Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [ratio]

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

3
votes
3answers
1k views

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 ...
0
votes
1answer
289 views

Relationship of aspect ratio to the homography matrices between a rectangle and an arbitrary quadrilateral

I've been reading everything I can on the perspective mapping between a 2D rectangle and the projection onto the plane in 3D space of a rectangle. I've learned that any such quadrilateral resulting ...
0
votes
1answer
221 views

Alligation or mixture [closed]

A vessel is filled with liquid,3 parts of which are water and 5 parts syrup.How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? ...
2
votes
3answers
2k views

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 \...
85
votes
8answers
14k views

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 ...
1
vote
2answers
637 views

Ratio of sines given, find ratio of cosines?

Is it possible to find $\displaystyle{\cos x \over \cos y}$ if $\displaystyle{\sin x\over \sin y}$ is given? If so, how would one approach this problem? Thank you in advance!
-2
votes
1answer
127 views

Ratios of Four Numbers That Total 1285 [closed]

The sum of 4 numbers is 1285. The ratio of the first to second is 2:3. The ratio of the second to third is 4:5. The ratio of the third to fourth is 5:6. Find the third number. I had absolutely no ...
1
vote
2answers
537 views

Interpolating Between 2 Angles

I'm trying to understand how this works, and mathematically I'm having difficulty. Given 2 angles between $(-2\pi, 2\pi)$: $\theta$ and $\phi$ I want to interpolate between them by the ratio: r. My ...
1
vote
3answers
2k views

What is the difference between ratio change vs percent change ? (finance question)

I had a question which asked us to calculate the percentage decrease in operating income between years 2012-2013 and wanted us to predict the decrease rate for the next year. When I calculated the %...
-1
votes
3answers
802 views

How to get ratio of a,b,c from 2 equations in a,b,c

I have 2 equation in terms of $a,b$ and $c$ . $3a + 10b + 5c =0$ and $4a + 6b + 2c =0$ I need to find a:b:c and answer is $\dfrac a5 = \dfrac {b}{-7} = \dfrac {c}{11}$ I want to know how to get ...
4
votes
2answers
107 views

How is the Radius of Convergence of a Series determined?

Consider $$\sum_{n=0}^{\infty}\frac{(-1)^nx^n}{(n+1)^2}$$ which by the ratio test the ratio of two consecutive terms converges to $|x|$ as $n\rightarrow \infty$ and has a radius of convergence equal ...
2
votes
3answers
390 views

Find ratio / division between two numbers

I am reverse engineering custom software for a stepper motor. The original software eases in and out of any motion, and the duration of the ramping up to speed is directly related to the speed that ...
1
vote
1answer
119 views

What will be quantity of wine at the end in the vessel?

There are two vessels containing 12 liter of water the other contains 6 liters of wine respectively.One liter of mixture was taken out from each vessel and poured into the other and if this process is ...
0
votes
2answers
845 views

solve ratio word problem without algebra

Four gallons of yellow paint plus two gallons of red paint make orange paint. I assume this makes six gallons. So the ratio is 4:2, or 2:1. Question: how many gallons of yellow paint, and how many ...
4
votes
5answers
2k views

Math Behind Creating a “Perfect” Star

I am busy looking to create star paths in my app, and I was wondering how to determine the ratio between the inner radius and the outer radius of the points of a star so that the star has "straight" ...
1
vote
2answers
304 views

Can a graph with 3 vertices have a ratio greater than 1 of edges to vertices

A graph with three vertices has a beta index no greater than 1. A beta index of a graph is the ratio of number of edges to the number of vertices. The answer key says true but I think it's false. If ...
1
vote
1answer
85 views

Difficulty in proving a result

If $\frac{ay-bx}{c}$ = $\frac{cx-az}{b}$ = $\frac{bz-cy}{a}$ , prove $\frac{x}{a}$= $\frac{y}{b}$ = $\frac{z}{c}$. My attempt: $\frac{(ay-bx)z}{cz}$ = $\frac{(cx-az)y}{by}$ = $\frac{(bz-cy)x}{ax}$ ...
1
vote
1answer
375 views

Normal Ratio Distribution with CDF Method

I think I'm missing something glaringly obvious here that's causing problems for me in the entire subject. I have two independent standard normal random variables, X and Y ~N(0,1), and I need to find ...
1
vote
2answers
865 views

Distribution of ratio of uniform and exponential random variables

This is a homework question, I feel like I'm doing it right, but I can't seem to get the answer to match up. I have a uniform RV from 2 to 4, and an exponential with mean 4, so $X \sim \text{UNI}(2,4)...
0
votes
2answers
45 views

Ratio of money distributed among friends [closed]

Some money (dollars) is divided among friends A,B and C in the ratio of 5:6:9 After A gives fifty dollars to his mother, the ratio becomes 3:4:6 Find the amount of money A has after giving fifty ...
0
votes
2answers
22 views

Given a ration x:y, make it to ratio of 1:1 or 3:4 or 4:3 by only adding some values to x or y or both.

This problem is related to programing, for which I am searching an optimal solution. Problem: I have some images in different height to width ratios. I want to make them in ratios of 1:1 or 3:4 or 4:...
0
votes
1answer
3k views

How to calculate a distance with different fraction ratios?

This is the math question for my sixth grader son. The answer is $136$ meters but could not figure it out. Can someone please explain how to solve it. Thank you. Adam first walks $3/8$th of a road. ...
-1
votes
1answer
91 views

alligation and mixture concept clarity [duplicate]

i want to clear my concept of alligation. a vessel is filled with liquid, 3 parts of which are water and 5 parts are syrup. how much of the mixture must be drawn of and replaced with water so that the ...