Ratio Definition and 1000 Threads

Hi everyone :smile: When determining the radius of convergence of a power series, when should I use the ratio (a[sub n+1] / a[sub n]) test versus the root (|a[sub n]|^(1/n)) test? I know that I'm supposed to use the ratio only when there are factorials, but other than that, are these tests...

Poisson's Ratio coursework - Urgent help needed! hello, I'm currently working on a coursework for my A2 physics on Poisson's ratio i'm finding the ratio for aluminuim using aluminuim foil and strain gauges, adding masses to a clamp on the end of the foil (so foil is under tension) and...

I have been stuck on this question for a while and have not got much success from class mates...can somebody please help? Using an appropriate convergence test, find the values of x \in R for which the following series is convergent: \sumn=1n \frac{1}{e^n * n^x} So, Un = \frac{1}{e^n...

Homework Statement In a scaled solar system: Earth's radius is 6,375 km, it's scaled radius is 12.75 cm. Neptune has a radius of 24,766 km; using centimeters, what would the scaled radius of Neptune be?? Homework Equations I'm not sure what to put here; I put down what I tried below...

Homework Statement In this investigation, you mix .5g of Mg(s) with 115mL HCl. You measure the temperature change which turns out to be 25.5 degrees C. The equation is as follows: Mg + 2HCL --> MgCl2 + H2 Use the specific heat of water (c=4.184) to find the heat of formation. What is the...

I've been reading and reading and trying to figure this out, but I just can't. Any help anyone can give will be appreciated. It is probably simple as hell, but for some reason my stupid brain can't get it.. The formula/equation is: What I have to do is: Now, I'm not looking for...

Is there a general formula for the even partial derivatives of a ratio, where both A and B are functions of f? \frac{\partial ^{(2n)}}{\partial f^{(2n)}} \left( \frac{A}{B} \right) Thanks

Homework Statement q: show that for an ideal hcp structure the c/a ratio is equal to (8/3)^(1/2) = 1.633 this question has come up before in the forum but still it has not fully answered: Kouros Khamoushi Dec30-05, 12:27 AM This is the mathematical calculation ^ means to the power of...

So a friend of mine was trying to figure out cooling rates for a pot of coffee. He wanted to see how much faster the coffee would cool when he doesn't fill the pot all the way. He is starting from the assumtion that the main determinant for cooling rate will be how the ratio of Surface Area to...

Hey guys, I joined after struggling with a few problems for the past two days. I feel as if the answers are blantanly obvious and I'm just missing the simplest and most important bit(s). Homework Statement From the set of equations: p=3q pr=qs (1/2)pr2 + (1/2)qs2 = (1/2)qt2 involving...

Im working on a part off my course and it covers this, but its not clear. \phi= half (1+\sqrt{5}) \varphi=half (1-\sqrt{5})The question asks \phi-\varphi =\sqrt{5} It is written in my book, the answer but it does not explain how the maths cancels and manipilates. Could you show me a way that...

Homework Statement Use vectors to find the position vector of point P if P divides AB in the ratio 3:2 given A (-1,6,4) and B (4,1,-1) The Attempt at a Solution Well I assume it's sort of like finding the midpoint, except I would do something like (-1+4)/1.5 etc. Am I correct? Do I...

Homework Statement Measurements show that a honeybee in active flight can acquire an electrostatic charge on the order of 93 pC. a)How many electrons much be transferred to produce this charge? Ne = * b) Supposing two bees, both with this charge, are separated by a distance of 12 cm...

hi,I was wondering if anybody would know the following: If I have a 200hp motor that has 600ft/lbs of torque at 1750 rpm and reduce the speed to 190 rpm with pulleys 9.2:1 does that give me 600ft/lbs x 9.2 = 5520 ft/lbs torque @ 190 rpms? thanks

Homework Statement What is the ratio of mass of a 12C atom to a 13C atom The Attempt at a Solution 12.011/13 = .9239230769 Solution given at back of book = .92286

I'm trying to calculate the ratio of e/m, I've plotted the given data points to get a straight line graph with a gradient of 0.848. I know that the ratio of e/m is given by e/m = (4.49*10^8 * gradient^2)/volts where volts = 3000. When I plug the numbers in I get a value of 107625 which...

Homework Statement Hint:Disregard any dissipative effects of the atmosphere of the planet. A projectile is launched from the surface of a planet (mass M, radius R) with a launch speed equal to 60 percent of the escape speed for that planet. The projectile will rise to a maximum height and...

Hi all, I'm new to this forum so sorry if this post is a bit scrappy! Homework Statement This is part of a lab report I am doing: Plot a graph of V against I^2 and find the e/m ratio from the gradient. Homework Equations e/m = 2V/B^2 r^2 where B is magnetic field, r is radius of...

For an industrial parallel axis gearbox with a transmission ratio 10:1, what is the reasoning behind the use of 2 stages rather than a single stage? The one I can think of is the reduction in size of the gears using 2-stage as opposed to a single stage, thus reducing costs. Are there any...

Homework Statement Determine how old is a fossile where a 14C/12C ratio of 6.1 x 10^-13 is measured. 14C desintegration has a half-life of 5760 +- 40 years and proportion 14C/12C in living tissue is 1.17 x 10^-12. Determine the error in your calculation. Homework Equations Radioactive...

i am given a siquence An of positive numbers how to prove this expression: lim sup(1/An)= 1/(lim inf An) lim inf is the infimum of the group of the limits of the sequences lim sup is the supremum of the group of the limits of the sequences those groups of limits doesn't have to be...

1. The ratio of the melting temperature of gold and of silver is 1.10614, if both temperatures are measured using the Celsius temperature scale, and 1.08265 using the Kelvin scale. What are the temperatures? 2. I'm guessing we're supposed to use this to find the answer: Tkelvin = Tc +...

Homework Statement A sample of radioactive isotopes contains two different nuclides, labeled A and B. Initially, the sample composition is 1:1, i.e., the same number of nuclei A as nuclei B. The half-life of A is 2 hours and, that of B, 4 hours. What is the expected ratio A/B after 8 hours...

Homework Statement Cobalt has an HCP (hexagonal close packed) crystal structure, an atomic radius of 0.1253 nm and a c/a ratio of 1.623. Compute the volume of the unit cell for cobalt. Homework Equations area of hexagon = apothem*perimeter/2 The Attempt at a Solution calculate 1 of...

Hi! I'm designing a human powered vehicle and I need to use a CVT (Continuously variable transmission) in its drive line. I want to know the widest range that the speed ratio of a normal CVT (One that's not very big, heavy, or expensive because our vehicle needs to be as light and cheap as...

Homework Statement There's actually 2 problems that I'm totally stuck on: A. Bullets from two revolvers are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2. Gun #1 weights three times as much as gun #2. The ratio of momentum imparted to gun...

I had a typical A4, 80 gsm sheet of paper and I had determined that its dimensions were: 210 x 297 x 0.11 mm. The last dimension was obtained using an old micrometer I possesses and is close to the average of four measurements taken in various places on that piece of paper. Thus the volume of...

I understand Common-mode rejection ratio. I do not however understand common-to-common Mode rejection or common to differential mode rejection or differential to common mode rejection. I am looking at this in regard to twisted differential pair cabling, specifically jacks. I can find the term...

Hi I have to design a gearbox for a drum, the drum should be brought uniformily to a speed of 7rpm in 8 seconds, I have choosed a motor of 715 rpm output, what's the gear ratio I should use in designing the gearbox? Thanks

1. In class we are discussing sub atomic particles and I approached my teacher with this question: If a electron is 2000 times smaller (roughly) than a proton, then the concentration of energy in the electron must be roughly 2000 times greater correct? She informed me that the charge to mass...

Homework Statement Two disks have the same radius R and the same mass M, but one of the disks is twice as thick as the other. Disk A has thickness t, and disk B has thickness 2t. How does the moment-of-inertia of disk A about an axis through the center compare to that of disk B...

Homework Statement There is a triangle(AOB). One of its median is drawn. BO is divided in the ratio 2:1. The resultant point(say C) is joined with the vertex A. Find the ratio (y) in which E divides CA . http://img88.imageshack.us/img88/8496/vectorszx0.png The Attempt at a Solution Let O b...

Homework Statement Find a polynomial function of lowest degree with rational coefficients and 2 and 3-2i as some of its zeros. Multiply the factors to make sure it has rational coefficients. The Attempt at a Solution zeros=2, 3-2i, 3+2i I am not sure how write out the factors...

Homework Statement A thin uniform ring carrying a charge Q and mass M, rotates about its axis (see Figure). a) Find the ratio of its magnetic dipole moment to its angular momentum. This is called the gyromagnetic ratio. b) What is the gyromagnetic ratio for a uniform spinning sphere...

Particle A has three times the mass and twice the kinetic energy of particle B. what is the speed ratio Va/Vb

I was wondering if someone could explain the fibonacci series and golden ratio to me, I'm very curious, but I don't have that much experience in math as a high school trig student.

Homework Statement A 6.91x106 kg spherical spaceship in deep space explodes into two pieces, one 4.77 times the mass of the other. a) Suppose the ship is initially at rest, and after the explosion the smaller piece is moving 57.6 m/s. - Find the speed of the larger piece. -Find the energy...

Homework Statement Let X = (xn) be a sequence of positive real numbers such that lim(xn+1 / xn) = L > 1. Show that X is not a bounded sqeuence and hence is not convergent. Homework Equations Definition of convergence states that for every epsilon > 0 there exist some natural...

What is the energy ratio (Ef/Ei) of a system on Earth that has a final velocity of 3901.5 cm/s, initial velocity of 249.9 m/s, and a height of 0.006 km. E = K + U = 1/2mv^2 + mgh Ef = 1/2mvf^2 + mghf Ei = 1/2mvi^2 + mghi It appears that the object is being forced upwards since...

Ratio between change of Energy(Gravitational Potential) I would like some assistance in understanding the ratio of change in energy between two objects. In this case, if object A goes from rest to an altitude (h) above Earth but does not begin an orbit versus object B goes from rest to the...

I'm having trouble understanding how you would divide the charge of an object by its mass. How can you divide a charge - I mean isn't it either positive or negative? I understand that the charge is equal to the 6.25 × 1018 so an electron would have a charge of −1.602 x 10-19. I guess my...

Homework Statement Electrons from a heated cathode are accelerated through a potential difference of 25.0 V. Calculate the speed of the electrons escaping through a hole in the anode. Homework Equations v = (2eV/m)^(1/2) The Attempt at a Solution v = (2*25*1.759*10^11)^(1/2) =...

Hi all, since scattering amplitude is given as: f(theta) = summation over l(from o to infinity)(2l+1)/k exp(i(phi))sin(phi) Pl(cos theta).But what happen if i want to calculate the ratio of f(theta=0)/f(theta = pi/2). Can anyone tell me the value of Pl(0). Thanks

hi, I am studying aerospace engineering in oz, and I am doing an assignment on turbojet engines and I am looking for a chart on Combustion chamber temperature rise versus fuel air ratio with chamber inlet temperature as a parameter but I am having no luck lin finding one can anyone point me in...

Homework Statement Two blocks, masses m1 and m2, are connected by a massless cord as seen below. If the two blocks are pulled with a constant tension on a frictionless surface by applying a force of magnitude T2 to a second cord connected to m2, what is the ratio of the tensions in the two...

Hello! Anyone can help me to find the best blockage ratio between for a small ball in tube? so the pressure can stay up (not drop). How to calculate it. Thank You.

Homework Statement Water flows into a nozzle at 3.00 m/s at a pressure of 1.31*105Pa. What should the ratio of input to output diameter be if the flow is to remain steady? What is the flow speed at the exit? Homework Equations P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2}...

Hi All, How to work out the expansion ratio of a gas fireball. Eg: Just say we have a ball of gas-- no container, 1 liter in volume suspended in mid air & we ignite it, how far would the flame front extend to form the fireball, what volume would it occupy once ignited?. An example of...

I was wondering if the Golden ratio base (phinary system) has any use somewhere and if arithmetics with it is easy? I programmed a surprisingly simple algorithm to calculate the logarithm yielding digits in base phi using nothing more than 2 multiplications/divisions per result digit. Can it...

how the heck do you simplify this ? (Ln (2x/y) / Ln (x/y)) = m/n HELP ME!