Ratios Definition and 224 Threads

Euclid defines equivalent ratios as the following : "Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former...

A shop sells small chocolate bars and large chocolate bars The small bars are sold in packs of 4 The large bars are sold in packs of 9 On one day; packs of small sold ; packs of large sold = 5:2 A total of 95 bars were sold How many small bars were sold? * My question; Is this an example...

my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the...

I have the solution: ## \dfrac{2x-3y}{3z+y} = \dfrac{z-y}{z-x} = \dfrac {x+3z}{2y-3x} ## (1) ## \dfrac{2x-3y}{3z+y} = \dfrac{3(z-y)}{3(z-x)} = \dfrac {x+3z}{2y-3x} ## (2) ##= \dfrac{(2x-3y)-3(z-y)+x+3z}{(3z+y)-3(z-x)+(2y-3x)} ## (3) ##=\dfrac{x}{y}## My question is how is it possible to go...

I have been doing the resolutions of vectors on x and y-axis with making triangles and reference angles in all quadrants. But I want to calculate now how to find something like ##\sin 235## without the help of reference angles. I know we don’t need to. Calculator and Taylor theorem is handy here...

I need help with how to use bar models with these kinda stuff. Thanks

In competitive rowing, the more people in a boat, the faster it goes, but what is the ratio of additional human to speed, and what is the theoretical limit? If I could fabricate a boat where each additional person added 100kilos, 100watts of power, and 1 meter of length to the wetted surface...

Hi everyone! I am studying Higgs phenomenology, in particular its BRs My line of reasoning is this: I first had a look at the decays where the Higgs particle couples directly (i.e. without intermediate particles) to the products; those are ##H^0 \to b \bar b, \ H^0 \to \tau \bar \tau##...

I'm new to composite materials. I've studied mechanical engineering but I am actually usually involved in hydrodynamics (in which I've done my masters). However for a project we do fluid structure interaction with composites, and as these things go, you cannot get away with the 'black box'...

I'm wondering if anthropogenic climate change (C13: C14 and C14:C12 ratios) is still contentious on these forums. Counting the amount of fossil emissions in the last 100 years isn't particularly difficult, and matching the curve with NOAA measurements seems trivial, so I'm wondering what kind of...

I was thinking it would 3 or 9 times the tension rather than 1/3 or 1/9 but that is just a guess. an explanation would help very much!

Now I don't really know much about the subject, I'm primarily just peaking into my textbook to see how to solve this or that exercise. I believe I can figure out how to solve the third question. However I couldn't find how to solve the first two. I know how to find a 95% confidence interval for...

Hello guys I have a motorcycle engine in which I know the ratios of the transmission. and given the diagram of Power and rpm I made a function of P(ω) which is a polynomial of 6 order. Then I said that F(friction)*u=P(ω) then I substitute ω=u*r/v v(ratio) and have F(u).Next knowing the Pmax...

a) In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual fact, the outer layers of rock have...

Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworks to Geoffrey, then Amal and Geoffrey will have in a 2:3 ratio. If Julia has 1/5th as many as Geoffrey (after Amal gives half his fireworks to Geoffrey), then what is the ratio of the number of fireworks Amal...

Lets say we got a larger cylinder-piston combo and a smaller one. First we move the larger cylinder, filling in with vacuum. Then we pump in air, using the smaller cylinder, isothermally, with variable expansion ratio. Here, we clearly have exp ratio > P_atm/P_final We then compress the larger...

Hello, I am confused about something. I will take the time to work it out, but right now, I am using it to remember. And I am now confused. Go here: https://www.smlease.com/entries/mechanism/gear-train-gear-ratio-torque-and-speed-calculation/ Scroll down to the section on...

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 have a mathematical term of the form tan(A.x)/tan(B.x)=C.How do I find out the value of x?

As a 'non-mathematician' (somebody who sucks at maths) I've been enjoying reading up on a lot of the stuff that flew over my head in maths class many years ago. I've encountered some examples of weighted averages and I've been puzzling over how one might derive the weights in the following...

I understand that In general, the branching ratio for a particular decay mode is defined as the ratio of the number of atoms decaying by that decay mode to the number decaying in total. But I can’t get this specific branching ratio.

The mass of vehicle with driver is 150kg. The specification of motor are 12kw, 27Nm torque, using 110/80 R17 wheels . 1. what is the general consideration to do transmission calculations of bikes 2.How to select gear ratios and sprocket ratio?

I already know the fact that angles are physical quantities, but sin, cos of some angles are quantities? Quantities are those things, which can be quantified, are sin, cos, tan be quantified through measurement, if yes then other mathematical functions should also be categorised as physical...

The concept of naturalness as dimensionless ratios of parameters of order unity has recently come under criticism, most obviously because Sabine Hossenfelder wrote a book (Lost In Math) criticizing it. Very recently however, Peter Shor and Lee Smolin had a discussion about this over at Peter...

Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...

In square ABCD point M is the midpoint of side CD. Find the ratios of the areas of the four regions (∆MPC, ∆BPC, ∆APB, and quadrilateral APMD) that are formed. Justify your result.

Homework Statement Triangle ABC is shown in the diagram below. A C AC = 3AB <BAC = 120° Respectively <BCA = Show that angle BCA can be written in the form...

Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...

This may not be the proper forum but i need to find a way to calculate how much effort it will take to move a cylinder using a manual helm pump. The hydraulic cylinder i intend on using is a 32mm bore with a 16mm diameter. Stroke of 178mm. Volume of 107 cc The helm pump (attaches to a steering...

So I've found the following formula for calculating the gear ratio of a planetary gear. Tr Turns of the ring gear Ts Turns of the sun gear Ty Turns of the planetary gear carrier R Ring gear teeth S Sun gear teeth P Planet gear teeth ( R + S ) ×Ty = R × Tr + Ts × S The example I saw on the same...

This is from labwork experiments. I have no background in mathematics. We have an experimental setup that measures the levels of two targets: The Reference (R) and the target of Interest (I). We are interested in the ratio I/R. For healthy individuals we know this ratio to be precisely 1. For...

Here is a setup that only uses fixed detectors. Will the ratio between the number of detections at D0 and the sum of the numbers detected on D1 and D2 be close to 1? For this question instead of the coincidence counter, 3 simple counters are needed. Also the detectors D1 and D2 need some lenses...

Hello, I was doing some research on enthalpy of water-ethanol mixtures at different ratios, and when looking at all the information graphed, I don't understand why it produces the trend line it does. Why doesn't it produce a 'quadratic' trend line? Shouldn't having a 10:90 water-ethanol exert...

Hi, I'm undergraduate researcher and my professor is interested in the answer to this question. He's kind of left me in the dark on why this is important to us, but that is another matter. We want hadrons that are produced at LHC conditions and decay before reaching the detector. So far all...

Sun produces neutrinos by sundry reactions: p+p→d+e++νe - called "pp" p+p+e→d+νe - called "pep" 3He+p→α+e++νe - called "hep" 3He+p+e→α+νe - never mentioned. What should it be called? "Heep"? Now, heep neutrinos should form a sharp line at a quite high energy. What is the intensity of heep line...

It is commonly known that the solution to the brachistochrone problem is a cycloid. However, in order for a solution curve to be a cycloid, the ratio between points A on the y-axis and B on the x-axis has to be r/pi*r, since that is the ratio between the "height" of the cycloid and half of its...

So I have been looking into efficiency, My system is high radius with the motor located outside. This motor is small, and thus the gear being driven by the motor, is also small for space requirements. I have wanted to use a ratio of about 22:1 to make this system, and everything seems to work...

Hi guys. We're on a new topic in math now which has to do with ratios and proportions but with scaling. A few questions I have are How can I express the following scales in ratio? 1/2" = 1" 1/8" = 1'0" Also we're doing a Job and Drawing scale A dimension on a job is 24 in. Using scale...

I'm trying to calculate the required gear sizes for the system shown below: The driven wheel is connected to a 600mm diameter bicycle wheel and the driver wheel connected to a 580 mm long lever arm which has a forward driving force of 40 N. I want to calculate the most efficient sizing of...

In a recent election, the ratio of the number of voters for the Purple Party to the number of voters for the Pink Party was 15:16 and the Pink Party won the election. Had 300 more people voted for the Purple Party and 200 fewer people voted for the Pink Party, the ratio would have been 11:10 and...

Homework Statement A person has come to a world full of pets. He notices right away that dogs are the most prevalent of all pets. But that's not all. He notices these 8 ratios: Dog:Cat = 5:1 Dog:Rodent = 1:5 Dog:Lizard = 1:3 Dog:Snake = 2:1 Dog:Turtle = 1:3 Dog:Alligator = 3:1 Dog:Crocodile =...

Homework Statement The number density of 1H nuclei in the body is roughly 600 times greater than that of 13C nuclei. By what factor is the magnetisation M0 of 1H greater than 13C in the same external magnetic field? Homework Equations 3. The Attempt at a Solution [/B] Surely it can't be as...

Homework Statement The question states to find the primary trig ratios for (7π)/4 Homework EquationsThe Attempt at a Solution I got sin= (-√2)/2 cos=(√2)/2 tan= -1 csc= 2/(-√2) sec= 2/(√2) cot= -1 I got all of them correct except for csc and sec, and I am unsure why the solutions are telling...

Homework Statement The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below: What is the ratio of their inertias? Homework Equations the ratio i am looking for is mB/mA The Attempt at a Solution I believed that the ration was 1/2 however that is not...

Homework Statement A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P. Angle p is on the same line as the 90 degree angle and I found out that it must be sine. Homework Equations sine = opposite/hypotenuse The Attempt at a Solution sin p = 11.8/13.5 sin p =...

Homework Statement A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...

Hello! I'm having some trouble understanding stress and strain rations in sheet metal forming. I understand that they're constants, but how do you calculate them? Or are they usually given? Thank you!

Homework Statement Branching ratios of tau lepton decay: hadrons 66% muon 17% electron 17% Use your knowledge of the decay of W bosons to justify these rates. Homework EquationsThe Attempt at a Solution [/B] The W+ boson can decay to any combination of quarks with +1 charge, but the CKM...

To make it useful for any angles. I need a good explanation for this.

The gear ratio is the ratio of angular displacement, angular velocity, angular acceleration, torque etc of the input with respect to output. However, I would like to know that which of these variables will be scaled exactly to the gear ratio in reality, as there might be some friction in the...