Radius Definition and 1000 Threads

Homework Statement sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity? after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x). is this right? if not can you steer me in the right direction, please. Homework Equations The Attempt...

Homework Statement These conditions include the following: (1)radius must be as small as possible. (2)It needs to be possible to park a car on the curve without sliding off on an icy day when coefficients of static and kinetic friction are .2 and .1 respectively. (3)Cars need to make the...

a disc of radius r we have to find electric flux at a point which is at a distance r from the centre i have used e=(sigma/2eo)(1-x/sqrt(r^2+x^2)) the area da=2pir*dr i know flux=closed integral (e.da) and x=r after that what should i do Reply With Quote

Homework Statement Homework Equations i guess its r=sqrt(I/A) where A is the area of the circle thing and I is the moment of intertia. The Attempt at a Solution I guess I'm just having trouble getting I. A is 33pi

The problem: "A convex spherical mirror is 25 ft from the door of a convenience store. The clerk needs to see a 6 ft. person entering the store at least 3 inches tall in the mirror to identify them. What is the radius of the mirror?" d_obj = do = 25 ft = 300 inches h_img = hi = 3 inches...

Homework Statement How would I find the radius of convergence of this series? f(x)=10/(1-3x)2 is represented as a power series f(x)=\sum from n=0 to \infty CnXn Homework Equations The Attempt at a Solution Okay so I tried deriving, using d/dx(1/1-3x)=3/(1-3x)2 and ended up with...

Homework Statement If Dr is a closed disk of radius r centered at (a,b) find lim r->0 (1/pir2) \int\intfdA over Dr. The Attempt at a Solution From mean value equality, \int\int fdA = f(x,y)A(D) where A(D) is the area of the region which here is pir2. So the lhs becomes lim r->0 f(x,y)...

Homework Statement This is the question of mine that I'm having a little confusion about. I know the whole process in which you use the ratio test to determine the radius of convergence and using that you test the end points of the summation to see if they converge at the end points aswell...

Homework Statement A child holds a candy bar 16.5 cm in front of the convex side-view mirror of an automobile. The image height is reduced by one-half. What is the radius of curvature of the mirror? 1Your answer is incorrect. cm Homework Equations 1/f = 1/do + 1/di...

Hi, Does the following inequality hold regarding the product of 2 matrices A and B: p(AB) <= p(A)p(B), where p denotes the spectral radius. Thanks!

Homework Statement Determine the radius of convergence, the interval of convergence, and the sum of the series Summation from k=2 to ∞ of k(x-2)^k+1. Homework Equations ratio test? The Attempt at a Solution possibly take the derrivitive of the power series, then find the sum then integrate...

Homework Statement \Sigma (from index k = 1 until infinity) Within the Sigma is the series : (k! * (x^k)) Homework Equations Ratio Test : lim as k approaches infinity |a(k+1) / ak| The Attempt at a Solution When I apply the ration test to the series and simplify I get lim k...

Greetings everyone and thanks in advance for any help you can offer. I am currently part of a team tasked with designing and constructing an autonomous, mechanically powered two-axle vehicle capable of making left-hand u-turns around a set track. I have designed a steering mechanism I...

Hello everyone! I'm trying to find out how to precisely construct three congruent circles inside a larger circle, each tangential to both the outer circle and the other two circles. For example: http://img4.imageshack.us/img4/1044/verybasicdrawing.png An image I found on the internet...

A method to get the Laurent series of a complex function is by undetermined coefficient.For example f(z)=cot(z)=cos(z)/sin(z).If we want to get the Laurent series of cot(z),we can expand cos(z) and sin(z) to Taylor series respect,then assume the series of cot(z) is a_{ - 1} z^{ - 1} + a_0 z^0...

Homework Statement There wasn't a figure given. All that was given was that the figure is a circular ring. Theta is the angle between the electric field direction and a unit vector normal to the surface area of the ring. Flux versus costheta was plotted and a slope was found to be m = 0.172. E...

Homework Statement My professor mentioned something called "areal radius" briefly in class, but it's I'm unclear as to what it means. It doesn't appear in the index of any textbook I have, and google is pretty unhelpful since it parses it as "area" or "a real" and returns lots of results like...

Homework Statement A carnival ride has a large horizontal steel disc of radius 5.0 m from which cars are suspended by 6.0 m long chains. The disc is rotated about its axis so that the cars swing out and revolve in a circular path. At its operating speed, the angle of the chains to the...

Homework Statement A disc shaped object is made of a non-uniform material. Its radius is r and it is fre to rotate about an axis through its centre. If a force F applied tangentially at the edge of the object produces the angular acceleration a, what is its moment of inertia for rotation...

Homework Statement We are given the mass of the sun, ms = 1.99 x 10^30 and the mass of the venus, mv = 4.83 x 10^24. The distance from each other radius is r = 1.08 x 10^8. What is the centripetal acceleration? mv = 4.83 x 10^24 kg ms = 1.99 x 10^30 kg r = 1.08 x 10^8 km G= 6 67x10^-11 N m2...

A circle has Centre 0 and radius 2. A, B and C are points on the circumference of a circle such that AB is the perpindicular bisector of 0C. Find the area of the segment of the circle bounded by the line segment AB and the minor arc ACB. Give the area in exact forms in terms of surds and...

Homework Statement \sum from n=1 to inf (1+ 1/2 + ... 1/n)x^n Find the radius of convergence and the interval of convergence of the given power series. Homework Equations Dunno.. The Attempt at a Solution Stuck thinking about it. I'm not sure if I can combine what's in brackets with the...

Homework Statement I think I've just majorly confused myself here... In the above diagram, since the ball doesn't "slip" we know that R*\frac{d\theta}{dt} = V where theta is the angle of rotation on the disk itself. I need to relate the angle phi to the angle theta. If I use...

How do you derive the average abs(y) value of points on the surface of a sphere with a radius of 1 centered at (x,y,z)=(0,0,0)? I'm assuming that the points are sampled evenly, or that you can integrate for all points without any distortions that result by averaging over the xy-plane. How do...

Creating metallic hydrogen has proved more difficult than expected. One explanation would be that the Bohr radius of Hydrogen is smaller than expected. Is there any other evidence of an error in Bohr radius predictions?

Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...

:cool:Hi all, I've been trying to solve the attached question for a long time, but it didn't help. I don't know how to start solving it. Could someone help me please :( Thnx Ted

Electron orbiting proton--orbital radius?? Homework Statement In the Bohr model, the electron is imagined to move in a circular orbit about a stationary proton. If the speed of the electron were 8.9e5 m/s, what would be the corresponding orbital radius? 2. Homework Equations 3...

The Problem: Why is it that r = rrE + h? r = distance from Earth's centre to satellite rrE = Earth's radius h = altitude Why is it that you find altitude by subtracting Earth's radius from radius? How does that make sense..

Homework Statement In the Bohr model, the electron is imagined to move in a circular orbit about a stationary proton. If the speed of the electron were 8.9e5 m/s, what would be the corresponding orbital radius? Homework Equations The Attempt at a SolutionFe=ma Fe=ma a=Fe/m (v^2)/r=(kqq/r)/m...

Homework Statement Suppose the coefficient of static friction between the road and the tires on a car is 0.789 and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of 39.3 m radius? Homework Equations i know the equation for...

Homework Statement If a pipe is between two blocks... one block being 1 inch tall and the other block being 2 inches tall. Between the two blocks is an arc that is 6 inches... What is the radius? Can some one please help me... I have no Idea what to do.. thank you.

Hello, we been set a physics assignment where we are given a table of data, a spaceship approaches a planet, and the velocity and radius are given at certain points, we have to graph velocity against 1/r and hence find the mass of the planet. I really don't get this question, i tried slope...

The question: A particle in a cyclotron gaines energy q \Delta V from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T = \frac{2 \pi}{\omega} = \frac{2 \pi m}{q B} so the particle's average rate of increase in...

Homework Statement Given the potential energy V(r)=-\frac{1}{4\pi \epsilon_0}\frac{e^2}{r} (where e is the unit charge), use the uncertainty principle \Delta x \Delta p \geq \hbar to find the Bohr radius r_B for a hydrogen atom and the ground state energy E_0. Hint: write down the kinetic...

Homework Statement If the attractive forces between an electron and proton only due to gravity is F=(Gx Me x Mp)/r^2. What is the lowest gravitational Bohr radius? c=2.99799 x 10^8 m/s Me= 9.10939 x 10^-31 Mp=1.67262 x 10^-27 h= 1.05457 x 10^-34 G= 6.67259 x 10^-11 Nm^2/kg^2...

Homework Statement [PLAIN]http://img153.imageshack.us/img153/4822/radiusm.jpg Homework Equations The Attempt at a Solution Using the ratio test: \left | \frac{e^{i(n+1)^2 \theta} \theta^{n+1} z^{(n+1)^2}}{e^{in^2 \theta} \theta ^n z^{n^2}} \right | = | \theta...

Homework Statement I'm doing a report on an electron diffraction experiment, where a carbon crystal is used as a diffraction grating. There are two line spacings d1, and d2. Observed in the experiment in two cocentric rings. What I'm unsure about is which spacing correlates to which spacing...

Homework Statement The diameters of fine fibers can be accurately measured using interference patterns. Two optically flat pieces of glass that each have a length L are arranged with the fiber between them, as shown below. The setup is illuminated by monochromatic light, and the resulting...

How can I give a fictional planet a realistic mass and surface gravity based on radius? Mercury and Mars are near equal in surface gravity strength, so it does seem that I have some room for variation. From Wikipedia: Earth Average radius 6,371.0 km Surface gravity 9.8 m/s2 Mass...

Homework Statement Find the radius of convergence of \sumcnz^{n} if c2k = 2^{k} and c2k-1 = (1+1/k)^{k^{2}}, k = 1, 2, 3... Homework Equations 1/R = limsup as n=> infinity |cn|^1/nThe Attempt at a Solution I'm not really sure where to start with this. I know that it's a power series, and to...

Gauss's Law - A hollow sphere with inner and outer radius! Homework Statement A spherical shell of inner radius R1 and outer R2 carries a charge Q that is uniformly distributed throughout its volume. No other charges present. a)calculate E inside the sphere b)within the volume c)outside...

Homework Statement There are 3 circles, each tangent to 2 lines and to each other (as in the picture). The radius of the right (largest) circle is 8, and the radius of the left (smallest) circle is 4. What is the radius of the middle circle? The Attempt at a Solution I tried using...

Homework Statement A golfer hits a golf ball from point A with an initial velocity of 50 m/s at an angle of 25° with the horizontal. Determine the radius of curvature of the trajectory described by the ball (a) at point A, (b) at the highest point of the trajectory.Homework Equations p = V2/an...

Homework Statement Consider a star made up of ionized hydrogen. First, take the electrons to be non-relativistic. If the mass of the star is M, derive an estimate for the radius R. As the mass increases, how does the radius change Homework Equations p~(h2 /Me) n5/3 The Attempt at...

Homework Statement Say you have a sphere of radius r centered at the origin, and a vector v <r,0,0>. Let v' be the vector v rotated about the y-axis by angle theta. What is the shortest distance between the end of the vector and the z-axis? Homework Equations The Attempt at a Solution I...

Homework Statement Find the radius of convergence of the power series: a) \sum z^{n!} n=0 to infinity b) \sum (n+2^{n})z^{n} n=0 to infinity Homework Equations Radius = 1/(limsup n=>infinity |cn|^1/n) The Attempt at a Solution a) Is cn in this case just 1? And plugging it in...

Homework Statement S = theta * radius I don't understand how they came up with this formula... can some one show me the proof how they derived this formula or can someone send me a link and I will just read it. Thank you. Homework Equations The Attempt at a Solution

Hello all, We know that for some well-behaved, smooth/continuous, twice differentiable function of x, f[x] there exists at each point a slope (f ' [x]) and a radius of curvature \rho [x]=\frac{\left(1+f'[x]^2\right)^{\frac{3}{2}}}{f\text{''}[x]} It also seems intuitive to think that at...

Homework Statement A positively charged Helium atom has two protons in the nucleus and one electron in the shell, in a classic model of the atom, this electron is in a circular orbit around the nucleus with an angular momentum of 4.718x10^-34 Js. What is the radius of the orbit?Homework...