Activity for msh210
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #286991 |
Yes, precisely so. (more) |
— | over 2 years ago |
| Comment | Post #286991 |
If your order is 54321 and you pick book 2 from the fourth spot, you'll put it back in the second spot, yielding 52431. (more) |
— | over 2 years ago |
| Comment | Post #286991 |
Obviously for $n=2$ the maximum is $1$. It's not much harder to see that for $n=3$ the maximum is $3$ (just go through the cases). I ran a script to pick books at random repeatedly so I don't know for certain that I found the maximum, but the highest number I got was $7$ for $n=4$ and $15$ for $n=5... (more) |
— | over 2 years ago |
| Edit | Post #286991 | Initial revision | — | over 2 years ago |
| Question | — |
organizing a library Suppose you have $n>1$ books lined up on a shelf, numbered $1$ to $n$, not in the correct order, and you wish to put them in order. Here's your method: Choose a misplaced book[1] at random, and put it in its correct spot. For example, if $n=5$ and you pick book number $2$ out of spot number $4$, ther... (more) |
— | over 2 years ago |
| Comment | Post #286150 |
[cross-posted](https://math.stackexchange.com/q/4412172) (more) |
— | over 2 years ago |
| Edit | Post #286150 | Initial revision | — | over 2 years ago |
| Question | — |
equilateral triangle inscribed in an ellipse A high-schooler I know was given the following problem: > In the ellipse $x^2+3y^2=12$ is inscribed an equilateral triangle. One of the triangle's vertices is at the point $(0,-2)$. Find the triangle's other vertices. The book has one answer: $(\pm1.2\sqrt3,1.6)$. But I know of two more answers... (more) |
— | over 2 years ago |
| Edit | Post #286140 |
Post edited: |
— | over 2 years ago |
| Edit | Post #286140 |
Post edited: |
— | over 2 years ago |
| Comment | Post #286140 |
[cross-posted](//math.stackexchange.com/q/4409542) (more) |
— | over 2 years ago |
| Edit | Post #286140 | Initial revision | — | over 2 years ago |
| Question | — |
Finding distance to parabola's focus, given some points A high school student I know has the following problem: > A parabola is given by $y^2=2px$ with $p>0$. The point $D$ is on the parabola in the first quadrant at a distance of $8$ from the $x$-axis. > > 1. Find the distance of $D$ from the directrix of the parabola, in terms of $p$. > > We dr... (more) |
— | over 2 years ago |
| Edit | Post #284709 |
Post edited: |
— | about 3 years ago |
| Edit | Post #284709 | Initial revision | — | about 3 years ago |
| Question | — |
ratio of partial sums of the same geometric sequence My kid was given this question: > In a geometric sequence, the proportion of (the sum of the first $12$ terms) to (the sum of the first $8$ terms) is $\frac{819}{51}$. Find the common ratio of the sequence. The only formula thus far covered for the partial sum of a geometric sequence $(a1qi){i\ge... (more) |
— | about 3 years ago |
| Comment | Post #281724 |
@r~~ oh good point. Yes, I think so, actually. (more) |
— | over 3 years ago |
| Edit | Post #281724 | Initial revision | — | over 3 years ago |
| Question | — |
proving relative lengths on a secant My kid was given this question. (Well, my statement of it actually includes some results that my kid had to find in previous parts of the question.) > Triangle $ABC$ is equilateral. $D$ is the middle of side $\overline{BC}$. $AD$ is the diameter of a circle centered at $O$. $\overline{AC}$ meets the... (more) |
— | over 3 years ago |
| Edit | Post #281723 | Initial revision | — | over 3 years ago |
| Answer | — |
A: difference between quotient rule and product rule > is it OK to use Product rule instead of Quotient rule in University and Real Life? Sure. For whatever reason, I long had a hard time remembering the quotient rule, and instead used the process you describe. (more) |
— | over 3 years ago |
| Comment | Post #280462 |
Yes, @celtschk . (more) |
— | almost 4 years ago |
| Edit | Post #280462 | Initial revision | — | almost 4 years ago |
| Answer | — |
A: What surface do I get by attaching $g$ handles as well as $k$ crosscaps to a sphere? > My question is, what happens if I attach a handle and a crosscap to a sphere? By Dyck's theorem, the connected sum of a torus (sphere with one handle) and a projective plane (sphere with a cross-cap) is the same as the connected sum of three projective planes. So you get the sphere with three cr... (more) |
— | almost 4 years ago |
| Comment | Post #280204 |
Thank you for the comment! (more) |
— | almost 4 years ago |
| Comment | Post #280204 |
Out of curiosity, once he shows $\mathcal M$ is the identity, how does he complete the proof? (more) |
— | almost 4 years ago |
| Edit | Post #280064 | Initial revision | — | almost 4 years ago |
| Question | — |
Why always rationalize a denominator? Schoolteachers will insist that their students present answers to problems with rational (indeed integral) denominators. Never $1/\sqrt3$, for example, but instead $\sqrt3/3$. That's also how math textbooks present answers. I understand why it's important to learn how to rationalize a denominator, wh... (more) |
— | almost 4 years ago |
| Comment | Post #279044 |
-1. "Using solely the original meaning of 'unless' below" is a restrictive condition you've added in for no apparent reason. (more) |
— | about 4 years ago |
| Comment | Post #279026 |
This sounds almost like the small inductive dimension. (more) |
— | about 4 years ago |
| Comment | Post #278872 |
@TripleFault I don't think it would be appropriate to edit your question post to include that proof. After all, you asked whether your proof was good, I gave a good answer. If you now edit your question to make my answer nonsensical, that's unfair to me (making me look foolish) and to readers (making... (more) |
— | about 4 years ago |
| Edit | Post #278872 | Initial revision | — | about 4 years ago |
| Answer | — |
A: Proving the Equation of the Pencil of Two Intersecting Circles The proof is not quite correct. I mean, it's correct as far as it goes, but all it proves is that the curves $\lambda C1+\mu C2=0$ are contained in the desired pencil. You haven't proven that every circle that goes through your two points is of the form $\lambda C1+\mu C2=0$. (more) |
— | about 4 years ago |
| Comment | Post #278724 |
What browser? I find the same happens in Chrome on my Android device but not in Chrome on Windows. (more) |
— | about 4 years ago |
| Edit | Post #278697 | Initial revision | — | about 4 years ago |
| Answer | — |
A: Equation of a line given some parametrized points on it and an area Because $(6,6)$ is on the line, we have the slope $\frac{6-0}{6-b}=\frac{6-2a}{6-a}$, which simplifies to $3a+3b=ab$. We already know that's $48$ so $a+b=16, ab=48$, and thus $\lbrace a,b\rbrace=\lbrace4,12\rbrace$. This gives two possibilities for where $A$ and $B$ are; finding the respective equati... (more) |
— | about 4 years ago |
| Edit | Post #278696 | Initial revision | — | about 4 years ago |
| Question | — |
Equation of a line given some parametrized points on it and an area My kid has this question for homework: > A line passing through the point $(6,6)$ crosses the line $y=2x$ at the point $A$, and the $x$-axis at the point $B$ (the $x$-coordinate of $B$ is positive). Find the line's equation if the area of the triangle $ABO$ is $48$ ($O$ is the origin). If we s... (more) |
— | about 4 years ago |
| Comment | Post #278647 |
These may help: https://doi.org/10.1007/11615798_4 , https://arxiv.org/abs/math/0407300 (more) |
— | about 4 years ago |
| Edit | Post #278419 | Post edited | — | about 4 years ago |
| Suggested Edit | Post #278419 |
Suggested edit: difference not modulo (more) |
helpful | about 4 years ago |
| Comment | Post #278338 |
Your alternative proof for the problem my kid had is a good one, and is probably the one intended by the problemsetter. Thank you! (more) |
— | about 4 years ago |
| Edit | Post #278337 | Initial revision | — | about 4 years ago |
| Question | — |
Similar triangles with the same area My kid was assigned this problem: > Given > > line segments ADB, AEC, COE, and BOE; > > $\overline{AC}\cong\overline{AB}$ and $\angle B\cong\angle C$. > > Prove (a) $\overline{CE}\cong\overline{BD}$ and (b) $\overline{OB}\cong\overline{OC}$. (I apologize for the ugly sketch. ... (more) |
— | about 4 years ago |
| Comment | Post #278174 |
@Moshi https://www.w3.org/Provider/Style/TITLE.html (more) |
— | about 4 years ago |
| Edit | Post #278174 | Initial revision | — | about 4 years ago |
| Question | — |
Page title with math looks very wrong. When someone includes $\TeX$-like math between dollar signs (`$`) in a title, the title renders nicely but the HTML title renders raw (with the dollar signs and all). The latter is terrible for readability — and, I assume, screenreaders. This affects, presumably, wherever the HTML title appears... (more) |
— | about 4 years ago |