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.
When applying for entry level positions (flipping burgers for McD's), how many applications do you have to fill out to get a job? I've been applying for about 5 years, and did exactly 60 applications in the last two weeks alone. I have never been contacted by any employer, and have no paid work...
Homework Statement
Let A, B be points in R3 with position vectors
a:(7,-2,3)
b:(1,-5,0)
Let Q be the point on AB such that AQ= 2/3 AB
Find q, the position vector of Q
Homework Equations
The back of the book says the answer is: (2,-3,-1)
The Attempt at a Solution
First, I found...
Homework Statement
A rod with a diameter of 1.00 in and length of 6.0 ft undergoes an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip. The diameter of the rod decreases by 0.0007 in at this load. Determine the modulus of elasticity, Poisson's ratio and the shear...
I was hoping someone might be able to help sort out where I am going wrong in my calculation of the ratio of relative difference.
Value1= .0759
Value2= .0544
SqRt(.0759 / .0544) = 1.181195
The above calculation seems to work, but in a situation like below where the values are...
A secondary textbook said that if there is no flux leakage,
Vp/Vs=Np/Ns, no matter what is the efficiency of the transformer. May I know will the ohmic loss and eddy current contribute to the loss and modify the voltage ratio? thanks!
I am working on creating a mid size trebuchet with a projectile arm length of 3 feet. The counterweight is about 3500 grams, with the projectile being 60 grams.
I know that the ratio of the projectile arm length to the counterweight arm length changes depending on several factors, most...
Homework Statement
Calculate the velocity ratio of the attached lever.
Homework Equations
Velocity Ratio = Distance moved by effort * Distance moved by load
The Attempt at a Solution
Ok I'm having some confusion over this question. I cannot figure out whether the 'Distance...
Homework Statement
Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fourth terms of an arithmetic progression.
a. Find the value of r.
b. Find which term of the arithmetic progression will next be equal to...
Homework Statement
A solid fuel supplied to a furnace had the following composition by mass.
Carbon: 86%
Hydrogen: 5%
Oxygen:4%
Incombustibles: 5%
Dry volumetric analysis of the combustion products showed the flue gas contained 15%
and 1.5% of CO2 and CO respectively. The test on the...
Homework Statement
A radio tuner built by connecting an L=0.58mH inductor and variable capacitor in series with an antenna. The driving voltage is provided by the radiowaves that pass through the antenna, and the total internal resistance of the circuit is R=2.6Ohms.
The variable capacitor is...
The question is "Make a simple estimate of the order of magnitude of the ratio of the cross sections (electron,positron->2photons) and (electron,positron->3photons)"
Now I know that cross section is proportional to (1/q^4)*(Phase space factor)*(Coupling constant) where q^2 = E^2 - p^2. We are...
Homework Statement
An engine provides a constant force F to a car of mass M that carries a box of mass m on the top of it. After traveling from rest with constant acceleration a1 for 20 seconds, the speed of the car becomes 40m/s and at that instant the box falls off the car. In the next 20...
Homework Statement
The 2-D image of a faint galaxy observed by a CCD covers 50 pixels. For an
exposure of 5 seconds a total of 10^4 photo-electrons are recorded by the CCD
from these pixels. An adjacent section of the CCD, covering 2500 pixels, records
the background sky count. During the...
Ratio Test, SUPER URGENT, help?
Consider the series
∑ n=1 to infinity of asubn, where asubn = [8^(n+4)] / [(8n^2 +7)(5^n)]
use the ratio test to decide whether the series converges. state what the limit is.
From the ratio test I got the limit n-> infinity of
[8^(n+1+4)] / [(8(n+1)^2...
Homework Statement
I was supposed to use dimensional analysis to approximate the length scale (in classical and quantum mechanics). The results I got(same as those in the answer sheet): classicalyl_c≈\frac{e^2}{4πm_ec^2ε_0}≈2.8*10^-15m In quantum mechanicsl_q≈\frac{h}{m_ec}≈2.4*10^-12m...
Homework Statement
Calculate the velocity ratio of the system.
Third Class Lever
Efficiency = 65%
Mechanical Advantage = 1/6
Work Put In 3000J
(I know if the system was theoretically 100% efficient the velocity ratio is 1/6 or 0.167)
Homework Equations
Velocity Ratio =...
If the damping ratio of a damped circuit is increased, does the circuit become more or less damped?
I would think it would become more damped, but what exactly is the definition of the damping ratio?
Hello,
I’m designing a 2D wind tunnel model for my master thesis. It will be a profile equipped with a fixed hinged trailing edge flap. I’m going to measure at different angle of attacks and different flap settings at low speeds (about 70 to 100 m/s). The aim is to measure steady and unsteady...
Homework Statement
A uniform square bar lies horizontally across two supports, A and B. B is fixed to the floor, and A is moved toward center O of the bar with uniform speed. Initially, A slides along the underside of the bar, while the bar remains at rest with respect to B. When A reaches...
Homework Statement
Hi,
How do I solve for y in this triangle? (picture in attachment)
Homework Equations
So I use the special angel ratio and get
sqrt(3)x = y + 20
and then from the smaller triangle I get
tan(theta) = 20 / x
What do I do next?
Thanks.
The...
Homework Statement
In an engine test the dry exhaust gas analysis is CO2: 5.27%; O2: 13.38%: N2: 81.35%.
Assuming that the fuel is a pure hydrocarbon of the form CxHy, and that it is completely
burnt, calculate the ratio, by mass, of carbon to hydrogen in the fuel and the air to fuel...
Relation b/w slip ratio and drag force...Race car Vehicle Dynamics help...
hii guyz...
this is the first time i am posting on this forum and hope i ll get help...
I was going through Race car vehicle dynamics by milkins and found a relation given on pg 64
which says...
Drag...
Homework Statement
A solid cylindrical bar 18.34 mm diameter and 180 mm long is welded to a hollow tube 18.34 mm internal diameter and 120 mm long to make a compound bar. Determine the external diameter of the tube in (mm) if when loaded with an axial force of 40 kN, the stress in the solid...
It's my perception from random remarks that have been made here over the years that most people's math/science classes have been populated by a markedly higher proportion of men than women, and that interest in math/science dooms guys to a sort of involuntary monastic existence, as far as...
Hello,
Second term of a geometric series is 48 and the fourth term is 3... Show that one possible value for the common ratio, r, of the series is -1/4 and state the other value.
ar=48, ar^3= 3... so ar^3/ar=3/48 which simplifies to r^2 = 1/16, therefore r = 1/4
Can anyone explain where...
Homework Statement
So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I...
Hi,
Can anyone help explaining the points of action of drag and thrust forces on an aeroplane in flight and also the realtionship between Lift-Drag ration and wing configuration?!
Any help would be great!
I am trying to prove e^z converges on all C. Here is my attempt.
e^z=series(z^n/n!)
use the ratio test on the coefficents 1/n! gives lim(1/(n+1))=0, which from rudin means radius of convergence R=1/0 -> R=infinity.
Homework Statement
The problem is that using a human powered bike-like machine we have to climb up a 16 meter long rope. The total weight of the machine + human is 1300N and the theoretical force delivered by the human is 250 Newtons. The crank is 17cm long (that's the length of the arm, the...
Hi,
there is a proof of the ratio test that I have seen a couple of times here:
http://tutorial.math.lamar.edu/Classes/CalcII/RatioTest.aspxI don't know how to use latex, so abs(x) will mean absolute value
I am ok with this:
abs( aN+1) < r abs(aN)
I don't understand where the r2 come from in...
$$\sum\limits_{n = 0}^{\infty}\frac{2\pi^{n+1}M}{(n+1)!}z^n$$
So we get $\lim\limits_{n\to\infty}\left|\frac{\pi z^n}{n+2}\right|$.
This converges but I don't see how. z is in C.
Homework Statement
Sodium is, to a good approximation, a monovalent free-electron metal which has the
body-centred cubic structure.
(a) Calculate the ratio of the Fermi wavevector to the radius of the largest sphere that
can be inscribed in the first Brillouin zone. Remember that the...
Say we shoot the surface of the moon with various sized steel balls of size a cm and larger, say up to a km in size. Say the balls hit the surface of the moon moving at 20,000 mph. Is there a simple formula for the mass of the ejecta as a function of the mass of the projectile? Will the formula...
The ratio of integrals
∫〖a(x) b(x)dx〗/ ∫c(x) b(x)dx
can be maximized by choosing b(x) equal to the delta function at the point where a(x)/c(x) is a maximum.
Can anyone provide the solution for choosing b(x) when b(x) cannot equal the delta function, b(x) is greater than zero with a...
A few years ago for every fresh PhD graduate in MIS, there were three open faculty positions. Then the ratio of graduates to positions dwindled to 1: 2, then to 1:1.5, later to 4:1. Finally MIS departments all over started shutting down or being merged into Management, Operations or other...
Homework Statement
Air at sealevel is composed of 80% nitrogen and 20% oxygen, but at the top of Mount Everest the composition of air is different. Give an expression for the ratio (f_O) of oxygen in the air as a function of height z above sealevel, assuming the temperature T is constant and...
Hi All;
The following attachment shows a diagram of the ratio
R[2m] = g^2[2m]/g[2m-2]*g[2m+2] where g[2m] is the number of goldbach partitions for the even number 2m.
What is the reason for the "forbidden zones". I understand this is somehow to do with the factors of the even number...
Homework Statement
Two identical satellites orbit the Earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v . At what distance from the center of the Earth does the second...
This isn't a homework question in its entirety, I'm just wondering what the difference is between a Mode ratio and a mode shape? I'm taking a mechanical vibrations course and trying to figure out what the problem is asking for when it wants a mode shape...
Hey guys,
I've been given a worksheet with a couple of questions concerning radioactivity, half-life etc. It is high school level and for me, it seems like the first year doing physics as our current teacher is the first one who really knows something about the subject. :) So please be patient...
Homework Statement
Investigate the convergence of the following series.
(2n)!/(n!n!)
The Attempt at a Solution
Number one, I don't see how they get that
if an = (2n)!, then an+1 = ((2n+2))!, it should be (2n+1)!
Number two, I don't see how they go to the second step, why is the second step...
Homework Statement
The drawing shows two positive charges q1 and q2 fixed to a circle. At the center of the circle they produce a net electric field that makes an angle 28.6° with the vertical axis, measured counterclockwise. Determine the ratio q2/q1.
[the drawing shows a circle with two...
Homework Statement
Two body move apart by force. Frictional forces are considering. How to calculate the ratio of weight?
m1<m2
Ft1=k*g*m1
Ft2=k*g*m2
Homework Equations
v1(t1)=\frac{F_{t1}-F}{m_{1}}*t_{1}
x1(t1)=\frac{F_{t1}-F}{m_{1}}*\frac{t^{2}_{1}}{2}...
Pentagon diagonal - parallel ratio proof
Homework Statement
Suppose P is a convex pentagon such that each diagonal is parallel to one side. Prove that the ratio of the length of a diagonal to that of its corresponding side is the same for all five diagonals, and compute this ratio...
The ratio of Pu238 and O2 in Plutonium dioxide?
Hello, guys.
I was wondering if I can find a ratio of Pu238 and O2 in PuO2.
In my problem set, these are all I have.
- 238/94 Pu -----86yrs----> 4/2 He + 234/92 U + 5.59 Mev
- 238PuO2 : 6000 gram in a sphere (10 cm diameter)
-...
Homework Statement
According to genetic linkage theory, observed frequencies of four phenotypes
resulting from crossing tomato plants are in the ratio 9/16 + a : 3/16 - a : 3/16 - a : 1/16 + a.
In 1931, J.W. MacArthur reported the following frequencies:
Observed...
Homework Statement
A round bar of 10 mm diameter is made of
aluminum alloy 7075-T6 (see figure). When the bar is
stretched by axial forces P, its diameter decreases by
0.016 mm.
Find the magnitude of the load P. (Obtain the material
properties from Appendix H.)
From Appendix H:
Modulus of...