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.
I've never really heard of Young, Bulk, or Poisson's ratio before. I have done some research but I can't seem to find the relationship between the three in order to calculate Poisson's ratio. Could someone please point me in the right direction?
Thanks
Hi everyone, does the scattering irradiance ratio between blue/red change with distance with Rayleigh scattering?
I would think that it would remain generally constant..
I am not sure if this is the right section for this, but i didn't find it anywhere and I really need it. Can someone point me towards a place/tell me a program where I can get/compute the first (at least) 50 digits in the hexadecimal representation of the golden ratio? Thank you!
I couldn't really understand how to approach this problem with just given the inertia with Pierre have a mass of 70% less than Jean-Claude. As I understand it, because Jean-Claude is heavier, he must not have traveled as far as Pierre, but I am unable to find exactly how far each of them went...
Setup: Let ##\hat{\mathbf{e}}_1,\hat{\mathbf{e}}_2,\hat{\mathbf{e}}_3## be the basis of the fixed frame and ##\hat{\mathbf{e}}'_1,\hat{\mathbf{e}}'_2,\hat{\mathbf{e}}'_3## be the basis of the body frame. Furthermore, let ##\phi## be the angle of rotation about the ##\hat{\mathbf{e}}_3## axis...
I appreciate that this is perhaps a strange question but it's been bugging me a little.
For instance, velocity is defined as the time derivative of position, so will always appear as the gradient a graph of x vs t. However, something like resistance as R = V/I is defined in terms of a ratio...
I used the two equations i listed by using B1=B2 and by doing that i ended up finding that N1/N2=λ.
However i am not sure if that's the correct answer as λ is just a variable and not an actual number. Do you think it has to be an actual number or is it not really necessary?
I was trying to look for an L/D ratio published everywhere on the web and I can't seem to find it for our project. Since I couldn't find it, I wanted to try calculating myself. Can't seem to find $$C_l$$ or $$C_d$$ though without some sort of paywall on research papers.
So L/D would just be...
Hi, I have Force vs velocity graph. From the graph, I need to calculate the gear ratio of every Gear.
This is the formula what I can use to find the gear ratio,
V= 2*pi*r.n(1-i)/ε
v= vehicle speed m/s ( I consider from the graph lowest speed 3.61 m/s or 13km/h
r= radius of drive wheel...
Homework Statement: In a double slit experiment let d=5.00 D=30.0λ. Estimate the ratio of the intensity of the third order maximum with that of the zero-order maximum.
Homework Equations: interference diffraction
i guess the goal is this equation
##I_{(\theta)}=I_0 \times(cos^2\beta)\times...
71.15 Two vectors $\vec{A}$ and $\vec{B}$ lie in xy plane.
Under what conditions does the ratio $\vec{A}/\vec{B}$ equal $\vec{A_x}/\vec{B_x}$?
Sorry but I had a hard time envisioning what this would be?
also thot I posted this earlier but I can't find it
Wondering why moisture ratio tables related to temperature and air only go up to roughly 50 C or so? is that temperature a "boundary" on the amount of water air can hold?
Hi,
I built the attached ratio detector circuit and it works but I can't understand the reason for the connection marked in green.
I need an explanation, please.
Thanks in advance.
GR
A friend of mine said he would share the price with me by 3:1 ratio.
I have left school for many years. I'd like to know, what does it mean? For example, he gets 3 and I get 1, and the price is $1000, how much will I get? Will I get 1000 x 1/3 or 1000 x 1/4
Diagram
Calculations as follows
$$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{I_{R_1}+I_{R_2}}{I_0}*100=\frac{R*I_0+(R*T)*I_0}{I_0}$$
Subbing in the relevant equations given in the question
$$\frac{I_{total \...
I got the compression for the first one.
Second one, i am a bit confused. But i got ## x_2 = \frac{F}{2k} ##
In the third one, what will the compression be?
I have to get the ratio ## x_2 : x_3 ## . Then i will be able to get my answer.
Thanks.
Hey all!
I am working on my first ebike build and posted a question about friction drives earlier. Now, I have decided to go with a Mid-drive. I made calculations and found out the torque and rpm required for the build. But I am having difficulty find the right motor and gear ratio. I am trying...
A parallelogram ABCD has angle A = angle C = 45°. Circle K with the center C intercept the parallelogram through B and D. AD is extended so that it intercepts the circle at E and BE intercepts CD at H. The ratio of the area of triangle BCH and triangle EHD is ...
Here I got that triangle BCH...
So, I recently heard about the Golden ratio fractal phase conjugation and I was wondering if it could possibly explain the solar system formation. Meaning, if you can imagine a torus energy dynamic shape (with the sun in the middle) maybe it could be explained by this theory?
Hello! In Modern Particle Physics by Mark Thomson, in the Electroweak Unification chapter, pg. 412 he talks about the branching ration of the W decay to quarks. And for this he includes both the ##W\to q \bar{q'}## and ##W\to q \bar{q'}g## i.e. the state with a gluon and 2 quarks in the final...
Hi,
I am working on a data set and I have log-transformed two variables a and b and would like to figure out the relationship between the respective ratios. I have a strong intuition that a/b should have a well-defined range for a given value of lna/lnb, but my maths is poor.
a and be are...
By Volume:
Butane 0.75x6.5= 4.875 moles of O2
Propane 0.1x5= 0.5 moles of O2
Butene 0.15x6= 0.9 moles of O2
Total O2 4.875+0.5+9= 6.275 moles
Air required 6.275/0.21=29.88 moles/m^3
With 10% excess air 29.88x1.1= 32.868moles
1 mole fuel:32.87 moles of air
By Mass:
CO2 Moles...
The graph is relationship between longitudinal force and slip ratio under the conditions of 0 longitudinal acceleration and flat road(0 angle of inclination). Which line represent FWD or RWD? Does FWD or RWD have higher maximum slip ratio?
Monthly Cycle numbers
Here is the cycle ratio:
$$2_{early}:2_{fertile}:1_{late}$$
And the numbers:
$$20,000_{early}:20,000_{fertile}:10,000_{late}$$
Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume...
Homework Statement
The decibel scale of loudness is L = 10 log##\frac{I}{Io}## where I, measured in watts per square meter, is the intensity of the sound and Io= ##10^-12## watt/m 2 is the softest audible sound at 1000 hertz. Classical music typically ranges from 30 to 100 decibels. The human...
I have a word equation i cannot figure out! anyone have any ideas?
There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the...
Hi guys,
I was sizing up a servo motor the other day and started thinking. While we all know gear ratios will effectively "convert" speed into torque. I couldn't help wondering about the initial starting conditions.. The problem below...
Lets say I have a motor with a max load of 1Kg...
Homework Statement
find the area of the shaded region as a ratio to the area of the square (kindly see attached diagram)Homework EquationsThe Attempt at a Solution
##A= \frac 1 2####b×h##
##A= \frac 1 2####×2x × 3x##
I trying to generate a random distribution
λe-λy
Which distributed exponentially.%matplotlib inline
import numpy as np
from matplotlib import pyplot
N = 1000
r = np.random.random(N)
xlambda = 0.1
x = -np.log(r)/xlambda
binwidth=xlambda*5
pyplot.hist(x,bins=np.arange(0.,100...
So we have the theorem:
if ##a_n>0## and ##\lim_{n\to \infty} a_{n+1}/a_n = L## then ##\lim_{n\to \infty} a_n^{1/n}=L##.
Now, the proof that I had seen for ##L\ne0## that we choose ##\epsilon<L##.
But what about the case of ##\epsilon>L##, in which case we have:
##a_{n+1}>(L-\epsilon)a_n## but...
Dear community,
For my electric vehicle project I want to select a gear ratio (single) of my gear box and send this information to the supplier. In order to calculate this ratio I thought of the following steps but am not sure and want some expert to recheck and answer my queries:
1. Calculate...
Hello.
I have some questions regarding Alan Guth's book on the Inflationary Universe.
The following, from pages 185 & 186, has piqued my interest. I have reproduced Figure 10.6, above. Please read on. My questions follow. Please also take note that I can only understand these matters at a...
Hello.
In this issue of the American Scientist magazine,
https://www.americanscientist.org/magazine/issues/2018/september-october, there's an article by Dominik Kraus of the Helmholtz-Zentrum Dresden-Rossendorf Institute of Radiation Physics about the internal composition of the planets Uranus...
Homework Statement
In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED.
Homework...
Dear all.
I would like to know the general expression of the ratio of the electric field strength E to the magnetic flux density B. I know E/B = c, where c is the speed of light, for a vacuum, but I want to know if this is stil valid for any material where the electric and magnetic fields are...
Hi, if the velocity ratio is equal to the distance traveled by the effort divided by the distance traveled by the load, in a gears and wheels system, do you invert that in the case or gears? Making it number of teeth on driven gear divided by number of teeth on driving gear? Thanks
Hello all
I was hoping someone could help clarify Poissons ratio.
I understand that it is Lateral Strain / Axial Strain but I wanted to understand it in the context of an example.
The question is:-
At 5kN compression load
Original Depth = 30mm
Change in Depth = 2mm
Original Height = 100mm...
The ratio of Miss Chen's age to her father's age is 2:5. In 8 years' time, the ratio of their ages will become 1:2. How old is Miss Chen's father now?
My work.
Age of Chen = C
Age of Father = F
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Method 1...
Given an unconstrained (suspended without contact to anything) electric motor with its own power in total has mass m1
Given the motor shaft is connected to a payload of mass m2
If m1>m2 then: m1 no-spin + m2 spin
If m2>m1 then: m1 spin + m2 no-spin
What happens at the unit ratio (m1/m2 = 1...
Homework Statement
Find an approximate expression for the ratio of the power densities at the principal maximum to that at the first secondary maximum on either side, in the Fraunhofer diffraction pattern of an N-slit multiple aperture. Assume that the slits are much narrower than their...
Homework Statement
A Ferris wheel 26 m in diameter rotates once every 14 s. What is the ratio of a person's apparent weight at the top of the ride to her apparent weight at the bottom of the ride?
Homework Equations
[/B]
FNT/FNB = mg - mv^2 / r / mg + mv^2/r
The Attempt at a Solution...
Homework Statement
A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0?
Homework Equations
I attached a picture.
We are currently studying the four...