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.
1. Uranium has two naturally occurring isotopes. 238U has a natural abundance of 99.3% and 235U has an abundance of 0.7%. It is the rarer 235U that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, which is a gas, then allowing it to diffuse through a...
Homework Statement
Harry and Sally are sitting on opposite sides of a circus tent when and elephant trumpets a loud blast. If Harry experiences a sound intensity level of 65dB and Sally only 55dB, what is the ratio of the distance between Sally and the elephant to the distance between the...
Homework Statement
Work out the branching ratio of (W --> e-Ve)
The book uses fermi's golden rule to do it, but I am wondering if my different solution is also valid?
Homework Equations
Γ = 1/τ and ΔEΔT = hbar
The Attempt at a Solution
If ΔEΔT = hbar, then i can write ΔT =...
Hi, my question is about determining the damping ratio for the upper spring-damper part of the system given in the link. Is it still r2/(2*sqrt(k2*m2)) or something equivalent should be determined?
http://img217.imageshack.us/img217/3148/sprdampmass.png
Thank you!
Homework Statement
Calculate the ratio of the magnitude of the attractive gravitational force to the repulsive electrostatic force between two protons. Homework Equations
Mass of proton = M = m = 1.672e-27 kg
g = 9.80665m/s2
Q = q = 1.60219e−19 C
k = 8.9875e9...
Homework Statement
Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about 107 K. Given that Jupiter actually emits approximately twice this much energy per second...
Homework Statement
Given:
(1/2) mol N2 + (3/2) mol H2 -> NH3 change in H = -46.11 kJ/mol
If the number of moles of N2 are changed to 10 and the number of moles of H2 to 35,
how much heat is generated if only 10% of the Nitrogen reacts?
The Attempt at a Solution
After setting...
Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about107 K. Given that Jupiter actually emits approximately twice this much energy per second, calculate what the average...
Homework Statement
I am asked to provide an anti vibrational support mount for equipment mounted on turbo-prop aircraft. The equipment has a mass of 40kg.
the vibrational response of the equipment to the environmental disturbances will need ot satisfy a safety limit prescribed by the...
Homework Statement
A boy of mass mboy stands at the edge of a merry-go-round of radius R = 3.4 m and mass mmgr, and both are initially at rest. The boy then walks along the edge of the merry-go-round. After walking a distance of 25 m relative to the merry-go-round, the boy finds that the...
Homework Statement
Hi
I want to see if you guys could check my work an tell me if i did it correct and also explain me how to cancel "look at the graph"
Homework Equations
The Attempt at a Solution
Homework Statement
A CD (radius 6.0 cm) is spinning freely with an angular velocity of 420 rpm when a bug drops onto the CD a distance 4.4 cm from the center. If the CD slows to 280 rpm, what is the ratio of the bug's mass to the mass of the CD? (Ignore the effect of the hole in the center of...
Homework Statement
An oxygen atom is four times as massive as a helium atom. In an experiment, a helium atom and an oxygen atom have the same kinetic energy. What is the ratio vHe /vO of their speeds?
Homework Equations
K=.5mv2
The Attempt at a Solution...
cal 2 ratio test "where is my mistake"
Homework Statement
I attached a pic
I solved the problem but i get 4^1 and the book says 4^2 I don't know why?
Homework Equations
http://img690.imageshack.us/img690/1518/problem15.jpg
The Attempt at a Solution
Homework Statement
Component 1 and 2 form an ideal solution. The vapor pressure of pure component 1 is 13.3kPa at 298K, and the corresponding vapor pressure of component 2 is approximately zero. If the addition of 1.00 g of component 2 to 10.0g of component 1 reduces the total vapor pressure...
Homework Statement
For u = (−1, 2, 1) and v = (3, 3, 6) find the ratio ||v|| / ||u||
Homework Equations
|| u || = (u^2 + u2^2 + ...un^2)^.5
The Attempt at a Solution
I found the || u || to be 6^(1/2) and || v || to be 54^(1/2)
Therefore the ratio should be 54^(1/2) divided by...
Homework Statement
Consider a rectangular block of isotropic material of dimensions a, b and c, with c >> a
or b. It is characterised by its elastic constants: Young's modulus E, shear modulus G
and Poisson's ratio .
The block of material is subjected to axial deformation along the c...
For collisions wouldn't the distance traveled during the collision be the same? The energy lost is from heat, sound, deformation, etc. but wouldn't the work done on each car be the same since during the duration of contact they have to move the same distance (as soon as they move different...
Homework Statement
Two objects are moving along the x-axis with velocities of 37 m/s (object 1) and -19 m/s (object 2). (b) What is the ratio of their masses
Homework Equations
The Attempt at a SolutionNo idea
Homework Statement
A 5 pound mixture of barley and oats is 4/5 oats by weight.
How much barley in pounds must be added to the mixture to make it 3/5 oats by weight?Homework Equations
-
The Attempt at a Solution
I honestly cannot figure this problem out. The book gives the answer and...
Does anyone know the highest alpha (Gilbert damping ratio) you could get on ferromagnets?
People for various reasons aim for the lowest alpha and it is around 0.008 these days (dimensionless). But I need to know whether higher values are possible or not.
A brief reminder on what alpha is: It...
If 100 bu of corn per acre remove 90lb of nitrogen, phosphorus, and potassium (N, P, and K, respectively), how many pounds of N, P, and K are removed by the yield of 135u per acre?
I try to figure out how to starting to solve this problem but don't know how
some help please
Homework Statement
2 stars rotating around the common centre of mass have masses m and 3m. What is the ratio of the force due to each star at the common centre of mass.
Homework Equations
None
The Attempt at a Solution
I tried to find the centre of mass and applied Newtons law of...
Homework Statement
Why would vibrational and rotational degrees of freedom affect the heat capacity ratio more for N2 and CO2 than He or Ar? Would this occur at room temperatures?
Homework Equations
d.o.f.: 3N
vibrational d.o.f., linear molecule: 3N - 5
nonlinear: 3N - 6
The...
Homework Statement
A person is standing on a sheet of ice so slippery that friction may be ignored. This individual fires a gun parallel to the ground. When a standard cartridge is used , a 13-g bullet is shot forward with a speed of 290 m/s, and the person recoils with a speed of vc. When a...
Homework Statement
You are given two unknown point charges, Q_1 and Q_2 . At a point on the line joining them, one-third of the way from Q_1 to Q_2 , the electric field is zero (see figure). The charges are separated by length, L.
What is the ratio of the charges Q1/Q2?
Homework Equations...
A steel bar of rectangular cross section 120mm x 60mm is compressed along its longitudinal direction by a force of 1500kN. Do the cross sectional dimensions increase or decrease ? Calculate and write down the resulting dimensions for both sides for both sides of the cross section. Youngs modulus...
1. Torsion test showed aluminum to have shear modulus of 4.60x10^6psi. Under a tensile test, the same specimen showed a modulus of elasticity of 12.2x10^6psi. Find Poisson's Ratio.
2. Poisson's Ratio=lateral strain/axial strain
3. The ratio is a function of both strains. The...
1. \sum_{n=1}^{\infty}ntan\frac{1}{n}
dont know where to start here
2. \frac{1*3*5*****(2n-1)}{n!}
\frac{2n-1}{n!}
\frac{2(n+1)-1}{(n+1)!}*\frac{n!}{2n-1}
\frac{2n+1}{(n+1)(2n-1)}
->0
my book is showing divergence
The masses of the elementary particles are renormalized somewhat, when the energy (the momentum) increases. Assuming that the standard model of particle physics is correct to all energies, is there any data on how the ratio M_W/M_Z between the two vector boson masses changes with energy? Does...
Substitute each of the letters by a different digit from 0 to 9 to satisfy this equation. None of the four numbers can contain any leading zero.
(REPAID)/(DIAPER) = (RA)/(RE)
Note: Each of the four numbers represent the concatenation of the digits, and does not denote the product of the...
Research-related question:
What is the typical on/off ratio of a silicon transistor? This seems like basic information, but I can't find it anywhere.
Also, how high does the on/off ration need to be in order for transistors (say, in a logic circuit) to function correctly?
Thanks!
Given positive integers a, b, c, d
and for fractions a/b and c/d,
it seems that ( a + c )/( b + d ) is between a/b and c/d.
There's likely an easy proof of this. I'd like to know if there's a formal name for ( a + c )/( b + d ) or the operation that brings it about.
Homework Statement
Now you take off to an unknown planet with the same pendulum as in part (a). You measure the period of the pendulum on that planet and you find it to be twice as much compared to the one of the pendulum while on Earth. What is the ratio of ge on Earth to the gx of the...
When a fuel/air mixture burns it expands. How much does it expand? Is there a formula or known volume increase?
After a fuel burns it contracts. How much does it contract? Is there a formula or known volume that it contracts?
Gasoline/Air mixture ratio is 15 to 1 for jet engines.
A...
Frequently, I have encountered optimization problems which involve finding the optimal function to maximize the ratio of two integrals (bounds from 0 to infinity). e.g: Maximize \frac{\int_0^\infty (g(x))^3 g'(x) dx}{\int_0^\infty (g(x))^3(1-g(x)) dx}
I am aware that variational calculus...
Hi guys, working a project where I need to guess the damping ratio (used for a numerical analysis) based on other properties of a material. We're looking to use an RTV as a vibration damper (we don't need a lot) but I can't seem to get any vibrational properties (called Honeywell, Dupond...
What is the Air/Propane mixture Ratio?
The Fuel Air Ratio of a Jet Engine is 15 to 1. This is for JP4.
What is the Fuel Air Ratio for Propane Gas?
I have learned the only difference between a rocket engine and pulse jet engine is the pulse jet runs on the oxygen that is in the air (30%...
If I dig 2 holes a little space apart, and then they intersect straight down, because of the curvature of the earth, then there is more than one up direction from the center. The closer 2 points at an equal distance down from the surface in separate holes get to the center, the less distance...
If a transformer with coil ratios 2:1 creates a voltage twice that of the primary in the secondary coil why is the current halved? I realize that this is a consequence of the conservation of energy, but there must be a physical reason behind this. What is causing the additional impedance that...
Homework Statement
During a total solar eclipse, your view of the Sun is almost exactly replaced by your view of the moon. Assuming that the distance from you to the sun is about 400 times the distance from you to the moon. Find the ratio of the Sun's diameter to moon's diameter.Homework...
Use the "bow-tie" diagram to state the value of each trigonometric ratio.
a) sin 45
b) cos 60
c) tan 30
d) tan 45
My Answer:
a) 1 / \sqrt{2}
b) 1 / 2
c) 1 / \sqrt{3}
d) 1
Once again with this text the wording has thrown me off. It asks for the ratios but throws in that you should...
Another transformer question: if I have an oil-filled transformer coil and I calculate the turns ratio with voltage in / voltage out at 60 Hz, why, when I increase the frequency to 23 kHz would the turns ratio appear to change? Is it because of the inductance of the primary coil? My boss'...
Homework Statement
In an experiment similar to J. J. Thomson's, charged particles are observed to travel through a magnetic field of 0.040 T with a radius of curvature of 0.20 m. The path of these particles is made straight again when an electric field is introduced by two parallel plates...
Homework Statement
Hi! I'm trying to calculate the energy ratio of EM-radiation in the visible spectrum and EM-radiation in the entire spectrum, of a body with known temperature.
Homework Equations
Planck's law: http://feps.as.arizona.edu/outreach/images/Blackbody_gr_3.gif.[/URL]...