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.
Hi, I'm having difficulty understanding why the interval of convergence is (0, 18].
When I tested x=18, I got the following conclusion using the ratio test.
When I attempt using AST, the function still diverges as the lim (n -> inf) = 2^n / n ≠ 0.
What am I missing?
Thanks!
Is the answer 1? Because the cord is connected to vibrating source and it vibrates with a frequency of 100 Hz so section A and B have the same frequency
Thanks
I read on a post here titled 'Understanding Fourier Transform for Wavefunction Representation in K Space' that if one represents the squared-amplitude as a ratio of differentials, the solution is given. Letting the squared-amplitude be ##\phi##.
$$\frac{d\phi}{dp}=\frac{d\phi}{dk}\frac{dk}{dp}$$...
When I am using the Saha equation, how i am suppose to know the electron pressure?
Which are required to calculate the ration?
Since: P_e = n_ekT (electron pressure and n_e is related to each other, but n_e is also unknown based on my understanding).
From Wikipedia:
"As an example, if share A is trading at $24 and the earnings per share for the most recent 12-month period is $3, then share A has a P/E ratio of $24/($3/year) = 8 years. Put another way, the purchaser of the share is investing $8 for every dollar of annual earnings; or, if...
For part(b)
The solution is, ##1:10##, however, is the wording correct? I don't see how to find the ratio of atomic mass, however, I can solve for the ratio of the molar mass.
##n_A = n_B## from part(a) by setting the internal energy equation for each ideal gas equal
##\frac{M_A}{m_A} =...
For my 12th grade school project, I'm planning to research on the effect of vent ratio on the drag coefficient of round parachutes. My idea was to make small model parachutes and drop them from a height, and derive the drag coefficient after certain assumptions. But I also thought it'd be...
So i found this on a journal, and im wondering what is n and how can i calculate the weight percentage ratio between the PEO and LiClO4. Here is the instruction.
To prepare PEO-LiClO4-Al2O3 PE samples, predetermined amounts of LiClO4 (such that oxygen to lithium ion ratio is n:1) and Al2O3 (as...
Consider the following:
We start with a positive integer: x
If x is even, do
x/2
If is odd, do
Floor function( x * y)
with y being some decimal number between 1 and 2
And repeat until a loop is reached. If 1 is reached, the next number will be 1 as well. So we reach a loop too.
An example:
x =...
I'd like to do some experiments with flames at different Equivalence Ratios - but I'm confused as to how I can find the Equivalence Ratio for different conditions. Wiki-article
So the stoichiometric balance for Methane + Air is
CH4 + 2(O2 + 3.76N2) -> CO2 + 2H2O + 7.52N2
Referencing equations...
Hello!
I was studying odds ratio and its relation to relative risk. By what I understood, the statistics that is indeed important for us and that have a nice interpretation for the context is relative risk (I was also wondering if odds ratio has any interpretation). But relative risk sometimes...
My wife is wanting to place an empty alcohol bottle filled with Dawn in the toilet tank. Have a 1//16 hole drilled 3 inches from the bottom so the fluid will come out when flushed and the water level gets lower than the hole. The Dawn will stop coming out once the water refills above the hole...
Hello,
I'm in the process of developing a sugar paste for hair removal and trying to find a good ratio between sugar, water and acid in order to get a gewy consistency. I currently use 8 tbs sugar, 4 tbs water and 2 citric acid and let it reach a temperature around 128 degrees Celsius (262.4...
*kindly note that i do not have the solutions ...I was looking at this, not quite sure on what they mean by exact fractions, anyway my approach is as follows;
##\dfrac {a}{243}=\dfrac{a(1-r^3)}{240}##
##\dfrac {1}{243}=\dfrac{1-r^3}{240}##
##\dfrac {240}{243}=1-r^3##...
My attempt;
The terms in the arithmetic sequence are ;##[ a, a+2d,a+5d]##.
It follows that;
Common ratio ##r=\dfrac{a+2d}{a}=\dfrac{a+5d}{a+2d}##
##⇒ar+2rd=a+2d+3d##
##ar+2rd=ar+3d##
##ar+2rd-ar=3d##
##2rd=3d##
##r=\dfrac{3d}{2d}=\dfrac{3}{2}##
The solution given on the textbook is...
For the dimensions of a right cylinder, I am given three significant digits for the diameter (17.4 mm) and the height (50.3 mm). The formula for the volume of a right cylinder is V = Pi x r^2 x h, which would lead here to Pi x (17.4 mm / 2)^2 x 50.3 mm = 11,960.69354 mm^3 before rounding to 3...
So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we...
In fact, the whole golden rectangle and ratio discussion seems strange to me. I am interested in knowing the kind of problems the ancient Egyptians and Greeks were grappling with when they encountered the golden number.
It would be great if you could point me to a book or website where I can...
My question is on part (c) only.
Find the markscheme solution below;
Mythoughts on this; (Alternative Method)
i used the simultaneous equation
##λ####\left[\dfrac {1}{2}a -\dfrac {1}{4}b\right]##=##\left[ -\dfrac {3}{4}b+ ka\right]## where ##OR=k OA##
##- \dfrac {1}{4}bλ##=## -\dfrac...
Greetings all
I have a question regarding the convergence criteria ratio, abs(an+1/an) or the n√abs(an) when the limit tend to a value less than 1 does it mean the serie is convergent or absolutely convergent?
Thank you!
Summary:: Averaging (a power of) semimajor axis to position ratio wrt to time - celestial mechanics
I evaluated it this far, but i don't know how to change the dt to d theta ... the final solution is
supposedly (1-e^2)^-(3/2) . Any help will be appreciated.
[Image re-inserted with correct...
I recently got a new correction tape. When I was staring at it today (ya I knew I should be studying for calc2), I noticed that the gear ratio between the two gears was notable and fixed. In particular, the bigger gear that unrolls the tape has more teeth than the smaller gear that rolls up the...
I am able to prove that it is 0.225 but how do I prove that it is also 0.414?
I need to find the max. and min. packing fraction values, which I got as a function of (r1/r2)
Please help
Would like help as to the method rather than the answer please. Classes haven't been very clear therefore everything is self taught. Many thanks. ' The Drag polar for an aircraft is given by:
CD = 0.025 + 0.08 C^2L What is the maximum Lift to Drag ratio '
Currently my task is to count number of iterations of golden section search verus interval bisection search of a function y = x^2. Golden section search took about twice the number of iterations than interval bisection search.
If I lowered the golden ratio from 0.618 to 0.5562 , the number...
Sutton writes that the mass ratio of a multistage rocket is the product of the individual vehicle stage mass ratios, does it mean the expression below?
$$MR=\prod_{i} \frac{m_{f,i}}{m_{0,i}}$$
So pretty confident I understand part (a) however for part (b) I'm not sure if I have carried it out correctly if someone could give me a pointer?
(b)
5dBmV Input as a voltage:
5=20Log(V/1mV)
V=105/10
V=1.77827941mV
Then the noise level is 20dbμV so changing to a voltage:
20=20*Log(V/1μV)...
Plants prefer C12 to C13 during photosynthesis, so that the C13 to C12 ratio in plants is less than that in the atmosphere (by around 20% for most plants, but less difference in C4 plants like maize). Do plants discriminate against C14 too? If so, won't that cause a considerable uncertainty in...
hmmmm this question is a bit confusing... i.e on the part of finding the number of women.
Looking at the graph, and say considering Red, it's pretty obvious that men are ##3##, now my confusion is on the number of women, is it ##5## or ##8##? my thinking falls on two perspectives,firstly that...
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Problem Statement: A survey of voter sentiment was conducted in four midcity political wards to compare the fraction of voters favoring candidate $A.$ Random samples of $200$ voters were polled in each of the...
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Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of independent random samples of sizes $n$ and $m$ selected from normal distributions with means $\mu_1$ and $\mu_2$ and common...
Hello I am trying to achieve 3500 rpm from 60rpm. The gear ratio I have worked out is 58:1. To minimize the size I have divided into 4 levels with the gear ratio of 2:1, 3.1, 3.1, 3,1, which rounds me up to 54:1 ratio is also ideal for me can anyone please help mw find the appropriate solution...
So I am having some difficulty expressing this series explicitly. I just tried finding some terms
##b_{0} = 5##
I am assuming I am allowed to use that for ##b_{1}## for the series, even if the series begins at ##n=1##? With that assumption, I have
##b_{1} = -\frac {5}{4}##
##b_{2} = -...
The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.
I never saw an age problem involving a ratio but let's see.
Abraham to Adam = 5 : 7
Let x = present age of Abraham and Adam.
Age of Abraham = 5x...
Hi everybody, first message on this forum !
I am building a machine for a friend who works with cardboard pulp, he is also a performance artist and would like a machine where 2 or 3 performers can activate the machine by hand with pulleys and wheels, and shred the pieces of cardboard that are...
Here are the answer choices:
a) F1 = 2F2
b) F1 = 8F2
c) 2F1 = F2
d) F1 = 4F2
e) F1 = F2
I figured that Coulomb's law would tell us the magnitude of the forces are identical, so I answered E, but that was incorrect.
(Screenshot of question attached)
To find ##\delta## for the 1st order, all I need to do is to square the diameter of the 2nd ring and subtract it to the square of the diameter of the first ring.
$$\delta_{1st \; order} = {d^2}_{2nd \; ring} - {d^2}_{1st \; ring}$$
To find ##\Delta##, I can use the below equation...
What counts as a low slendernous ratio. i was look at column slenderness ratios and stress, it was talking about a column with slenderness ratio of 80-90 and stress of 300MPA. Is 300MPA low or high stress.
Wanted to know so i can say wheather the low ratio says that it will fail at high or...
This has persistently bugged me in my intro plasma course. They keep using ##\gamma = 3## aka ##N_d = 1## (where ##N_d## is the number of degrees of freedom in the molecule) as an approximation. See for example, the Bohm-Gross dispersion curve. I can tell you from deriving this that the factor...
In the context of Survey of Dark energy stage IV, I need to evaluate the error on a new observable called "O" which is equal to :
\begin{equation}
O=\left(\frac{C_{\ell, \mathrm{gal}, \mathrm{sp}}^{\prime}}{C_{\ell, \mathrm{gal}, \mathrm{ph}}^{\prime}}\right)=\left(\frac{b_{s p}}{b_{p...
I have two capacitors in series across my bus. I have a some series resistors across the capacitors for voltage balancing. I would like to power some low voltage low voltage components tapping off of the voltage divider using that as the voltage supply.
The bus voltage will be approximately 2...
This source http://sustainableaviation.org/sas2017/session/prandtl-wing-maximum-efficiency/index.html claims : "Bell lift distribution can be applied to propulsion systems (no more “minimum induced loss”). We believe this results in a gain of 15.4% thrust for the same input torque/power."
Bell...
What is ideal lift distribution for propeller blade to get best thrust/power ratio?
To do this blade must has minimum drag, because drag releted to torque,and torque x RPM= power..
Hello, everybody:
I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of...
I was asked to find the ratio of the fluxion of x to the fluxion of 1/x using Newton's synthetic method of fluxions. I do not understand how to do this.