Ratio Definition and 1000 Threads

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.

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  1. R

    Branching ratio of particle question

    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...
  2. M

    How to Calculate the Concentration Ratio of Myoglobin in a Test Tube?

    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...
  3. M

    Proving part of the ratio test

    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...
  4. T

    Solve Ratio Problem: Minimum Number of Oranges in a Box | 50+ Fruit Pieces

    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...
  5. anemone

    MHB Find the value of the ratio of m/n

    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 $PCB$...
  6. K

    Ratio of Distances using Acceleration of Gravity

    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...
  7. R

    Signal to Noise Ratio: Solving 16-bit ADC Problem

    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...
  8. D

    Ratio Test Problem: Homework Statement & Solutions

    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...
  9. S

    Calculating Damping Ratio of SMAs Using Hysteresis Loops

    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...
  10. C

    How Does Time Dilation Affect Travel at Speeds Beyond Light?

    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...
  11. H

    Ratio test for finding radius of convergence

    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...
  12. R

    What is Nc in the R Ratio formula? re CDF detector measurements

    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...
  13. J

    FFTs, and ratio of FFTs Phase question

    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...
  14. M

    Calculating Lift-Drag Ratio of a Wing Under Flight Conditions

    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...
  15. E

    MHB Determine the ratio of the base to the perimeter.

    8) An isosceles triangle has two sides of length 9x+3. The perimeter of the triangle is 30x+10 a) Determine the ratio of the base to the perimeter, in simplified form. State the restriction on x Thanks for your help!
  16. T

    Minimum capacity rate ratio of a heat exchanger

    Homework Statement Here is the question: I am confused about the solution. In the solution they found that the minimum capacity rate ratio R = C_min/C_max was zero. This is because of the term I circled in the red which I do not understand why it goes towards infinity. Here is the solution...
  17. N

    Ratio of work done using pulley

    Homework Statement As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. There is no one around to help, so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. You pull up on the...
  18. D

    Ratio PV/RT dieterici's equation

    Hello Homework Statement Determine the ratio PV/RT at the critical point for a fluid which obeys Dieterici’s equation p(v-b)=RT exp(-a/RTv) Homework Equations The Attempt at a Solution First ofall i don't really understand this notion of critical point. I found an equation to find it that is...
  19. S

    Specific Tension Ratio of V-Belt Drive

    In a V-Belt Drive, it is said that when a New Belt is installed, the Tension Ratio shouldn't exceed 5:1. But isn't this ratio beyond control and is defined by T1/T2 = μ*α*cosecβ where T1/T2=Tension Ratio, μ=Coefficient of Friction, α=Angle of Wrap, β=Groove Angle of V-Belt. All of these variable...
  20. E

    What Is the Molar Ratio of Two Ideal Gases in a Mixture?

    Homework Statement A mixture of two gases, A and B, exists at pressure p1, volume V, and temperature T1. Gas A is subsequently removed from the mixture in a constant-volume process. The remaining gas B is found to have a pressure p2, volume V, and temperature T2. Express the ratio of the...
  21. Saitama

    MHB Finding the Coefficient Ratio of a Binomial Expansion Problem

    Problem: Let $\displaystyle (3x^2+2x+c)^{12}=\sum_{r=0}^{24} A_rx^r$ and $\dfrac{A_{19}}{A_5}=\dfrac{1}{2^7}$, then $c$ is A)4 B)5 C)6 D)7 Attempt: One way I know of to solve such a problem is by using the multinomial theorem but I am reluctant to use it here. It would take a lot of time to...
  22. E

    Spontaneous symmetry breaking and the photon/baryon ratio

    Hi, I am looking into symmetry breaking and how it (may have) affected the photon/baryon ratio in the primordial universe. I found this wonderful encyclopaedia of cosmology which relates the grand unified theory to an orthorhombic crystal, making analogies for symmetry, spontaneous symmetry...
  23. H

    What Is the Formulation for Wind Tunnel Blockage Ratio?

    Hello, i am asking a question: is there any formulation of wind tunnel blockage ratio? i will carry out experimental study in a wind tunnel, the aspect ratio (AR)=5, and what equals the blockage ratio? if someone helps me, i will be very happy :) thank you...
  24. B

    Can you confirm the value of the g-factor for the spinning electron in H1?

    I am studying the angular moment(s) in an atom of H (1s) in the classical model, can you help me understand some obscure points : The mechanical orbital angular moment of the electron in 1s is L = mvr J*s: (m) 9.11*10-31 *(v) 2.1877*106* (r) .52918*10-10 = 1.0546*10-34 J*s = h/2π, the magnetic...
  25. T

    What Is the Current Amplification Ratio in a Bipolar Junction Transistor?

    Homework Statement If IB and IC (IB = Base current and IC = Collector current) of bipolar junction transistor are 1mA and 100 mA respectively, determine its current amplification ratio in common emitter configuration.Homework Equations IC=β*IB Where β = current gain = \alpha/(\alpha-1) (is this...
  26. M

    Simplifying a series with the ratio test

    Homework Statement Determine if the following series is divergent or convergent: ## ∑_1^∞ \frac {(2)(4)(6)...(2n)}{n!} ## 2. The attempt at a solution I understand this can be simplified to: ## ∑_1^∞ \frac {(2^n)(n!)}{n!} ## This can easily be seen to be divergent. But when I...
  27. T

    Finding the gyromagnetic ratio of an axially symmetric body

    Homework Statement So, we can presumably write that m = g L, where L is the angular momentum, g the ratio wanted, and m magnetic dipole moment of an axially symmetric body. Total mass is M, total charge Q, mass density \rho_m(r)=\frac{M}{Q}\rho_e(r), where \rho_e(r) is charge density...
  28. adjacent

    Can someone do it the algebra way?Solve Ratio & Proportion Homework: 3:2 to 3:7

    Homework Statement A man and a women share a sum of money in the ratio 3:2. If the sum of money is doubled ,in what ratio should they divide it so that the man still receives the same amount? Just a gr.8 problem.Forgive me!Homework Equations nopeThe Attempt at a Solution What I couldn't do is...
  29. C

    Signal to Noise Ratio: Definition & Wiener Filter Calculation

    What is signal to noise ratio ? And how do I calculate it with the wiener filter?
  30. N

    Calc Gear Ratio: Helical/Spur Gears

    http://C:\Documents and Settings\design3\Desktop\piccs Hey, I want to know how to calculate the gear ratio of the given arrangement in the picture. I am not sure of how to calculate the gear ratio of two gears on the same shaft. Also the input gear is helical and the output gear is a spur...
  31. N

    Calculate Gear Ratio - Helical/Spur Gears

    Hey, I want to know how to calculate the gear ratio of the given arrangement in the picture. I am not sure of how to calculate the gear ratio of two gears on the same shaft. Also the input gear is helical and the output gear is a spur gear. I have mentioned the number of gear teeth, i hope...
  32. Albert1

    MHB Finding the Ratio of $a$ to $b$ for $a^2+ab-b^2=0$

    $a,b\in R$ $if:\,\, a^2+ab-b^2=0$ $find:\,\, \dfrac {a}{b}=? $
  33. T

    Wing Aspect Ratio (Newbie to Aerodynamics)

    Homework Statement A tailless aircraft of 9072kg mass has a delta wing with aspect ratio 1 and area 37m2. Show that the aerodynamic mean chord of a delta wing, \frac{\int_0^{b/2} c^2 dy}{\int_0^{b/2} c\ dy} is two-thirds of its root chord and that for this wing it is 5.73m. Homework...
  34. N

    What Does Higher Permittivity Substrates Mean for Unit-to-Wavelength Ratio?

    hi friends, can anybody clear my concept about the following sentence. " if we use substrates with higher permittivity, like quartz or GaAs that has been used in previous successful experiments, the unit cell will have smaller unit-to-wavelength ratio".
  35. Spinnor

    High energy e- e- scattering, ratio inelastic/elastic cross-sections?

    If we were to scatter high energy (say E>>m_e) electrons off each other is there a hand wavy argument to come up with a rough estimate for the ratio of inelastic to elastic cross-sections? Would the dominate inelastic collision between two high energy electrons result in a single photon...
  36. N

    Expectation of ratio of 2 independent random variables ?

    Hi, i was wondering if the following is valid: E[x/y] = E[x] / E[y], given that {x,y} are non-negative and independent random variables and E[.] stands for the expectation operator. Thanks
  37. N

    Ratio of flight times at angles 45degree +/- alpha

    Homework Statement Consider two projectiles launched on level ground with the same speed, at angles 45°\pm \alpha. Show that the ratio of their flight times is tan 45°\pm \alpha. The Attempt at a Solution projectile 1 launched at Θ = 45° + \alpha: vyf1 = vyi1 + gt tapex1 =...
  38. Z

    Ratio of positive to negative hydrogen ions in the universe?

    Hi this may sound like a simple question but I'm trying to find out the relative abundance of hydrogen in its various forms in space: H, H+, H-, H2, H2+, H2- I'd like to know these for our stellar neighborhood involving the solar wind and also for interstellar space outside the heliopause...
  39. B

    Damping ratio from Eddy current breaking

    Hello All, I have been asked to design and build a rig that will introduce the concept of a mass spring damper system to mechanical engineers in their early years of university. To make it slightly more complex, the rig needs to be torsional rather than linear. My design so far is to use a...
  40. J

    CONVERGENT nozzles contraction ratio and length

    I am currently designing a convergent nozzle for use in experiments and wanted to check something: Will the pressure and density of the flow always expand to ambient (following the isentropic relations) when it reaches the nozzle exit regardless of nozzle contraction ratio and length? Any...
  41. C

    Determine domain for a trig ratio and the general solution of angle me

    Problem statement Given sin theta (sqrt 3)/2 Determine the domain for the following solution https://www.physicsforums.com/attachments/655052) determine each general solution using the angle measure specified. Revelant equations Attempt at solution1What is the reasoning behind that? For...
  42. O

    Signal to noise ratio for thermal and shot noise

    Homework Statement The output of a sensor which produces 10000 electrons is connected to parallel RC circuit with Resistance= 50 ohm, and the capacitance=10pF. Calculate the signal to noise ratio at temperature 300K. Homework Equations SNR= 10 log (power of signal/ power of noise) Or...
  43. B

    Limit of Ratio Function with Dots and Filled Numbers: Understanding the Results

    Homework Statement This is not homework Could you help me understand what happens to this function \frac{1}{\sqrt{100..1^2+199...9}- 100...1} when the dots are filled with 0's and 9's , shouldn't the result be 1/.99999...)= 1.? but if to this input...
  44. C

    Understanding Velocity Ratio and its Impact on Lever Orders

    Velocity ratio is defined as the ratio of the distance moved by effort and load, in the same time interval. It is said and known : that in the first order of lever, velocity ratio is usually greater than 1 but could be less or equal to 1. Why do we say that? And what does it mean? In the...
  45. S

    Current ratio expressed in nepers

    ^{}Homework Statement The current input of a system is 250mA. If the current ratio of the system is 15dB , determine (i) the current output and (ii) the current ratio expressed in nepersHomework Equations \alpha[dB]=20log_{10}(I_{out}/I_{in})The Attempt at a Solution current ratio...
  46. tartaneto

    Charge/mass ratio of moving particles (SR)

    Hi guys. I have something stuck in my head since a few days and I'd like to have your opinion about that. I don't know if I am missing something in my assumptions so please feel free to enlighten me. Here's the thing: considering two protons (or electrons), one fixed at the origin of the frame...
  47. anemone

    MHB Proving Area Ratio of Equilateral Triangle Divided by Line

    A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.
  48. W

    Calculating Ratio of Electrical Current to Light Speed: A Challenge!

    Homework Statement If a 0.505m long wire is excited into its lowest electrical resonance by a 2.2E7 Hz electrical oscillator, what is the ratio of the speed of the electrical current to that of light? Assume that the wire is like a tube with both ends closed. f=2.2E7 L=0.505 v=...
  49. J

    How to do this using series. Rep as ratio of two integers

    Homework Statement Express the number as a ratio of integers. 10.1(35) = 10.135353535 the part in the left in () is where is is over lined to indicate it is repeating Homework Equations Geometric series The Attempt at a Solution 10.1(35) = 10.1 + .035 = (101)/ (1000) +...
  50. R

    Determining the damping constant from the ratio of amplitudes

    Homework Statement I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the...
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