Ratio Definition and 1000 Threads

Hey everyone, I was recently reading a paper on surface enhanced Raman scattering, and it mentioned that plasmons (and for that matter surface plasmon polaritons-where my interest lies) are sensitive to the surface to volume ratio of the structure. I can begin to understand intuitively with...

1. The problem statement, all variables and given/known dat If f and g are differentiable functions with f(O) = g(0) = 0 and g'(O) not equal 0, show that lim f(x) = f'(0) x->0 g(x) g'(0) The Attempt at a Solution I know that lim as x→a f(a) = f(a) if function is continuous. since its...

hey all, I'm stumped so I thought I'd try posting here. I am in the early stages of design of a vehicle where we have a rough approximation of weight, no idea what gear ratios or power/torque to use yet, but have an acceleration requirement. I am trying to graphically model the relationship...

I think that if you're good at maths you'll be able to help me without having heard of this before, assuming you know about classical conditioning it's explained here; http://brembs.net/classical/suppress.html The measure of the extent to which the CS suppresses responding is called the...

Hi, I'm wondering if someone can point me in the right direction with this question. A material has a modulus of rigidity of 100 GNm-2 and a Young's Modulus of 250 GNm-2. Calculate the expected value of Poisson's Ratio for the material. Poisson's Ratio is expressed as transverse strain / axial...

I'm thinking about the following function, which is a ratio of two finite power series. I'm trying to prove the monotonicity of this function, for arbitrary K. \frac{\sum_{j=0}^k [(at)^j/j!]}{\sum_{j=0}^k [(bt)^j/j!]}, and a>b>0, t>0 I know that if k goes to infinity, the function becomes an...

Homework Statement A shock absorber is to be designed to limit its overshoot to ##15## percent of its initial displacement when released. Find the damping ratio ##\zeta_0## required.Homework EquationsThe Attempt at a Solution My question is since log decrement, ##\delta = \ln\frac{x_1}{x_2} =...

Hi all, I am relatively new to compressor theory and I am looking for a good explanation as to how volumetric flow affects pressure ratio between the stages within a centrifugal compressor. My current knowledge is that as volumetric flow decreases, pressure ratio increases as stated in one of...

Question: The damped frequency (f) is 100 Hz. The ratio of the amplitude of two successive maxima is one half. What is the undamped frequency? My first problem is I don't understand the basic equations I'm working with. If W is the undamped angular frequency and w is the damped frequency, I...

We have a constant ratio of them in vacuum. Is it same in a medium also? Or not? And in any case, what is the reason?

Homework Statement A point mass M is concentrated at a point on a string of characteristic impedance ρc. A transverse wave of frequency ω moves in the positive x-direction and is partially reflected and transmitted at the mass. The boundary conditions are that the string displacements just to...

I was given this question from the Pascal Math contest 2001: __________________________________________ Cindy leaves school at the same time every day. If she cycles at 20 km/h, she arrives home at 4:30 in the afternoon. If she cycles at 10 km/h, she arrives home at 5:15 in the afternoon. At...

Homework Statement Find D2/D1. See attachment. Homework Equations The Attempt at a Solution Ans: D2/D1 = 0.68 I can't figure this one out. Any special trigonometric identities that might help here? Thanks.

Hellow I did these three math problems and I wonder if my answers are right. (1.03 : 10^-1 + 17) : (4.5^-1 + 5/18)^-2 my answer here is 3. (0.2 : 10^-2 -2 ) : (1/0.9 - 1)^-1 my answer here is 2. Now the last one 1/a^2+a - a+2/a+1 + a+1/a and here my anser is 2. Thank you.

How does the flap angle affect lift to drag ratio of a wing?

Hello All, Padmanabhan's discussion of dynamics mentions that in general the two dimensional harmonic oscillator fills the surface of a two torus. He further notes that there will be an extra isolating integral of motion provided that the ratio of frequencies is a rational number. This last...

Hello all, I am in the process of designing a tesla coil for a research paper, and, just when I thought I had seen all the crack science there could possibly be, I came across a claim concerning the golden ratio. (The natural progression of events, I guess...) There is a real problem when...

I am trying to understand my superchargers isentropic chart. For an example case where a supercharger outputs 10m3/hr but the engine only takes 6.57m3/hr in capacity, I get a volume ratio (VR) of 1.52 - easy... I can then work out a pressure ratio by VR^k = 2.0^1.4 = 1.8 The theoretical...

Why does "per" in 3 miles per hour mean division? Why are gradients and rates a ratio?

Homework Statement Doing my own independent study, and I've come across a textbook question I'm rather lost on. Problem: Over the distance between two seismic recording sites at different ranges from a seismic source, seismic waves have been attenuated by 5dB. What is the ratio of the wave...

Homework Statement On a planet not entirely unlike earth, the ratio of the partial pressure of N2 to that of O2 equals 1 at an altitude of 1 km: \frac{p_{\text{N}_2}}{p_{\text{O}_2}} = 1. Assuming that T = 200 K, and the gravitational constant is 5 m/s2, what is the ratio...

Suppose I have around 20 exposures that potentially affect an outcome and I want to see which exposures have bigger impacts on the outcome. So I want to calculate each exposures' odds ratios by exponentiating the coefficients obtained from logistic regression. So I have the following input set...

When changing rear end gear ratios, or tire sizes on a vehicle, you can buy different speedometer gears with tooth counts to restore speedometer accuracy. The worm(driver) is inside the transmission and is not changed. It is a 7 or 8 tooth in my application. The speedometer gear(driven) is...

Question is attached. I don't know how to find the golden ratio I really did try to solve this one, but i couldnt please please help me out

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Consider two independent random events A and B. Is the event A/B independent from event B? My real problem stems from a debate between myself and a colleague dealing with using the arithmetic mean vs. the geometric mean. My colleague used an example of rolling dice to discredit arithmetic...

I don't have a clear perception of how the following question is answered: "Two primary cells of emfs E1 and E2 respectively are joined in series with (i) the same polarity, and (ii) opposite polarities. The combination is connected through a galvanometer and a jockey to a potentiometer. The...

Hello all, I am looking for exact forms (as real number expressions) of the golden ration that are not rewrites of the one we all know and love, i.e. g.r. = 1/2(5^(1/2)+1) Searches in Google have yielded nothing so far :P

Help me to solve algebra 1 homework In a college boys and girls are in the ratio of 5 : 8. This year number of boys and girls increased by 20% and 15% respectively. So what is the present ratio of boys and girls in the college? Thanks

Is the ratio of matter to radiation density constant in the universe? Or does it vary over time, as matter annihilates to radiation and vice-versa?

Hi, I am trying to understand the Overlap Ratio (OR) / axial contact ratio of a helical gear pair. Unlike transverse contact ratio, I am unable to understand OR so easily. What does it mean if the OR is exactly 1? What will happen practically when it goes less than one? Thanks.

Homework Statement i have attached the sample ans here. hand written photo is my working. Homework Equations The Attempt at a Solution since the question doesn't same string . so i assume it's a same spring. so i would get t is directly propotional to sqrt root (m). is my...

I have a psychological testing instrument that produces an ordinal measure (0, 1, 2, 3, 4, 5). I want to change this to a ratio scale with range 0 to 5. The instrument is designed so the first 5 questions are very easy (Level 1), the next 5 questions are harder (Level 2), the next set is...

what is the ratio of inertial mass to gravitational mass and how we can calculate it?

Hello fellow PF members, This is my first post. I am wondering if there is a mechanism that alters the gear ratio in worm gear-worm wheel setup.. Something like a variable pitch worm gear that can be used instantaneously to alter the gear ratios. If not for worm gear, is there anything in...

Homework Statement The J/Ψ has mass 3097 MeV, width 87 keV and equal branching ratios of 6% to e+e− and µ+µ− final states. What would you expect for these branching ratios if the J/Ψ decayed only electromagnetically? What does this tell you about the “strength” of the strong interaction in...

Myoglobin is a globular protein, with molar mass m ≈ 17,000g/mole. The buoyant correction typically reduces m to m' ≈ 0.25m. Calculate the concentration ratio of the protein at the top of a 4 cm test tube and that at the bottom. Here, m' stands for effective mass. I tried as below. I...

This is not a homework problem. I'm doing it for fun. But it is the kind that might appear on homework. Homework Statement I'm trying to prove that if lim n→∞ |an+1/an| = L < 1, then \Sigma an converges absolutely and therefore converges. Homework Equations The Attempt at a Solution Here's...

Hi all I have a ratio problem which i was hoping someone could help with. The question is this:- Barry bough a box full of fruit. The contained some apples, oranges and lemons in the ratio 5:3:1. Given that there were more than 50 pieces of fruit in the box work out the minimum number...

In triangle $PQR$, the points $A,\,B,\,C$ lie on the line segments $QR$, $RP$ and $PQ$ respectively, such that $A$ is the midpoint of $QR$, $RB=3BP$ and $\dfrac{PC}{CQ}=\dfrac{m}{n}$. If $y$ is the area of triangle $RAB$, $x$ is the area of triangle $AQC$ and $z$ is the area of triangle $PCB$...

Homework Statement A constant-density planet of radius R has a gravitational acceleration ag = as at its surface. There are two distances from the center of the planet at which ag = as/2. Show that the ratio of these distances may be given by R = 2√2 Homework Equations ag= GM/R2...

Homework Statement I need some help with the following problem (from an old exam): A 16-bit single-ramp ADC has a sampling interval of T=1 μs and an input voltage range of 0 to 10V. Since for this ADC the input must be positive, its design includes a fixed DC input of 5 V upon which...

Homework Statement See attached image. (it should say "ratio" not "ration") Homework Equations Ratio series test: An+1/An The Attempt at a Solution I have worked this problem over and over and continue to get the same solution. Some guy worked it on the board a couple of days ago and got...

G'day guys, I am currently trying to calculate the damping ratio for Shape memory alloys using hysteresis loops. The damping ratio is usually represented as ΔU/2∏U, where ΔU is the energy lost due to material damping and U is the elastic strain energy. My problem is trying to find this...

Hey guys, I have what I'm sure is a very simple question that I can't seem to find a simple answer to. I'm wondering what the ratio of time passage is between someone traveling at X times the speed of light versus someone on the surface of a planet. Say for a scenario I was traveling at 10...

Homework Statement I've found that the typical way for using ratio test is to find the limit of an+1/an However, my tutor said that radius of convergence can be found by finding the limit of an/an+1 and the x term is excluded. For example:Finding the interval of convergence of n!xn/nn my...

Ive attached the R ratio formula to this post, please could someone who is familiar with it tell me what Nc is? Does it relate at all to centre of mass energy? Thanks in advance for any help. source...

Q: How do you find the phase between an input and output signal? These signals are swept-sin (chirp: https://en.wikipedia.org/wiki/File:Linear-chirp.svg) signals for system identification, so I'm looking to find a transfer function. Background: A frequency-domain Transfer Function's magnitude...

Homework Statement "The lift gradient of a wing under actual flight conditions is 0.1179 per degree. Calculate the lift-drag ratio of the wing with an angle of attak of 3 degrees?" Given is: altitude=5000 m velocity=225 m/s wing area S=149 m2 wing span b=34.5 m span efficiency factor e1=0.82...