Mathematics

Questions tagged [ratio]

For questions concerning the ratio of a certain quantity to another.

In mathematics, a ratio is a relationship between two quantities indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, $8:6$, which is equivalent to the ratio $4:3$). The numbers compared in a ratio can be any quantities of a comparable kind, such as objects, persons, lengths, or spoonfuls. A ratio is written "$a$ to $b$" or $a:b$, or sometimes expressed arithmetically as a quotient of the two.

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Is there a size of rectangle that retains its ratio when it's folded in half?

A hypothetical (and maybe practical) question has been nagging at me. If you had a piece of paper with dimensions 4 and 3 (4:3), folding it in half along the long side ( once ) would result in 2 inches and 3 inches (2:3), which wouldn't retain its…
Pyraminx
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Evaluating $\left.\int_0^{\pi/2}\sqrt{1+\frac1{\sqrt{1+\tan^nx}}}\text dx \middle/\int_0^{\pi/2}\sqrt{1-\frac1{\sqrt{1+\tan^nx}}}\text dx\right.$

Evaluate the integral ratio $$\dfrac{I_1}{I_2}=\dfrac{\displaystyle \int_{0}^{\frac{\pi}{2}} \sqrt{1+\frac{1}{\sqrt{1+\tan^nx}}} \mathrm{d}x}{\displaystyle \int_{0}^{\frac{\pi}{2}} \sqrt{1-\frac{1}{\sqrt{1+\tan^nx}}} \mathrm{d}x}$$ Using…
V.G
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How is $\sin 90° = 1$ possible?

How can two angles of a triangle be equal to $90°$ ? If two angles were $90°$ , this would mean that the two sides would be parallel and the angle of the third side would be equal to 0 . Thus, there would be only two vertices and this wouldn't be a…
Sarvesh Thiruppathi
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Dividing a rectangle into 4 parts in the ratio 1:2:3:4, with only 2 lines

I have a rectangle made up of 30 identical squares (5 tall and 6 wide). By only drawing two lines on the rectangle, split the rectangle into 4 parts where the areas are in the ratio 1:2:3:4. How would one go around doing this? I tried for a solid…
Kevin fu
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Finding all possible proofs

I'm now working on a geometry problem I'll have to explain in front of my class this week (I'm in the $10^{th}$ grade). I've found so far some proofs, which might, nevertheless, be a bit complicated for my classmates (since they've barely worked…
Dr. Mathva
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Is $\sin n/\sin m$ irrational for nonzero integers $n\neq m$?

As shown in Is sin(x) necessarily irrational where x is rational? , the sine of any rational except for zero is transcendental. But what about the ratio of two such numbers, at least for integers? I thought about expanding $\sin n$ in terms of $\sin…
Tobias Kienzler
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How did they get this equation comparing three ratios?

I was reading from an old maths textbook. It was giving some examples on how to solve ratios. I stumbled upon this example and felt perplexed after reading only part of it. We're given this equation. $$\frac{x}{l(mb+nc-la)} = \frac{y}{m(nc+la-mb)} =…
ssharma
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Ratio of two binomial distributions

How to estimate $$ E\left[\frac{X}{X+Y}\right] $$ for two independent random variables $X\sim Bin(n,p)$ and $Y\sim Bin(m,p)$ ? Are there any connection with $\frac{n}{n+m}$ e.g., $1-\varepsilon\leq E\left[\frac{X}{X+Y}\right]/\frac{n}{n+m}\leq…
hiratat
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Is there a mathematical description of three-part ratios?

Rational numbers have many interpretations, but one of the simplest is as a ratio of one number to another. The fraction $1/2$ can be interpreted as the ratio 1:2 (i.e. one apple for every two oranges). Rational numbers are also considered an…
MathTrain
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Rates and Ratio work problem

I've encountered this problem It takes $60$ minutes for $7$ people to paint $5$ walls. How many minutes does it take $10$ people to paint $10$ walls. The answer to this one is $84$ minutes. However, How did it come up to this answer? can someone…
KyelJmD
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Is this a correct/good way to think interpret differentials for the beginning calculus student?

I was reading the answers to this question, and I came across the following answer which seems intuitive, but too good to be true: Typically, the $\frac{dy}{dx}$ notation is used to denote the derivative, which is defined as the limit we all know…
Ovi
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Maximizing a ratio of integrals

Let $a < b \in (0,1)$ and for $x \in [a,b]$ define $ \omega(x)= \begin{cases} b-x \text{ if } x \in [a,m]\\ x-a \text { if }x \in [m,b]\\ \end{cases} $ where $m=\frac{a+b}{2}$ . Let also $C \ge 1$ and $0 \le c \le 1$ . I am looking for the maximal…
Skywear
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Ratio. Number of sheep and chickens

At a farm, the ratio of the number of chickens to the number of sheep was 5:2. After the farmer sold 15 chickens, there was an equal number of chickens and sheep. How many chickens and sheep were there at the farm in the end? My work: Number of…
RukaiPlusPlus
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Ratio test with limsup vs lim

Could I prove that the ratio test still works using $\limsup(\frac{a_{n+1}}{a_n})$ instead of $\lim(\frac{a_{n+1}}{a_n})$? I think for $\limsup<1$ I could show that for $\epsilon>0, N>1 \limsup(\frac{a_{n+1}}{a_n})<1-\epsilon.$ From there I can…
sebastianross
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A dishonest shopkeeper claims he sells at cost but his 1 kg weight actually measures 800 grams when selling. Find his profit/loss %

This kind of question has been asked on the forum before as well, but the doubts I have regarding it are not being resolved by the answers provided in those threads hence posting this as a new question. The solution given in the book does as follows…
Fin27
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