Questions tagged [ratio]
For questions concerning the ratio of a certain quantity to another.
1,128 questions
3 votes
1 answer
185 views
Is there really a difference between proportionality in algebra and geometry?
Sorry for the super basic question! While reading the chapter on similarity in my textbook, I found myself confused when trying to explain proportionality to myself. After some research, I put this in ...
- 33
1 vote
2 answers
176 views
Ratio between two investment results shrinks as stock price goes up-why is that
Imagine there are two investors-Mark and Jack. Mark's position in a certain security has an average cost per share of 66.67 USD and the total number of shares that Mark holds of this security is 150. ...
- 121
2 votes
5 answers
407 views
Concrete Definition for a Ratio
I had a question about ratios. I couldn't seem to find a rigorous definition on them. I understand the concept of fractions being numbers of the form a/b where a is divided by b (or a multiplied by 1/...
- 29
3 votes
2 answers
310 views
Ratio of the Area of Triangles
In the figure that follows, $BD=CD, BE=DE, AP=PD$ and $DG\parallel CF$. Find $$\dfrac{area(\triangle ADH)}{area(\triangle ABC)}$$ I figured $BE=\dfrac{BC}{4}\implies area(\triangle ABE)=\dfrac{area(\...
- 650
0 votes
1 answer
107 views
Ratio and proportion : dividing ratios
This is a ratio and proportion based question from my math book. There is something I can't understand in the second solution. "Dividing the ratios from (1) and (3), we get $\frac{b - c}{b + c}=\...
- 716
0 votes
0 answers
63 views
Closed-form solution to limiting ratio of matrix elements
I have a $3\times 3$ real matrix $A$, which is parameterised by $\alpha\in(0,2),\beta\in(0, 1)$ and $d\in\mathbb{N}$: $$ A = \begin{pmatrix} 1-2\alpha+(d+2)\alpha^2 & 2(1-\alpha(d+2)) & d+2 \\ ...
- 255
-1 votes
1 answer
78 views
Prove that exists a unique point dividing a segment in a given ratio
I'm looking for a proof that for each line segment and each given ratio there is a unique point on a segment that divides the segment in a given ratio from a given endpoint. I know a classic proof ...
- 157
5 votes
2 answers
493 views
Area of a Quadrilateral Formed by Intersecting Lines in a Triangle
Suppose $\triangle ABC$ has area $420 \text{ cm}^2$. Points $P$ and $Q$ are chosen on sides $AB$ and $BC$, respectively, so that $PQ$ is parallel to $AC$ and $\triangle AXC$ has area $84 \text{ cm}^2$,...
- 149
4 votes
2 answers
807 views
How to prove in general terms using trigonometry that the median perpendicular will divide the diagonal in such a ratio
The sides of a quadrilateral, taken in order, are equal to 2, 3, 4, and 5. In what ratio does the perpendicular bisector of the diagonal marked in the figure divide its other diagonal? $AB=2, BC=3, ...
- 370
1 vote
1 answer
86 views
Construct a rhombus under given conditions
I need to construct a rhombus $ABCD$ given that a line perpendicular to side $BC$ intersects diagonal $AC$ at point $M$ and its diagonal $BD$ at point $N$. The ratios $AM:MC = m:n$ and $BN:ND = p:q$ ...
- 157
1 vote
0 answers
93 views
The diagonals of convex $ABCD$ meet at $O$, and $F$ is on $AC$. Given $BO$, $DO$, $AC$, and the ratio of areas of $ABCD$ and $FBC$, can we find $AF$?
Here is the problem I'm solving. Is there even a general solution? The diagonals of a convex quadrilateral $ABCD$ intersect at point $O$. Point $F$ is placed on diagonal $AC$. Given $BO = a$, $DO = b$...
- 157
5 votes
1 answer
162 views
Does the ratio of a generalized circle's circumference to its area have a minimum between $2$ and $\infty$?
The equation for a generalized circle in Cartesian coordinates is $$|x|^n + |y|^n = |r|^n$$ where $r$ is the radius of the circle. The parameter $n$ dictates how "circular" the circle is -- ...
- 2,386
0 votes
0 answers
49 views
Is the character of basic probability arithmetic logically determined or a convention?
Probability is, classically interpreted and in general at least spiritually, a division-centric way to relate outcomes we target to the totality of possible outcomes. If $40$ out of $70$ balls are ...
- 2,184
8 votes
1 answer
293 views
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 $C \ge 1$ ...
- 383
2 votes
5 answers
262 views
Why are positive and negative percentages not inverses? [duplicate]
I'm looking for an ELA10 / intuitive way to explain qualitatively (and perhaps even quantitatively), without an example but really conceptually (and without doing the corresponding math), why $+x%$% ...
- 39