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Questions tagged [ratio]

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

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Find the ratio of the area of ​the triangle $PRQ$ ¸and the area of ​the triangle $ETA$

the problem On the side $BC$ of the triangle $ABC$, the points $D$ and $E$ are considered such that $BD = DE = EC$. Let $M$ the middle of the segment $AD$, $BM ∩ AE = {P}, CM ∩ AE = {Q}$. $RM$ ¸and $...
Pam Munoz Ryan's user avatar
1 vote
0 answers
51 views

Finding the general convolution of probability function with hypergeometric PDFs.

I am trying to find the generalized convolution of this PDF distribution. $$f(n, \sigma; v)= \frac{2^{\frac{3}{2}-\frac{n}{2}} \sigma ^{-n-1} v^\frac{n - 1}{2} K_{\frac{ n - 1}{2}}\left(\frac{v}{\...
DysonSphere's user avatar
0 votes
0 answers
28 views

Reference for the lemma that, given $0<A<180^\circ$, function $f(x)=\frac{\sin x}{\sin(A-x)}$ is injective for $0\leq x\leq A$

There is a geometry lemma used in my mathematical community which states: Given an angle $A$, $0 < A < 180^\circ$, the function $$f(x) = \dfrac{\sin(x)}{\sin(A-x)}$$ is injective, for $0 \leq x ...
TheSega's user avatar
  • 27
4 votes
2 answers
121 views

Understanding this ratio trick

Two numbers are in the ratio $3:5.$ If $9$ is subtracted from each, they become in the ratio $12:23.$ Find the smaller number. Solution Let's denote the two numbers as $3x$ and $5x$. According to the ...
vj Maths's user avatar
-1 votes
2 answers
29 views

What would be the best position in pick order when picking a card out of a bowl with one bad card? [duplicate]

Let's say there are 10 people, and each person has to pick a random card out of a bowl consisting of 10 cards; 9 good ones and 1 bad one. I was wondering what position to pick a card from the bowl ...
DVD Music's user avatar
0 votes
1 answer
23 views

Efficiency of ratios

Suppose we have a computer application and we want to calculate the influence of the frequency in the final runtime. If this application is executed at 2 GHz this takes 1000s, whereas if the ...
Manolete's user avatar
  • 165
2 votes
1 answer
57 views

Linear coupled recursive relations and finding the limit of the ratio

Let $a_0,b_0$ be any two positive integers. Define $a_n,b_n$ using the relations: $$a_n=a_{n-1}+2b_{n-1}, b_n=a_{n-1}+b_{n-1} \forall n \in N$$ Find: $$\lim_{n \to ∞} \dfrac{a_n}{b_n}$$ My attempt: I'...
Cognoscenti's user avatar
0 votes
0 answers
21 views

Converting ratio with range [0<x<inf] to range [-inf<x<inf]

I am creating some statistics, one of them is a ratio of positive integers, each in range [0<x<inf]; the ratio takes on the same range. I am interested in using a formula to convert such a ratio ...
JLosc's user avatar
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0 votes
2 answers
48 views

Proof for $\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = \frac{\sqrt{x^2 + y^2 + z^2}}{\sqrt{a^2 + b^2 + c^2}} $ [closed]

My teacher used this relation to prove another result, but I can not seem to wrap my head around it. $\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = \frac{\sqrt{x^2 + y^2 + z^2}}{\sqrt{a^2 + b^2 + c^2}} $ ...
Is_this_my_username's user avatar
1 vote
1 answer
47 views

Why is a resolution of portrait mode 480 x 640 described as 4 : 3 instead of 3 : 4?

As I've read that: The aspect ratio of an image is the ratio of its width to its height. For instance, if a rectangle has an aspect ratio of 2:1, then it is twice ...
Z0q's user avatar
  • 113
1 vote
1 answer
76 views

Sharing of profit in a partnership

I have two theories and I was pondering on what basis we are choosing one over the other. Let me take specific example and describe the two theories and any discussion in this regard would be helpful ...
Yathi's user avatar
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0 votes
0 answers
26 views

Given the direction cosines of two mutually perpendicular lines, show the direction cosines of the lines perpendicular to the above two lines are:

I just want to ask that if it is written two equations of relations of l, l1, m, etc. How did he write it in that ratio or fractional form like l upon something and m upon something etc and made it ...
seven65ive's user avatar
0 votes
0 answers
15 views

Mean and variance when sampling temporal rates

I having some trouble understanding how mean and variance are be used in sampling rates and temporal rates (per unit of time). Example If I eg. wanted to evaluate car crashes per hours driven I would ...
Adam Andersson's user avatar
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0 answers
20 views

Adjusted nominator for a more reflective ratio change

Two variables change every year, e.g. $a_1=500$, $a_2=600$ and $b_1=1000$ and $b_2=800$. Their ratio change is $$YoY=a_2/b_2-a_1/b_1=600/800-500/1000=0.25$$ The negative change in the denominator is a ...
balintd's user avatar
0 votes
0 answers
14 views

Ratio Scale transformation

I am in a pickle, and I would genuinely appreciate it if you could guide me. I spent 2 years to find a way to develop a ratio scale, and I did it; however, it cannot be used the way it is. The scale ...
Parham's user avatar
  • 1
-1 votes
1 answer
115 views

Mixture of wine and water [closed]

I'm new here, so kindly bear with me if this question is too trivial for the forum. I tried working it out but to no avail. A solution contain wine and water in ratio 2:1. Out of it 36 litre solution ...
user avatar
1 vote
1 answer
50 views

Find the best ratio between grid size and the square size

Let's say I have a bunch of squares of side x and the grid of square sectors, each of side y. I am placing the squares randomly in this grid - the sides of squares are parallel to sides of the grid, ...
Amae Saeki's user avatar
1 vote
1 answer
76 views

Trend of median of ratios vs average of ratios

Suppose I want to create a daily trend of how people support 5 candidates for presidency. Per day across a month I have 20 small surveys. Randomly selected from the whole country . Instead of using ...
bilanush's user avatar
  • 433
3 votes
2 answers
45 views

Ratio test for power series with arbitrary terms?

im goin through Petersons, Kelleys Difference equations textbook and in one exercise following idea appeared. $a_k$ is coefficient of power series. “Returning to the difference equation, we have $\...
anddrypv7's user avatar
0 votes
1 answer
57 views

On Ratios in Isosceles Triangles

It is known that the formula for the perimeter $P$ of an isosceles triangle on a plane is $$P=2L+B$$, where $L$ is the length of the leg and $B$ is the length of the base. Now, let us study some ...
Michael Ejercito's user avatar
7 votes
3 answers
435 views

Ratios of lengths in a triangle

Problem I'm trying to solve: My Attempt: To be honest, I don't have any clue on how to solve it and the method I'm about to give is severely overcomplicated. We first isolate triangle $\triangle BEG$ ...
d0uble_a_b4ttery's user avatar
0 votes
0 answers
56 views

Direct and Indirect relation concept

Que - 100 million bacteria can completely decompose a garbage dump in 15 days and 60 million bacteria can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump ...
Anuraj's user avatar
  • 3
0 votes
2 answers
61 views

How to find Radii of Convergence for power series with alternating 0s

I was working on finding the Radius of Convergence of $\cosh{x}$, which is $1 + \frac{x^2}{2}+ \frac{x^4}{24}+ \frac{x^6}{720}+ \frac{x^8}{8!} + \cdots$. The radius of convergence can be found with $\...
SupersonicMan12's user avatar
0 votes
0 answers
14 views

Compare positive and negative percentages

I know that is a very, very trivial question... But I'd be super thankful for any help. Lets say you have three values where each describes the velocity of a car. 50 kmh, 100 kmh, 150 kmh I just want ...
Lenn's user avatar
  • 103
0 votes
0 answers
48 views

Scaling that preserves the ratio between any two values

Is there a function $f$ such that for all $x$ (on a bounded domain): $f(x) \in [a,b]$ $r \times f(x) = f(rx)$ If it makes things easier, we can assume that $\forall x: x \geq 0$. Though a more ...
Dong Cao-Huu's user avatar
1 vote
0 answers
40 views

Find the limit of this series using the ratio test.

$a_n=\frac{c^n(n^2+3n+5)}{5^n(4n^n+3n+5)}$ where $c$ is a real constant Find the limit as $n \to \infty$ of this series. I’ve used the ratio test and written it in the form $\frac {a_{n+1}}{a_n} $ ...
Amy D's user avatar
  • 11
0 votes
0 answers
17 views

The mean and deviation of two sets with unequal lengths

I want to determine the mean and the deviation (e.g., mean squared deviation or mean absolute deviation) the ratio of two independent sets (J/K) with unequal lengths. J = {x_1, x_2, x_3} K = {y_1, y_2,...
mAthletic's user avatar
12 votes
3 answers
302 views

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 ...
Tobias Kienzler's user avatar
0 votes
1 answer
36 views

Calculating cold temp on mixing valve

I need a formula to calculate the cold temperature on a mixing valve system when given the hot temp, mixing percentage, and mixed temp. I can determine the hot and mixed temps with temp probes, but ...
Geo's user avatar
  • 37
0 votes
1 answer
36 views

Divided Diamonds : a proportionality & ratio problem

Problem For stones of the same quality (e.g. the same colour), the monetary value of a diamond is proportional to the square of its mass (i.e. $C\propto M^2$). Find the monetary loss ($\Delta C$) ...
burgler's user avatar
2 votes
2 answers
153 views

Constant area and ratio peculiarities regarding equilateral triangles.

I'm just writing this problem out of curiosity, so let me know whether I make any mistakes. FYI this problem was inspired by the 1998 AIME problem 12. Also, if you have a better name for this question,...
crxyz's user avatar
  • 356
1 vote
1 answer
41 views

relationship between proportions

consider some variables $x_1,x_2,y_1,y_2$ that are positive and for which $\frac{x_1}{y_1}=\frac{x_2}{y_2}=p$. Is it true that $\frac{x_1+x_2}{y_1+y_2}=p$?
user3761743's user avatar
-1 votes
1 answer
73 views

Absolute Convergence of a Series (maybe use ratio test) [closed]

Let $p:=\lim_{{k \to \infty}} k(1-|\frac{a_{k+1}}{a_k}|)$ Prove $p>1$ or $p=\infty \implies \sum_{n=1}^\infty a_n $ converge absolutely
John Frank's user avatar
0 votes
1 answer
41 views

Is Basic Proportionality theorem applicable to trapezium? [closed]

I was studying vectors and came up with this question Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their ...
Aanchal Jha's user avatar
0 votes
1 answer
54 views

Turning division by zero to zero with basic math operators

I need to compute $\frac{const}{y}$, where $y$ may equal $0$ to present PC state in a human-readable format from exposed internal registers. Is it possible to build an expression of basic math ...
Trudy's user avatar
  • 133
0 votes
0 answers
23 views

Contribution of a single value in a Division of Sums

I need to isolate contribution of a single entity in a Division of Sums as shown below. For example, find the contribution of variable a in the following: (a 1 + b ...
Maddy's user avatar
  • 101
0 votes
0 answers
18 views

Determine point from one aspect ratio to an equivlent aspect ratio

I am working on a code program and get the X and Y coordinates of my cursor. My aspect ratio is 1280x720 and a point I am using for an example is (710, 300) however my x and y values must be 0.0-1.0, ...
semiflourcesentpenguin's user avatar
0 votes
2 answers
65 views

Converting a ratio into percentage.

As per many websites and text books, 3:4 converted into % is 75%. But as per my understanding, its not. If 3:4 is the ratio of boys and girls in a class, then it means that 3 out 7 are boys and 4 out ...
Nidhi Mittal's user avatar
0 votes
0 answers
35 views

Ratio of two Jensen's Inequality

I have these pair of numbers $ (a, b) = (\frac{4}{9}, \frac{1}{9}) $ and $(c, d) = (\frac{1}{2}, \frac{1}{6}) $. (Number mean nothing, just for illustration and simplification) Note that - (a, b) are ...
Elina Gilbert's user avatar
2 votes
2 answers
91 views

formula for reducing (as little as possible) one or both sides of a rectangle to match a given aspect ratio

I am writing a small program (for personal use). In the program, I need to be able to give a base ratio (such as 16:9), take a rectangle (such as 2048 x 1536), and reduce one or both sides of the ...
apex2022's user avatar
  • 123
1 vote
1 answer
78 views

Algorithm for allocating whole gold bars amongst thieves by % share of the booty

I have N big gold bars and 1 small gold bar equivalent in weight to some fraction x of a large bar. E.g N = 10 and x = 0.5 then I have 10.5 large bars worth of gold, in 10 large bars and 1 small bar I ...
Greedo's user avatar
  • 201
0 votes
1 answer
23 views

Find the ratio of recursive integrals

Given $ I_n = \int_0^{\pi/2} \sin^n\theta d\theta $, the recursive formula can be found as $$ I_n = \frac{n-1}{n}I_{n-2} $$ The lecture notes later state that $$ \frac{I_{2n-1}}{I_{2n+1}} = 1 + \frac{...
tudou's user avatar
  • 3
0 votes
1 answer
173 views

Find the ratio of the perimeter of a square and of a triangle.

Problem: Let the square $ABCD$ be on the side $l$ and the points $E$ and $F$ on the sides $BC$ and $CD$ respectively so that $\angle EAF= 45$. Find the ratio between the perimeter of the square and ...
IONELA BUCIU's user avatar
0 votes
1 answer
264 views

TV aspect ratio

I am working through "Geometry" by McDougal Littell. Doing self study. There is a problem that has me stumped: A standard 27 inch analog television screen has an aspect ratio of 4:3. Use ...
Frank S's user avatar
0 votes
1 answer
154 views

If you need 3:2:1 ratio of X,Y,Z to make a something, doesn't that mean you need 6 units:4 units:2 units to make two units of that thing?

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of ...
user avatar
-2 votes
1 answer
59 views

Algorithm to make every number in a set positive but keep the ratios between them?

I don't know what tags to use for this question so if I am using the wrong ones, please suggest others. I have a set of numbers (ex: -20, -3, 5, 8, 30). I need to ...
Almost Aiming's user avatar
1 vote
0 answers
37 views

Finding the fraction for a given segment by only knowing its ratio.

I'm studying analytic geometry in Khan Academy and I'm struggling at dividing segments when given ratios like 1:3, 5:6, 2:1 and finding their fractions. According to what I read and learned from them ...
twelve tone music enjoyer's user avatar
3 votes
1 answer
91 views

Jigsaw puzzle ratio question.

I was doing a puzzle when this question popped into my head: Assuming a puzzle had an equal amount of pieces in each row, and an equal amount of pieces in each column, what would be the least amount ...
zurtle's user avatar
  • 31
1 vote
2 answers
90 views

Finding $x:y:z$ when $\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$. What is the reason for this peculiar behaviour in the equations?

I am solving this old book and this question is really interesting. Suppose $$\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$$ We are asked to find $x:y:z$ Now here is what I've done. Suppose all of this ...
Priyanshu Kalal's user avatar
0 votes
1 answer
39 views

Expressing ratios verbally

$\frac{1}{3}$ of angels are demons, and $\frac{2}{3}$ are good angels. Does this mean there are: $2$ good angels for every $1$ bad angel(∵ $2+1=3$ total angels, but this ratio seems to be $1:2$ not $...
Geremia's user avatar
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