Radius Definition and 1000 Threads

Homework Statement Ʃn!(x-1)n I need to find the radius of convergence for this summation from n=0 to n=∞ The Attempt at a Solution I started off with the ratio test: (n!(n+1)(x-1)(x-1)n)/(n!(x-1)n) = (n+1)(x-1) (x-1)lim(n+1)...Now at this point it looks to me like the series does...

Homework Statement You placed a 10cm high object in front of a mirror and got 5cm high virtual image at (-30cm). (Hint: watch the sign convention) a. Find the magnification b. Find the object distance from the mirror c. Find the radius of curvature of the mirror then I have to know if...

at what radius can you send peer-to-peer text messages / SMS over "ham radio"? suppose we have lots of people concentrated in a small area, like a college campus. Maybe a mile or so in diameter. We would like to set up a packet switched peer-to-peer SMS transmission using low cost long wave...

Homework Statement Suppose that the power series \sumanxn for n=0 to n=∞ has a radius of convergence R\in(0,∞). Find the radii of convergence of the series \sumanxn2 from n=0 to n=∞ and \sumanx2n.Homework Equations Radius of convergence theorem: R = 1/limsup|an|1/n is the radius of...

Homework Statement Suppose that the following series converges when x = -4 and diverges when x = 6. ∑{n=0 -> ∞} c_n • x^n What is the interval of convergence? The Attempt at a Solution I think it is [-5,5) but my friend reckons that it is [-5,6). I don't think [-5,6) is correct because this...

Is "radius" a misnomer in a polar equation? Often I see the description of "r" in a polar equation r = r(theta) as being "radius", but "radius" is a length, and here you can have a negative r. Hence "radius" is a misnomer, as far as I can tell. Perhaps it would be better described with some...

Hi, I have another query related to rolling motion. Lets say a disc is rolling purely with a velocity vo (this being the vcom). It encounters a step.lets say that the step has a height h, where h < r, i.e., the step has a height less than that of the height of the center of the disc. SO...

i see people discussing the convergence radius of a perturbation series in the literature i am really baffled generally, one can only get the first few coefficients of a perturbation series that is, the perturbation series is not known at all how can one determine the convergence...

Homework Statement Given the numerical value of a0= 5.3X10^11m in the Bohr hydrogen atom, find the radius of the first five orbitals as well as the radius for n=100. Homework Equations Rn=a0 x n^2 The Attempt at a Solution Could it be as simple as typing in for the third orbital...

two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster? i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine...

Hi there, My textbook says "When a beam of high energy electrons is directed at a thin solid sample of an element, the incident electrons are diffracted by the nuclei of the atoms in the foil." What does this mean exactly? Are the atoms diffracted by the gap between different nuclei? It...

Homework Statement Derive a relationship between the speed v, of a body moving in a circle of radius r, and the frequency f, of the revolutions. Homework Equations v=2πr/T T=1/F The Attempt at a Solution Well, I thought this would be as simple as solving for F in the second...

Homework Statement A circle of maximal area is inscribed in the region bounded by the graph of y = -x^2-7x+12 and the x axis. The radius of this circle is of the form (sqrt(p) + q)/r where, p, q and r are integers and are relatively prime.What is p+q+r Homework Equations Vertex form...

Homework Statement Sodium is, to a good approximation, a monovalent free-electron metal which has the body-centred cubic structure. (a) Calculate the ratio of the Fermi wavevector to the radius of the largest sphere that can be inscribed in the first Brillouin zone. Remember that the...

What exactly is the radius of curvature of an object? And how would this be applied to a question such as the following: A glass porthole of a submerged craft has parallel curved sides, both of radius of curvature R. What would R be in order that an object in the water 2m away from the...

Homework Statement k is a positive integer. \sum^{\infty}_{n=0} \frac{(n!)^{k+2}*x^{n}}{((k+2)n)!} Homework Equations The Attempt at a Solution I have no idea.. this is too confusing. I tried the ratio test (which is the only way I know how to deal with factorials) but I get...

Two soap bubbles of radius r and R are in touch find the radius of curvature of their point of contact? (Both bubbles are touching each other with their external surfaces) I have no idea about this question. can you please try to help>

Homework Statement Two identical satellites orbit the Earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v . At what distance from the center of the Earth does the second...

Hi, Suppose I have an analytic function f(z)=\sum_{n=0}^{\infty} a_n z^n the series of which I know converges in at least |z|<R_1, and I have another function g(z) which is analytically continuous with f(z) in |z|<R_2 with R_2>R_1 and the nearest singular point of g(z) is on the circle...

Hey, If initially I have some solid sphere spinning at some initial angular velocity and in its final state I have the same solid sphere spinning at a different angular velocity except some of its mass has moved to a ring 45 degrees in latitude from centre , such that this ring of mass is...

I am looking at inflation at the moment, and it says in my textbook that (aH)^(-1) is constantly increasing in matter or radiation dominated epochs. a is always positive and always increasing. This tells me that da/dt is positive. I think that setting the universe to MD/RD means that da/dt...

How fast must a plan fly in a loop-de-loop if the pilot experiences no force from either the seat or the safety belt when he is at the top of the loop? I just need to be pointed in the right direction. Thanks in advance for your help.

Homework Statement how to prove that radius of convergence of a sum of two series is greater or equal to the minimum of their individual radii i don't know how to begin, can someone give me some ideas?

A hologram with "vibrational energy" to neutralize EMF radiation within its radius? http://www.safespaceprotection.com/qanda.aspx How do the products work? Our products 'repattern' the electromagnetic field by creating a 'coherent polarizing field effect'. When the charged particles are...

Homework Statement A 1200-kg car is traveling at 10 m/s on a road such that the maximum frictional force between its tires and the road is 4000 N. The minimum turning radius of the car isHomework Equations I need the equation to solve.The Attempt at a Solution 30m?

These are my equations for the total Universe_mass-energy equivalence based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters and the observable Universe radius in Systeme International units. I attempted to collapse the Lambda-CDM model...

Homework Statement Find the radius of convergence and interval of convergence of the series: as n=1 to infinity: (n(x-4)^n) / (n^3 + 1) Homework Equations convergence tests The Attempt at a Solution i tried the ratio test but i ended up getting x had to be less than 25/4 ...

Homework Statement Let A be a real nxn matrix with non-negative elements satisfying \sum_{j=0}^n a_{ij}=1. Determine the spectral radius of A. Homework Equations Denote spectral radius \varsigma(A)=max(\lambda_{i}) We know \varsigma(A) \leq ||A|| for any norm || || 3. Attempt at the solution...

A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x.,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.7 m in the x-direction. The proton leaves the field...

Gamma is a circle of radius 2 oriented counterclockwise. $$ \int_{\gamma}\frac{dz}{z^2+1} = \int_{\gamma} = \frac{i}{2}\left[\int_{\gamma}\frac{1}{z+i}dz-\int_{\gamma}\frac{1}{z-i}dz\right] $$ $\gamma(t) = 2e^{it}, \ \ \gamma'(t) = 2ie^{it}$ $$ \int_{\gamma}\frac{2ie^{it}}{2e^{it}+i}dz $$...

Homework Statement If f(z) = \sum an(z-z0)n has radius of convergence R > 0 and if f(z) = 0 for all z, |z - z0| < r ≤ R, show that a0 = a1 = ... = 0. Homework Equations The Attempt at a Solution I know it is a power series and because R is positive I know it converges. And if...

Homework Statement A solid nonconducting sphere of radius a has a has a total charge +Q uniformly distributed throughout its volume. The surface of the sphere is coated witha avery thing (negligable thickness) conducting layer of gold. A total charge of -2Q is placed on this conducting layer...

In this link the proton charge radius is calculated based on an experiment involving a muon and a proton http://www.sps.ch/en/artikel/progresses/muonic_hydrogen_and_the_proton_radius_puzzle_20/ It talks about "In summary, we have measured the muonic hydrogen transition at a frequency of...

When dissolved in water, which of the following ions will form stronger ion-dipole bonds with the water molecules? Li+ or Na+? Both have roughly the same charge... Na has greater radius, but I don't see why or how that has any bearing on the problem.

Homework Statement You and a friend decide to determine the radius of the Earth. You synchronize watches; then your friend drives 50km due west, at latitude 40°. Each of you determines the time when the Sun lies due south -- on the meridian Your friend observes the Sun to be on her meridian...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

Homework Statement A block of mass m1=2kg is attached to a cord. The cord goes down through a hole in the table and is attached to mass m2=4 kg hanging below the table. The 2 kg mass moves on the table in a circle at a speed of 3.5 m/s the table top is friction less and there is no friction...

gamma is a circle of radius 2, centered at the origin, and oriented counterclockwise $\displaystyle\int_{\gamma}\frac{dz}{z^2+1} =\int_{\gamma}\frac{dz}{(z+i)(z-i)}=\frac{1}{2}\int_{\gamma}\frac{\frac{1}{z-i}}{z-(-i)}dz+\int_{\gamma}\frac{\frac{1}{z+i}}{z-i}dz = 4\pi...

The motivation: Hi, I am a bit of a space freak and I have been enthusiastic about this question for a while because there are lots of bodies in the solar system that are a few or many kilometers deep in ice. It occurred to me that if you landed your powerplant on this ice it could sink to some...

Hi all, How do I find the center of a circle given a point (tangent to the circle) and the radius. Thanks, CG

Hello! Okay so I understand that electric potential: V = kQ/r ...must be influenced by the radius doubling because it would make the potential energy half of what it originally was because of the proportionality law, v is proportional to 1/r. With electric fields though, how can...

\sum_{n=2}^{\infty}z^n\log^2(n), \ \text{where} \ z\in\mathbb{C} \sum_{n=2}^{\infty}z^n\log^2(n) = \sum_{n=0}^{\infty}z^{n+2}\log^2(n+2) By the ratio test, \lim_{n\to\infty}\left|\frac{z^{n+3}\log^2(n+3)}{z^{n+2}\log^2(n+2)}\right| \lim_{n\to\infty}\left|z\left(\frac{\log(n+3)}{ \log...

[SIZE="3"]Homework Statement Determine an expression for the Bohr radius (a_{0} from the following approximation. The electron moves to the nucleus to lower its potential energy, V(r) = -\frac{e^{2}}{r} If the electron is in domain 0\leqr\leq\bar{r}, then we may write...

I was going to post this on Earth-forum here but I thought that you guys here can help me better with this. I'm trying to get the radius of Earth on every latitude degree from 0° to 90°, knowing 0° at Equator is ~6378,137km and 90° at North/South Pole is ~6356,7523km (source Wikipedia). In...

Homework Statement By employing spherical polar coordinates show that the circumference C of a circle of radius R inscribed on a sphere S^{2} obeys the inequality C<2\piR The Attempt at a Solution I proved C=2\piR\sqrt{1-\frac{R^2}{4r^2}} So if r>R, then the equality is correct. Am I right...

Homework Statement A frustum of a right circular cone with height h, lower base radius R, and top radius r. Find it's volume. Homework Equations We are currently learning the Method of Washers and the Method of Cylindrical Shells so I believe we are supposed to use this somehow. The...

Out of many properties polymer scientists are interested to calculate one of the most common is "Rg" i.e. Radius of Gyration. Can anyone put more light on the physical significance of this value? Can Rg value of two polymers be compared? If yes what conclusion can be drawn from such comparison?

Homework Statement Estimate the radius of a spherical HII region which rests at a distance of 500 pc that subtends an angle of 20' at the observer. [1'=3x10-4 radians] Homework Equations L=D(theta) Where D is the distance, L is the angular size and theta is the angle. The Attempt...

How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?

Hi guys, The terms above (asperity density and asperity radius of curvature) have confused me for quite a while. I've no clue what they are. Could anyone give me a hand? And is there any relation between them and the summit radius & area per summit? Thanks! CC