Ratio Definition and 1000 Threads

In the figure, a 105 kg uniform log hangs by two steel wires, A and B, both of radius 1.25 mm. Initially, wire A was 2.50 m long and 1.80 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m2. What is the ratio dA/dB? I'm honestly at a loss for how...

Homework Statement Simplify this: y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) Ideally I would like to make rather than (k/l)/(l/k) simply (k/l) Homework Equations y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) The Attempt at a Solution y = (k^3/8)/(l^1/20)

I am trying to determine convergence for the series n=1 to infinity for cos(n)*pi / (n^2/3) and I am doing the Ratio Test. I found the limit approaches 1 but is less than 1. Does this mean that the limit = 1 or is < 1? I am somewhat confused since this changes it from inconclusive to convergent.

Homework Statement 1) If limestone (calcium carbonate) and clay (assume aluminum silicate) are mixed together and heated then the result is cement. Cement is a mixture of calcium oxide, carbon dioxide, aluminum oxide, and calcium silicate. These bags can be purchased at any building supplies...

Back in november I asked the forum about this fractal: http://en.wikipedia.org/wiki/File:Phi_glito.png At the time I couldn't figure out how to make it. Since then I've figured it out. I used MS Excel. I'm not completely satisfied though. There are some gaps between the major...

Homework Statement Find the turns ratio across the transformer such that a spark is given off at the points AB. The distance from point A to point B is 5.00 mm. AB is the distance across the secondary coil. The frequency and voltage of the primary coil is given. Homework Equations...

Let ABC be a triangle such that \frac{BC}{AB-BC}=\frac{AB+BC}{AC}. Determine the ratio \frac{\angle A}{\angle C}.

Homework Statement Base station transmits signal t which is received by two antennas such that: x = h1t + n1 y = h2t + n2 where n1 and n2 are independent additive white Gaussian noise with variances σ21 and σ22 respectively. h1 is the channel gain between the base station and receive antenna...

From control systems: I am asked to find the value of K that gives the closed loop damping ratio of 1/sqrt2. The value for the complimentary sensitivity is T(S)=(2KS +4K)/(s^3 +162S^2 +(320+2K)S +4K) so how do I find the value for K? I tried putting it in the general equation, but it...

I am currently studying the star Qatar-1 and its orbiting planet Qatar-1b on the Agent Exoplanet website: http://portal.lcogt.net/agentexoplanet/ where they are studying exoplanets and their transit times across their stars. After going through a 130-image process of using calibrators to...

Homework Statement \sum ftom n=1 to \infty (-2)n/nn. The Attempt at a Solution limn->\infty | (-2)n+1/(n+1)n+1) x nn/(-2)n | = |-2|limn->\infty |(n/n+1)n*(1/n+1) | If it were only (n/n+1) then would the answer be 2e? Either way, how do you sole this the way it is?

Hi guys, I have a question about gear ratio, sprocket or wheel ratio. So let's say I have a motor with connect to a small output sprocket, and I want to use this motor to pull some load, so in order to do this I need to connect the chain with a larger sprocket, let's say 2 time bigger than...

$$\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)}$$ progress: I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$

i am looking for the amplitude ratio and phase shift of this graph? could someone explain me how to obtain these results from this type of graph? thank you

I have a question wondering if you guys could check over for me . I have a solution no sure on its accuracy! the question is in two parts a bar has a 25mm diameter and is subjected to a tensile force of 61Kn, the extension on a gauge length of 50mm is 0.1mm. calculate the youngs modulus in...

Homework Statement Two particles are falling in a lab frame. The charge to mass ratio of particle one is held at 1, while the charge to mass ratio of particle 2 is changed from 1 to 0.5. How does the motion of the second particle changed with respect to the first. Would this change cause...

Some of you may be familiar with Dingle, an "opponent" of SRT. I can condense his argument (the only one I know about anyway) to a sentence or two. Solve the Lorentz Transform for delta-t-prime, then divide through by delta-t. delta-t-prime/delta-t = gamma - gamma*v*delta-x/delta-t...

Let's start with a generalized example: 3A + 1B -> 2C For the mole amount next to each molecule, am I always to consider these as relative to one another or absolute? Most of the videos I have seen are describing the above as "for every 3 moles of A and 1 mole of B you get 2 moles of C". I...

Homework Statement The amplitude of an underdamped oscillator decreases to 1/e of its initial value after m complete oscillations. Find an approximate value for the ratio ω/ω0.Homework Equations x''+2βx'+ω02x = 0 where β=b/2m and ω0=√(k/m) x(t) = Ae-βtcos(ω1t-δ) where ω1 has been defined as...

I have designed a test apparatus where I can apply known bending and torsion loads to thin sheets of foamed plastic. All test samples will be identical sized sheets with various treatments to improve stiffness..with the added weight of the treatment recorded. I will use the information to...

With four Rolls-Royce Turbojet engines attached on A380, I wonder, if the optimization of fuel efficiency as its prime design factor/variable? If so, may I know, what it is air by pass ratio?

I have the following summation where a is a positive constant and can be > 1 $$ \sum_{k=2}^{n}a^{n-k} $$ I am trying to find a general formula for this summation, which turns out to be a geometric series with a as the common ratio. I have worked out the following: $$ \sum_{k=2}^{n}a^{n-k} =...

The terminal speed of a sky diver is 188 km/h in the spread-eagle position and 320 km/h in the nosedive position. Assuming that the diver's drag coefficient C does not change from one position to the other, find the ratio of the effective cross-sectional area A in the slower position to that in...

I wasn't sure whether to put this in the mechanical engineering board or not but since electrical engineers typically design electric motors, I'll put it here. From what I hear, all types of electric motors have terrible power-to-weight ratios. So if we were to hypothetically one day have a...

Homework Statement An ideal simple gas turbine has a compression ratio of 5. What is its Homework Equations c=r(γ-1/γ) η=1-(1/c) The Attempt at a Solution I'm stuck, I think I need to use the above equations and possibly more. I just don't know how to find a value for the ratio of...

Homework Statement I desperately need to know something which I consider basic but yet I get different answers all the time for example ratio A:G=1:3 or A:G=1:2 or A:G=1:4 some students are telling me that the ratios should be divided with one another like 1/3=0.33 to get the...

Homework Statement Show that the ratio of the blackbody fluxes from a star at two different frequencies (i.e., a color) is measured, then, in principle, the surface temperature of the star can be derived, even if the star's solid angle on the sky is unknown (e.g., if it is too distant to be...

I take issue with the "Advanced Engineering Electromagnetics" 2nd edition by Balanis again. In Page 156, it claimed for AR=-ve, it is Right Hand rotation, AR=+ve is Left Hand rotation. For plane wave propagates in z direction and at z=0: A)Let Ey lag Ex by \frac{\pi}{2} \Rightarrow\;\vec...

Homework Statement In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat the athlete as a particle and let y_max be his maximum height above the floor...

Hi guys, Revision for an exam tomorrow, I hope someone can help? I've been given the answers but I can't work out how to find the damping ratio without being given a velocity or distance for the mass to travel?A mass of 6kg is suspended on a spring and set oscillating. it is observed that...

Hi all... I'm new here... Homework Statement this is not a homework question, I'm just solving practice questions for exam preparation Two wheels with masses M1 = 2 kg and M2 = 4 kg are connected. The ratio is R1 = 5 cm and R2 = 10 cm Considering an angular velocity of ωo = 10rads-1 for the...

Hi, I am wondering why radial variation in Poisson's ratio exists when a cylinder is compressed? Ie, Poisson's ratio toward the center is lower than what is measured at the circumferential edge. Thanks M

Homework Statement (see attachment for figure) A small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that small mass is at top. Find the least r/R ratio...

Homework Statement Calculate: (3 a + 3 b)/(a - b) If a/b = 2/5 No attempts, I don't know how to solve this. Help?

Homework Statement Part of an elecrial circuit for the olympic score board consisted of a single battery V and several resistors having on of two values. R or 2R. They are hooked up in the confriguration as shown. Calculate the ratio of the two currents shown Ib/Ia...

I am a little bit confused on what an extinction ratio is. I am looking at optical specs and it keeps on coming up. Would someone be kind enough to explain it to me and perhaps provide a mathematical background thank you!

Two spheres S1 and S2 hang from light insulating strings of the same length from points P1 and P2 which are on the same level. S1 is of mass M and has charge Q. S2 is of mass M and has charge 2Q. Repulsion between S1 and S2 causes their strings to be inclined at angles of theta1 and theta2 to...

I was messing around with cellular automata and wanted to test a theory i had. If you look close at the elementary cellular automata Rule 30 you'll notice that the right side is chaotic, while the left side has chaotic properties but it does have order and repetition. There is an imaginary...

Let B=(5,21), C=(40,-14) and $\frac{BP}{PC}$=1/6. What is the most efficent way to find P? My book just states P=(6/7)B+(1/7)C but no idea how they got that.

A=$\begin{bmatrix}1\\1\\0\end{bmatrix}$, B=$\begin{bmatrix}3\\1\\-1\end{bmatrix}$ C=$\begin{bmatrix}5\\3\\-1\end{bmatrix}$, D=$\begin{bmatrix}4\\0\\-2\end{bmatrix}$ Find the coordinates of a point E such that A,B,C,E forms a harmonic range. This means that the cross ratio is -1.

Does anyone have any idea about modulation ratio of voltage and modulation frequency in power systems?What is the relation between between two?

Homework Statement Use the Ratio Test for series to determine whether each of the following series converge or diverge. Make Reasoning Clear. (a) \sum^{∞}_{n=1}\frac{3^{n}}{n^{n}} (b) \sum^{∞}_{n=1}\frac{n!}{n^{\frac{n}{2}}} Homework Equations...

I've been fooling around in MS Excel trying to reconstruct this fractal: I haven't had any issues here making it. I totally understand the algorithm for generating the left turn/right turn ordering. What I really want to know is how this version is generated: Original image...

Homework Statement The binary star system Krell consists of two stars, Krell A and Krell B, orbiting each other, with no other ojects nearby. Assume Krell A, the smaller star of mass mA, moves in a circle of radius rA at speed vA. Krell B, the larger star of mass mB = 2.51mA), moves in a...

Hi, Without using l'hopital, how may I show that sin[(10pi)/(n+1)^2] / sin[(10pi)/n^2] converges?

Homework Statement Game of Head & Tails between 2 people. The first one to 8 is the winner. If the game is interrupted: when one person has 6 wins and the other has 4 wins, how should the prize money be split? 2. The attempt at a solution The obvious answer (at first) i got is 3:2...

In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? I...

Homework Statement Planet X has a radius double of Planet Y. Planet X also has a mass that is double planet Y. How do the surface gravitational fields of X and Y compare? Homework Equations g=GM/R The Attempt at a Solution So because were looking for the ratio of gx to gy, we can use...

∞ Ʃ (((n)!)^3)/(3(n))! Use the ratio test to solve n=1 So first i put it into form of (n!)^3/3n!, then applied ratio test. from ratio got ((n+1)!)^3/(3n+1)! times (3n)!/(n!)^3 from here I am on shaky ground i go reduce the terms to (n!)^3(n+1)^3/(3n!)(3n+1) times...

I am trying to understand something in the proof of the ratio test for series convergence. If a_{n} is a sequence of positive numbers, and that the ratio test shows that \lim_{n→∞}\frac{a_{n+1}}{a_{n}} = r < 1, then the series converges. Apparently, the proof defines a number R : r<R<1...