Radius Definition and 1000 Threads

Homework Statement What is the next radius outwards of this Apollonian gasket? R = radius of outer circle = 5 r1 = radius of largest inner circle = 3 r2 = radius of second largest inner circle = 1 a = unknown radius Homework Equations C = 2πr A = πr2 d = 2r The Attempt at a Solution Make a...

Homework Statement Given the ## r(t) = ae^{kt}## , ##θ(t)=kt## find the velocity function that is dependent on ##r##. ##v(r)=?## Homework Equations 3. The Attempt at a Solution [/B] My attempt: 1)##r(t) = ae^{kt}## 2)##{\dot r(t)} = ake^{kt}## From the first equation: ##\ln...

Hey! :o I want to find for the following series the radius of convergence and the set of $x\in \mathbb{R}$ in which the series converges. $\displaystyle{\sum_{n=0}^{\infty}\frac{n}{2^n}x^{n^2}}$ $\displaystyle{\sum_{n=0}^{\infty}\frac{1}{(4+(-1)^n)^{3n}}(x-1)^{3n}}$ I have done the...

Homework Statement In circle O , BC >CD Compare x & y (which is greater?) Homework Equations There are no eq. Rule: angle opposite larger side is larger The Attempt at a Solution In my view both triangles are isosceles triangle. So x & y should be equal because they are both opposite the...

This is a request for a good reference. I'm doing a report on dark matter and am wondering if there's any recent references that collects a bunch of galaxy clusters, their dark masses and the radius of the cluster. Preferably in a table that I can shred or download but I'll copy if I have to...

Homework Statement To avoid this stress, vertical loops are teardrop-shaped rather than circular, designed so that the centripetal acceleration is constant all around the loop. How must the radius of curvature R change as the car's height h above the ground increases in order to have this...

Learning about Schwarzschild radius from Wikipedia: Is it accurate to say any object of mass crossing the event horizon of a black hole is compressed sufficiently to have its own Schwarzschild radius, becoming a black hole itside of a black hole?

Homework Statement Ions having equal charges but masses of M and 2M experience a constant electric field while they travel a fixed distance d and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc...

Homework Statement [/B] The question is from chapter 9 of "Exercises in Introductory Physics" by Leighton and Vogt. The answer given in the book is ##R = 4.9 \times 10^{-5} \rm{cm}##. Homework Equations $$\sigma = \frac{\Delta P \cdot R}{4}$$ Where, ##\sigma## is the surface tension...

Hello, How do I calculate the critical bending radius of a single mode optical fibre? I'm using a polyimide coated fibre with coating diameter of 155μm. The wavelength is 1550nm. Let me know if you have any questions. Thank you

Hi I am stuck on this integral question: An oil tanker aground on a reef is losing oil and producing an oil slick that is radiating out at a rate approximated by the function (dr/dt)=20/√t, t is greater than or equal to 1 where r is the radius of the circular slick in metres after t minutes. If...

Homework Statement Planet X of mass mx = 2.1 × 1024 kg orbits S in uniform circular motion at a distance rx and with a period Px = 2.1 years (=66225600 s). The mass of the star S is MS = 2 × 1031 kg and its radius is RS = 3.2 × 108m. Homework Equations T=2pi * sqrt(r3/(GM) The Attempt at a...

Homework Statement There is a solid cylinder of radius a and then empty space then a shell cylinder of radius b. Show that half of the stored potential energy lies within a cylinder of radius $$\sqrt{ab}$$ Homework Equations In the attempt The Attempt at a Solution I'm not sure what they...

I am trying to calculate what we'd expect the uncertainty in energy would be for an electron in a hydrogen atom where it was confined to its usual radius (120 pm) versus if we confined it to the width of a proton (.88 fm) to try and make an argument about why the electron does not fall into the...

Homework Statement A monkey is swinging a coconut of 1 k in a pendulum like motion. When the monkey's motion is at the bottom of its swing it is .6 m above the ground. He releases the coconut when it it is in this position when the force is 250 N and it travels 10 meters before hitting the...

Homework Statement Homework Equations Vab = ∫ E*dr The Attempt at a Solution [/B] For part (b) I am not sure if I should set the upper and lower bound of the integral from "R" to "2R" or "2R" to "3R". If done so, this would give me V2R = Vab * ln|3R/2R| / ln |3| instead of what is on the...

First time posting on the forum - I've been coming here a lot the past year or so to seek answers. This one is concerning a lab. I think I've already done the legwork but am sort of looking for either something I'm missing or a confirmation of sorts. It's pretty messy and wordsy but if you...

Hi. I am trying to determine the size of a shaft for a motor I am designing. The thing is, I can't seem to find shear stress alone for steel. I can find shear modulus easy though... But I don't really know the angle of twist. I know torque and I am trying to figure out radius. Should I just...

Homework Statement [/B] We are heating a semi-infinite slab with a laser (radius of a stream is ##a##), which presents us with a steady surface heating (at ##z=0##), everywhere else on the surface the slab is isolated. How does the temperature change with time? Look at the limit cases: at ##t...

A spherical snowball is melting at a rate proportional to its surface area. That is, the rate at which its volume is decreasing at any instant is proportional to its surface area at that instant. (i) Prove that the radius of the snowball is decreasing at a constant rate. can someone help me?

https://i.imgsafe.org/5172eee94d.jpg For a closer look click https://i.imgsafe.org/5172eee94d.jpg We know that the area of the sector should be $\frac{40}{360}$*$\frac{22}{7}$*$r$*r Any ideas on how to begin? Many Thanks:)

Homework Statement A person's eye has a near point of 7 cm. The cornea at the outer surface of the eye has a refractive index of n_c = 1.376 and forms a convex shape with a radius of curvature of R_2 = 8 mm against air. The figure below shows the same eye with a contact lens (refractive index...

Including dark matter but not including dark energy, what's the Schwarzschild radius of the known universe? Actually, let me put it another way. What's the SR of all the matter and energy thought to be created at the Big Bang? So that would include not just all the matter we see but also all the...

I've been thinking about notions like the following: "How far can one be from the nearest road while in a particular country." "What's the 'maximum thickness' of a subset of \mathbb{R}^n?" "What mountain range has the biggest circular region entirely within it?" These sorts of questions lead...

Supposing I have this expression: $$\sum_{n = 1}^{\infty} \frac{x^n}{3^n}$$ and I need to find the values for x for which this converges and the radius of convergence. I can use the radius test: $$\lim_{{n}\to{\infty}} |\frac{{x}^{(n + 1)} 3^n}{{3}^{(n + 1)} x^n}|$$ and this equals...

The video:

I read in http://www-library.desy.de/preparch/books/vstatmp_engl.pdf page 29 (43 for pdf) that the mean volume is: <V> = \int_{-\infty}^\infty dr V(r) N(r| r_0,s) I have two questions. Q1: why do they take the radius to be from -infinity to +infinity and not from 0 to infinity? Q2: is there an...

Hi! I'm getting ready for an exam and want to make sure if I solved some problems correctly. I would be grateful for your feedback :smile: 1. Homework Statement After going through potential difference of 5000 V an electron falls in uniform magnetic field. It’s induction is 0.1T and the...

Hello, I have two questions regarding the Radius of convergence. 1. What should we do at the interval (R-eps, R) 2. It used definition to prove radius of convergence, but I am not sure if it is necessary-sufficient condition of convergence. I get that this can be a sufficient condition but not...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

Homework Statement The following image shows the parts A and B of a pipe where the middle part goes under a hill the length of both parts A and B is 30m and the diameter of them each is 2cm where as the middle part has a length of 110m to determine the middle part's diameter one engineer...

Hi again. I hope this is the right section to ask this question. Not home work (I'm retired) but yet another mind game I'm playing (and still getting nowhere). I have trying to work out the formula for how a ski will perform a carved turn. I have looked at many (many Many) websites and they...

Homework Statement We previously solved the heat conduction problem in a ring of radius a, and the solution is c into the sum, perform the sum first (which is just a geometric series), and obtain the general solution, which should only involve one integral in ϑHomework Equations...

Homework Statement Let f(x)= (1+x)4/3 - In this question we are studying the Taylor series for f(x) about x=2. This assignment begins by having us find the first 6 terms in this Taylor series. For time, I will omit them; however, let's note that as we continuously take the derivative of this...

I have a data set of 120k star systems that I'd like to import into a project, and, while it has a lot of useful infomation, I'd like to display these stars in a visual fashion. This means that I need to figure out the radius, when zoomed into the star system, and its mass, to simulate objects...

If there was a free-spinning effective weight of 20 lbs. at a 20" radius rotating at 180 rpm (15.7 fps?) and a force of 20 foot pounds was added, what would be the increase in velocity/speed? (Ignoring friction and wind losses).

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] How would you find the radius of convergence for the taylor expansion of: \begin{equation} f(z)=\frac{e^z}{(z-1)(z+1)(z-3)(z-2)} \end{equation} I was thinking that you would just...

Homework Statement Find all values of x such that the given series would converge Σ6n(x-5)n(n+1)/(n+11) Homework EquationsThe Attempt at a Solution By doing the ratio test I found that lim 6n(x-5)n(n+1)/(n+11) * (n+12)/[6n+1(x-5)n+1(n+2)] n→inf equals 1/(6(x-5)) * lim...

Homework Statement Hi everybody! I'm a little struggling to fully understand the idea of radius of convergence of a function, can somebody help me a little? Are some examples I found in old exams at my university: Calculate the radius of convergence of the following power series: a)...

I have an engineering project to do this semester. I'm not going to get into the specifics, but I (and my group) are going to be building a submersible servo-driven vehicle (it is basically driving underwater). The vehicle will be made of 4" PVC piping (thin-walled sewer variant). It must be...

Homework Statement A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.460 T magnetic field? Note: I hope this question is meant in advanced...

Homework Statement Block A has a mass of 3 kg, and block B has a mass of 8 kg. Determine the speed of block A if it moves upwards 2 meters, starting from rest. I can solve the problem pretty easily if the mass and radius of each of the pulleys is neglected. However, if they are not neglected...

Homework Statement So, I got the problem from a friend who told me he copied it down in haste, so it's possible that my confusion stems from a missing variable, but I just want to be certain as my exam is in a few days. So the problem states that there's a +2 helium atom that was accelerated by...

Homework Statement Okay, so the question seems really simple so I don't know what I'm missing A satellite orbits at a fixed point above the Earth's equator. Assuming the Earth has uniform density, radius R, and angular frequency of rotation, omega Find an expression for eta, such that the...

Homework Statement P=Kρ^2 is a solution to the equation of the combination of the Hydrostatic Support equation and the mass continuity equation. Find the radius of the star. Homework Equations ρ(r) = (A / r) sin (root( 2πG/K) r) The Attempt at a Solution The first part of this was to prove...

Homework Statement Find where θ is the biggest (largest) I'll have the picture of the problem included below (pic:1) Homework Equations (x-q)2+(y+5/2)2=r2 answer x= 2 The Attempt at a Solution Hi, so my prefesor gave me this problem and told me to try to solve it. We already did this problem...

Hello all, I am trying to remember (I did it in Uni) how to calculate the effective mean radius of an annulus that contains a pattern of holes on a PCD. Consider the following image (pinched from: https://www.solenoid-valves.com/ ): If one was to vary the value of PCD, then the effective...

In linear accelerators that use a disk loaded structure (traveling wave), how would you calculate the iris(disk hole) radius, cavity radius, and disk thickness according to the wavelength

Homework Statement i was told that the hydraulic diameter = 4Ac / p , while the hydraulic radius = Ac / p , where Ac = cross sectional area , and p = wetted perimeter of the pipe , why shouldn't the hydraulic radius = 2Ac / p ? because as well all know , diameter = 2 Radius , so hydraulic...