Activity for msh210‭

Type	On...	Excerpt	Status	Date
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 1 year 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)	—	about 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)	—	about 2 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)	—	over 2 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)	—	almost 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)	—	almost 3 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)	—	over 3 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)	—	over 3 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)	—	over 3 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)	—	over 3 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)	—	over 3 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)	—	over 3 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)	—	over 3 years ago