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.

learn more… | top users | synonyms

-3
votes
0answers
18 views

Exponential problem for phase calculation. Find periodic t [on hold]

Given $e^{2At{\pi}i} = - e^{2{\pi}(A-149)ti}\text{, where }A = 42.58\cdot10^6.$ Find periodic $t$.
2
votes
4answers
353 views

SAT Maths Question About Fractions

Whilst revising, a problem caught my eye and I cannot seem to find an answer. I am usually bad at these types of questions. On a certain Russian-American committee, $\frac23$ of members are men, ...
1
vote
1answer
50 views

Kill the creeps with minimum cost

Oz plays popular ARTS Dota 2. Invoker is one of the favourite Oz's heroes. Oz's skills are not perfect yet, so he uses only two spells - SunStrike and Tornado. Each of these spells takes some mana ...
9
votes
2answers
151 views

Proving $\sqrt{2}(a+b+c) \geq \sqrt{1+a^2} + \sqrt{1+b^2} + \sqrt{1+c^2}$

I've been going through some of my notes when I found the following inequality for $a,b,c>0$ and $abc=1$: $$ \begin{equation*} \sqrt{2}(a+b+c) \geq \sqrt{1+a^2} + \sqrt{1+b^2} + \sqrt{1+c^2} ...
2
votes
5answers
201 views

Help With SAT Maths Problem (Percentages and Numbers)

I usually solve SAT questions easily and fast, but this one got me thinking for several minutes and I cannot seem to find an answer. Here it is: In 1995, Diana read $10$ English and $7$ French ...
15
votes
2answers
131 views

$xf(y)+yf(x)\leq 1$ for all $x,y\in[0,1]$ implies $\int_0^1 f(x) \,dx\leq\frac{\pi}{4}$

I want to show that if $f\colon [0,1]\to\mathbb{R}$ is continuous and $xf(y)+yf(x)\leq 1$ for all $x,y\in[0,1]$ then we have the following inequality: $$\int_0^1 f(x) \, dx\leq\frac{\pi}{4}.$$ The ...
0
votes
0answers
26 views

Movement of birds - Acceleration, Velocity, Time and Displacement. Needed for an assignment

Hi so there are a quandary of birds sitting on a tree.There are $3$ teams observing the movement of the birds. Team $1$ observes that on their first flight the birds move a short distance across a ...
-9
votes
0answers
43 views

Limit of a particular series [on hold]

Please help me find the limit of the following series: $$1+1+3/4+1/4+5/16+3/16+7/64+5/64+\cdots$$ this is simple prove for it 1111-22=11(101)-11(2)=11(101-2) =11(99) =(11^2)(3^2) =33^2
-6
votes
0answers
72 views

IMO 2015 Problem 3 [on hold]

Let $n$ and $k$ be positive integers. Prove that if $n$ is relatively prime with $30$, then there exist integers $a$ and $b$, each relatively prime with $n$, such that $\frac{a^2-b^2+k}{n}$ is an ...
4
votes
3answers
152 views

Numbers with 2015

I like to build math problems; to solve the one below I should first find a certain square and use it in my solution. I would want to know if anyone can solve this problem otherwise. Thanks. ...
0
votes
0answers
28 views

A little bit more difficult problem regarding rooted plane trees

A question regarding rooted plane trees bothers me. We know that the number of rooted plane trees with $n$ nodes equals to $n-{th}$ Catalan number, that is $|Tn| = Cn$. But what is this number if we ...
1
vote
3answers
46 views

Simplifying $\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$

Simplifying $$\Big[\dfrac{5-\sqrt{a}}{5+\sqrt a}-\dfrac{\sqrt a+5}{\sqrt a-5}+2\Big]^{-2}$$ When I try, the numerator cancels out to $0$, yet the answer sheet says $(25-a)^2/10000$. Where am I going ...
1
vote
1answer
21 views

Fitting the closest coefficients in a system of millions of simultaneous equations?

I don't really know the correct terminology to describe this, but let's say we have many values of $(x_n, y_n, z_n)$. Also let's say that our description of 'many' means that $i$ ranges from $1$ to ...
2
votes
4answers
66 views

Solving equations with $x^x$ on any given side [duplicate]

How would you solve such an equation if it's infeasible to just start trying different $x$ values? Example: $$x^x = 6.$$
1
vote
4answers
30 views

Inequality for sides and height of right angle triangle

Someone recently posed the question to me for the above, is c+h or a+b greater, without originally the x and y lengths. I used this method: (mainly pythagorus) $a^2+b^2=c^2=(x+y)^2=x^2+y^2+2xy$ ...
1
vote
1answer
31 views

Help Obtaining Numerical Approximation of Lambert W Solution

I am studying a particular generating function $$\frac{2e^x}{e^{2x}+1+2x}$$ and I thought I would try to solve the equation $$e^{2x}+1+2x=0$$ to determine for what value of $x$ if any the function ...
3
votes
2answers
64 views

Solve first order nonlinear differential equations

I want to solve this nonlinear 1-st order ODE, $$\frac{1}{1+x}=(\frac{1}{x-y}-\frac{1}{y})\frac{dy}{dx}$$ I find it non-separable, and Wolfram Alpha does not give me a closed form solution, but the ...
2
votes
0answers
63 views

Cognitive processes involved solving IMO level problems [closed]

I am currently 16 years old and, though I'm obviously not as good as most of the people on this site, I have always been considerably better than most of my classmates in mathematics. This, of course, ...
1
vote
2answers
41 views

Finding the missing length

How do i find the ST?? What more information do I need? I used Pythagorean theorem, but I still can't find the answer.
0
votes
2answers
30 views

Traveling salesman problem (TSP): what is the Relation with number of vertices and length of the found route?

I know that there are many algorithms (exact or approximate) which implement the traveling salesman problem. I would like to know the relation between the number of the vertices (i.e., the places to ...
2
votes
1answer
131 views

Aliens to the Moon

$N$ Aliens want to reach their Moon ($D$ meters away), but they can only put on each other, making a vertical chain. Every $Alien(i)$ has an height $X(i)$ and a lenght of their arms $Y(i)$. ...
0
votes
1answer
18 views

Compute a basic Side of two rooms, given total Area and total perimeter

My Gf's professor asked her to solve this problem: Two square rooms have an area of $52m^2$. The two rooms have a perimeter of 40 meters. Given this, we need to compute the length of the side of the ...
-2
votes
1answer
24 views

How long will it take for one of them or both of them?

One knight can storm a castle in 15 days. He and his partner can do it in 10 days. How long does it take the partner to storm the same castle alone? Pipe A can fill a pool in 5 hours, while pipe B ...
0
votes
1answer
61 views

The Area of shaded region in a circle

I'm having trouble solving this problem. I can't solve this. I don't know where and how to start. I don't know there is any formula for finding the area for this kind of shape, and if it did, I ...
1
vote
0answers
25 views

Essential singularity of c.c.(z)

According to my lecture notes, $z^*$ has an essential singularity (asterix denotes complex conjugate). However, it is not explained why nor at which point. Can anyone elaborate where the singularity ...
1
vote
3answers
62 views

$f(x)$ is a polynomial satisfying $2 + f(x)f(y)=f(x)+f(y)+f(xy)$, find $f(f(2)$), given $f(2)=5.$

If f(x) is a polynomial satisfying $2 + f(x)f(y)=f(x)+f(y)+f(xy)$, find $f(f(2))$, given $f(2)=5.$ ATTEMPT:- $f(f(2))=f(5)$, We can find $f(0)$,$f(1)$ and $f(1/2)$ to be $1,2$ and $5/4$ ...
2
votes
0answers
11 views

Is there a test for tractability of nonlinear differential equations?

After lengthy attempts at tackling the problem one might say that coming up with a closed form solution for a nonlinear differential equation is not possible - that the problem is intractable. But is ...
1
vote
1answer
36 views

Working with mathematical models, HELP.

I'm currently doing a lot of self study with mathematics. I live in The Netherlands and hope to be admitted to Leiden University somewhere in 2016. Now, I have encountered a problem in my workbook ...
1
vote
3answers
37 views

Find the interval on which $ x^{2} - \lfloor x \rfloor - 3 < 0 $ holds.

On what interval does the equation $ x^{2} - \lfloor x \rfloor - 3 < 0 $ hold? My attempt: I tried sketching the graph, but it’s a bit complicated. Is there any other approach?
3
votes
3answers
509 views

Result of solving an unsolved problem?

I was mulling over currently unsolved problems in mathematics (as I, and many others, find them quite interesting) and began to wonder what would happen if these problems were to be solved. I know ...
2
votes
2answers
219 views

Making change with prime-valued coins

Am I understanding this question correctly and how do I approach these problems? In Numberland, the unit of currency is the El (E). The value of each Numberlandian coin is a prime number of Els. So ...
2
votes
0answers
45 views

Is the matrix with these coefficients invertible?

Let $0 \leq x_{i-1} < x_i < x_{i+1} \leq 1$. Let $p, q$ be functions that depend on that such that $p$ is positive and $q$ is non-negative. Let $c_i = a_{i+1,i} = a_{i,i+1}$. Let all other ...
0
votes
1answer
53 views

How to solve problems in elementary number theory?

I have studied and solved almost all of Elementary Number Theory by David M. Burton. Yet, tough problems in NT from Olympiads seen unapproachable to me. What should I do? What should I study? I feel ...
1
vote
1answer
68 views

Is this special matrix invertible?

The symmetric, tridiagonal $n-$by$-n$ matrix with the elements $a_{ii+1} = a_{i+1i} $ and off-diagonals' absolute values equal to the diagonal (except for row 1 and row n) is invertible. The elements ...
3
votes
2answers
50 views

Find all solutions to $2x \equiv p \mod 3p$

Find all solutions to $2x \equiv p \pmod {3p}$. $p$ is prime, and $p > 3$. I found that this is equal to $2x = p(3k+ 1)$ for some $k \in \Bbb{N}$. Since $k$ can't be even, then we have $2x = ...
2
votes
0answers
43 views

On the second part of solution of a question due to Erdos

Problem. Let $a_1<a_2<\dotsb<a_n\le 2n$ be a sequence of positive integers. Then $$ \min [a_i,a_j]\le 6\left(\Big[\frac n2\Big]+1\right), $$ where $[a_i,a_j]$ denotes the least ...
2
votes
1answer
65 views

Find with proof all solutions to $2^n = a! + b!$, where $a$, $b$, $n$ are positive integers and $a \leq b$.

So far I have looked at $n=1$ with $a=1$ and $b=1$ which is $$2^1 = 1! + 1! = 2 $$ and $n=2$ with $a=2$ and $b=2$, $$2^2 = 2!+ 2! = 4$$ and finally $n=3$ with $a=3$ and $b=2$, $$2^3 = 3! + 2! = 8$$ I ...
5
votes
2answers
72 views

How to decide which moduli to check when solving a “polynomial” congruence?

Consider the following problem: Find all integer solutions to $y^2 = x^5 - 4$. The solution goes something like – check modulo 11, where $x^5 \equiv 0, \pm 1$, and then check cases to arrive at ...
1
vote
2answers
54 views

Why is this the eigenvector?

For the eigenvector how are they getting \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} when you have \begin{bmatrix} 0 & -1 & -1 \\ 0 & -1 & -3 \\ 0 & 0 & -2 \end{bmatrix} ...
2
votes
0answers
34 views

Asymptotic Behavior of Differential Equation

physicist here. I'm studying some problems that involve the use of differential equations. The professor of the course has indicated that usually variable changes used to simplify the equations come ...
4
votes
1answer
73 views

How can I maintain notes while self studying Maths?

Thank you for stopping by this thread. I'm an engineering student rekindling an interest in Maths. I just love studying Maths in my free time (and sometimes it trespasses into my non free time). I ...
0
votes
1answer
38 views

Solving triangle

If side $a$ is known and the angles are given as functions of two variables (let's call them $x$ and $y$), what is the easiest way to find $y$ as a function of $x$. To make things easier, let one of ...
0
votes
2answers
37 views

Strategy to find the most money to use.

As a reward for a week of good behavior, Tommy was given 7 dollars to spend at the canteen. By the time Tommy got to the canteen, there were only chocolate bars, meat pies and pizza pieces left. The ...
3
votes
0answers
49 views

Please check my problem solved. The task was to calculate $M^{100}$, where M is a $3\times 3$ matrix

Again, o points for this problem. And there's a small mis-type in the beginning where t1=t2=t3=t=1, it's actually -1
0
votes
1answer
68 views

Verification of solution of a contest problem with a limit of nested radicals

They gave me 0 points for this problem. I think it's unfair. What do you think of this proof, is it correct? $\lim\limits_{n\to\infty} \underset{2n\text{ roots ...
1
vote
1answer
57 views

Proving the hat functions are linearly independent

$$ H_i(x) = \begin{cases} (x-x_{i-1})/(x_i-x_{i-1}), & x_{i-1}\le x\le x_i, \\ (x_{i+1}-x)/(x_{i+1}-x_i), & x_i\le x\le x_{i+1}, \\ 0, & \text{otherwise}. \end{cases} $$ How can I prove ...
0
votes
0answers
8 views

Finding solutions for a complicated derivative that tends to infinity

The original function goes like this: I differentiated the above function with respect to x, and obtained: I want to find the condition(s) which leads the above derivative to infinity. How can ...
1
vote
1answer
15 views

Asymptotic stopping time for a ball-drawing problem

Take two different boxes, one with $N$ red balls and one with $N$ blue balls. Remove balls one at a time from either box with equal probability. When only one color is left, the (expected value of ...
2
votes
0answers
63 views

How to learn problem solving strategy for Measure Theory?

I have taken both graduate level Algebra and Measure theory courses but found the latter much more difficult for me. I have put a lot effort on learning it by reading a few reference books and ...
1
vote
3answers
35 views

Units of Measure conversion

I was wondering if i could get some help trying to create a simple math formula. I recently was given an interview to work as a tier1 programmer and was asked to make a program. I made the whole thing ...