pursue all the steps I thot adding areas would be easier:cool:

Homework Statement The radius of a circle increases from 3 to 3.01 cm. Find the approximate change in its perimeter. Here's a link to the actual question, in case you need the answer for 6(a) to solve 6(b) http://imgur.com/a/nQt6M Homework Equations Perimeter of circle = 2πr Area of circle =...

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

Find the equation of the circle passing through the origin and centered at the point (3,5). Origin means the point (0,0). From the previous example, I found the equation of the circle centered at (3,5) to be (x - 3)^2 + (y - 5)^2 = 25. I do not understand what part the origin plays here. The...

Find the equation of the circle tangent to the x-axis and with center (3,5). Can someone get me started? I know this circle touches the line y = 0 and its center point (3,5) lies in quadrant 1.