Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

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4
votes
1answer
141 views

The no. of ways dividing a polygon with $n+1$ sides into triangular regions…

Please if any one can help me explaining this concept, I can't proceed further due to this.... Let $h(n)$ denote the no. of ways dividing a convex polygon region with $(n+1)$ sides into ...
2
votes
2answers
83 views

Difficulty understanding the solutions to $x'' = -\omega^2 x$

For some reasons involving physics, I'm supposed to consider the equation $x'' = -\omega^2 x$. Normally, I would say the solutions are of the form $x = A \cos(\omega t + \phi)$. But when $\omega = ...
1
vote
2answers
52 views

Damped simple harmonic oscillator, phase space

I want to calculate and draw the phase space trajectory of this damped harmonic oscillator: $$\ddot{x}+\gamma\,\dot{x}+\omega^2x=0$$ for the two cases $\gamma=2\omega$ and $\gamma=\omega$. I'm ...
4
votes
2answers
134 views

I have used Cauchy and Jensen. It is not helping me very much. Advice on solving this problem.

Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$ \frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $$ for each ...
1
vote
2answers
90 views

How to teach Critical Thinking

I am currently tutoring a few students in an entry level physics course and had some trouble recently when it comes to helping them with problem solving. The students I am helping don't have many ...
7
votes
4answers
243 views

100 sequential parking spaces

In my high school's math club today, we explored but did not solve this interesting problem: 100 autonomous robotic vehicles enter a warehouse in arbitrary order to park. Inside the warehouse, there ...
0
votes
1answer
73 views

How can I find x and z if: $\sqrt{(x-20)^{2} + (5-30)^{2} + (z-40)^{2}} = 100$ and $x \sqrt\frac{1}{6} + 5\sqrt\frac{1}{3} + z \sqrt\frac12= 0$?

How can I find x and z if: $\sqrt{((x-20)^{2} + (5-30)^{2} + (z-40)^{2})} = 100$ and $\left(x\times \sqrt\frac{1}{6} + 5\times \sqrt\frac{1}{3} + z\times \sqrt\frac{1}{2}\right) = 0$ ?
1
vote
4answers
34 views

How can one isolate x in a formula of the form:$ (x-20)^{2} = -(y-40)^{2} - 525$?

I am trying to isolate x in the equation $$(x-20)^{2} = -(y-40)^{2} - 525.$$ How can I do it?
1
vote
0answers
39 views

no. of regions a plane is divided into by $n$ lines in general position

My notes state the Counting process for knowing no. of regions a plane is divided into by $n$ lines in general position := Let $h_1(n)=$ No. of parts a line is divided by $n$ distinct ...
0
votes
2answers
31 views

Show that Mandelbrot set is contained within the closed disc of r=2 [closed]

Show that the Mandelbrot set is contained within the closed disc of radius 2 around the origin. How do I show this?
0
votes
3answers
35 views

How to solve $\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$

I have a problem with solving following equation: $$\left|\frac{1 + a + bi}{1 + b - ai}\right| = 1$$ (where $a$, $b$ are real numbers and $i$ is an imaginary unit) I tried to simplify its left side ...
0
votes
0answers
23 views

Bounded/Unbounded sets. [Mandelbrot set]

This is the last question from my assignment. For Part a I have: $z_{n+1}=z_n^2+c$ $\Rightarrow c =z_{n+1}-z_n^2$ $\Rightarrow |c|=|z_{n+1}-z_n^2|=|z_{n+1}-z_n^2||-1|=|z_n^2-z_{n+1}|$ ...
1
vote
1answer
29 views

Understanding $\Delta(\vert f \vert ^p)$ when $f$ is holomorphic, $p>0.$

Let $\Delta$ denote the Laplacian. I am trying to prove that if $f=u+iv$ is holomorphic on an open set $U\subset \mathbb{C}$ and $f$ is nonvanishing, then $$\Delta (\vert f\vert^p)=p^2\vert ...
1
vote
0answers
25 views

Solving N for HN=0, Given H is a special type of skew symmetric (n x n, n is a odd number) matrix.

Solving $N\ \mathrm{for}\ H \times N =0$, given $H$ is a special type of skew symmetric matrix $(n \times n, n\ \mathrm{is\ an\ odd\ number}\ n=2k+1)$, 0 on diagonal and 1, -1 in off-diagonal ...
3
votes
3answers
196 views

How does one spot an error in a math proof?

I hope this is not a dumb question but I truly would like to know: How do you know when a proof breaks down and when an error has occurred?
0
votes
0answers
66 views

Terence Tao's problem solution

Suppose you are trying to get from one end $A$ of a terminal to the other end $B$. (For simplicity, assume the terminal is a one-dimensional line segment.) Some portions of the terminal have moving ...
5
votes
1answer
79 views

When is the next palindrome?

Okay, this is more just for fun than anything else. I'm driving in my car today, (true story) and my odometer is about to hit $81,818$. So, being a math nerd and all, I immediately see the pattern ...
1
vote
0answers
27 views

Mathematical Rube Goldberg problem

Is there a book or website that has mathematical rube goldberg-style puzzles? In other words, puzzles that require you to compute something, then compute something based on that, and then iterate for ...
0
votes
2answers
40 views

Second Order Partial Differentiation

I don't have a clue on how to start this question. I have a feeling I will need to use the Clairaut's theorem: $f_xy=f_yx$ Can anyone advise?
1
vote
2answers
82 views

How to Think Better

I just took a quiz and am dumbfounded by my lack of insight. Consider what kind of idiot I'd have to be to do the following: Point A = (8,-15) and point B = (-8,15). P is the locus of points (x,y) ...
1
vote
0answers
58 views

Finishing a problem using equalities

This is my problem: Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$\frac{a^{n+2}}{a^n + (n-1)\,b^n} + \frac{b^{n+2}}{b^n + (n-1)\,c^n} + \frac{c^{n+2}}{c^n + ...
1
vote
1answer
29 views

Train distances leaving at certain times

A train leaves Boston to Fort Lauderdale traveling at $125$ mph. An hour later, another train leaves Fort Lauderdale traveling to Boston at a rate of $140$ mph. When the two trains meet each other, ...
0
votes
1answer
31 views

Number of Chess Moves that a piece is lost

Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you ...
4
votes
2answers
132 views

finding the difference of perfect squares

Find the difference between the smallest perfect square larger than one million and the largest perfect square smaller than one million. I did not want to use a calculator for this question. I ...
2
votes
0answers
57 views

Least sum of power of distances

Let $n$ points in a $3$-dimensional space. Find the point $X$ that minimizes the sum of distances $\|A_1X\|^q+ \|A_2X\|^q + ... +\|A_nX\|^q $ (where $q \in \mathbb{Q}$). Are there any general ...
0
votes
0answers
23 views

Criticise work with simple graphs & problem solving

So I'm studying graph theory at the moment and would like some constructive criticism or thoughts on my method. The problem can be formulated as follows. I'm looking for someone to verify my answer as ...
3
votes
1answer
61 views

Application of the Green-Tao theorem

I am currently trying to find some good exercises in analytic number theory, suitable for undergraduates. I have mentioned the Green-Tao theorem for arithmetic progressions of primes but I am ...
2
votes
1answer
29 views

Distinct elements in the Union and Intersection of A and B

Take a set $x$ with $10$ distinct elements. Rule: Everytime you have two subsets, $A$ and $B,$ you also have $A\cup B$ and $A \cap B.$ What is the maximum number of subsets you can have such ...
3
votes
1answer
60 views

How do I solve $x=\log^e{(x+1)}$ analytically?

How do I solve the following, analytically? $$x=\log^e{(x+1)}$$ It looks like it should be simple, but whether I take the $e$th root of each side or take the $\log$ of each side (ending up with a ...
1
vote
0answers
34 views

How to solve this Ricatti-like ODE

I have been trying to solve the following ODE \begin{equation*} \dfrac{d\pi}{dx}x=c_1+\pi(x) c_2 + \pi(x)^2(c_3-x), \end{equation*} where, for every $i=1,2,3$, $c_i$ is a constant real value. ...
0
votes
2answers
39 views

Lottery problem - Chance of 4 out of 5 balls matching?

In a lottery, an urn contains 40 balls that are numbered 1, 2, ..., 40. Each week, 5 balls are drawn from the urn without replacement. To enter, one chooses 5 numbers. Anyone who correctly predicts ...
4
votes
2answers
178 views

Least sum of distances

Problem: Let $A, B, C, D$ be points in a $3$-dimensional space. Find the point $X$ that minimizes the sum of the distances $AX+ BX + CX + DX$. Context: During a course, I was assigned a ...
0
votes
0answers
45 views

Setting up an integral for a physics question.

The problem begins like this: a charge distribution is given by $\rho(r,\theta,\phi)=\gamma r^3cos\theta,a<r<b,0\le\theta<\pi/2$ and is zero everywhere else. The distance from the origin is ...
1
vote
2answers
82 views

Solving equation involving binomial function

Solve for $x$ in terms of $i$ and $j$: $$ \binom{x}{i} = j $$ where $x$ is Real; $i$ and $j$ are Integers: $x \geqslant i$, $i \geqslant1$, $j \geqslant 0$. I came across this problem while trying ...
1
vote
1answer
40 views

What to do when a probability problem becomes unwieldy to check via simulation?

I am assuming that some probability problems cannot be solved easily since there may be a lot of cases to handle and it would make miscounting likely. However, some problems do not simulate well on a ...
1
vote
2answers
30 views

Curiosity - maximising a product with a constraint

I have integers greater than 4, for instance $i_1$, $i_2$, $i_3$, ..., $i_n$. We have to change the greatest of these integers (for instance $i_1$ if they are ranked by descending order) by adding to ...
2
votes
1answer
50 views

Integral of $\frac1{\cos^n x}$

Hi guys I have already proven for an assignment that: $$\int\cos(x)^n dx=\frac{1}{n}\cos(x)^{n−1}\sin(x) + \frac{n-1}{n}\int\cos(x)^{n−2}dx$$ Now we have been asked to calculate ...
1
vote
1answer
66 views

Finding limits of two functions of two variables

Show using the definition of limit that $$\lim _{(x,y)\to(0,1)}\frac{x^2-y^2}{x^2+y^2} = -1$$ and $$\lim_{ (x,y)\to(0,0)}\frac{ (1-\cos(xy))\sin y}{(x^2+y^2) }= 0$$ Definition of limit: ...
1
vote
1answer
34 views

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?

What I tried was: (9P4)/3!*2! This gave me a wrong answer (since the answer is 626). I'm unable to make use of the hint provided in my book: "make cases". Any help would be appreciated. :)
1
vote
1answer
36 views

how to write a differential equation for a problem like this

I've got a problem and i should solve it using differential equation.I don't know how to write the equation and start. A person is trying to fill a bathtub with water. Water is flowing into the ...
0
votes
2answers
29 views

replacing numbers to get final anser

I found this question in a random problem solving book that I was reading and wanted to know how you would solve it. I am not sure as how to go about this. Take any positive integer $n$ with fewer ...
3
votes
1answer
113 views

Limit of the sum of $\gamma_k(x)=xf((k+1)x)-\int_{(k+1)x}^{(k+2)x}f(t)\mathrm{d}t$

Let $f$ be a continuous, decreasing function, with $\displaystyle\lim_{x\rightarrow\infty}f(x)=0$. Let $\gamma_k(x)=xf((k+1)x)-\int_{(k+1)x}^{(k+2)x}f(t)\mathrm{d}t,\displaystyle x>0$. Let ...
0
votes
1answer
59 views

What is the probability the best case occurs? (Comp Sci Type Question)

I'm having trouble figuring out what's the probability the best case occurs? It's my first time bringing together probabilistic knowledge into computer science. The question goes as such. Consider ...
1
vote
1answer
30 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
1
vote
2answers
52 views

Problem Solving Question (Riddle)

this is my first time asking a question here, so sorry in advance if there's anything wrong with the format or place this is posted in. The problem I need to solve is written as the following: "Four ...
0
votes
0answers
24 views

Polynomial systems - conditions for real solution

I was working on the computation of equilibrium points for dynamical systems and arrived in the following system of $n$ polynomials in the variables $(x_1,\ldots,x_n)$ \begin{equation*} ...
3
votes
0answers
26 views

Iterations $n, n^n, (n^n)^{(n^n)},…$

(Note: I'm reposting this, as I posted the original too late in the evening to gain anyone's notice.) A contest problem (#2 on the 2010 Virginia Tech Math Competition) proffers the solver the ...
2
votes
1answer
54 views

Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
0
votes
3answers
42 views

Finding dimensions using quadratic formula

A 52 m long fence is constructed on three sides of a housing block with area 240 m^2. The fourth side facing the road is left open. Find the dimensions of the block. Also here's another question I ...
0
votes
1answer
25 views

Solving for x in equation for chem

In the answers to a chem problem is just gives this equation: (34.969) (x) + (36.966) (1 - x) = 35.453, and says solve for x. But I have no clue how to solve for x....