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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0
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2answers
33 views

Calculate number of sides of cylinder so each side is a certain width

I'm working on a video-game and as part of the level, I need to create one half of the room curved. For the cylinder, all sides should be of width 450cm, and the cylinder will have radius of 1475cm, ...
-2
votes
1answer
55 views

Balkan Olympiad in Mathematics 2001 [closed]

Where can I find the solutions of the problems from the Balkan Olympiad in Mathematics 2001, Belgrade?
0
votes
1answer
58 views

Finding the least number of dots to add into a 10x10 grid

I have a 10x10 grid where are some dots. What is the least number of dots that I need to add in order to have 3 dots in every row and column have odd number of dots in every row and column have ...
0
votes
2answers
49 views

How to find the maximum of this function $\dfrac{(1+x+y)^2}{(1+x)(1+y)}$?

The function with two variables is defined as follows: $$f(x,y)=\dfrac{(1+x+y)^2}{(1+x)(1+y)},$$ for all $0<x_{min}\leqslant x\leqslant x_{max}<\infty$ and for all $0<y_{min}\leqslant y\...
0
votes
5answers
68 views

380 is what percent less than 600?

I'm New to percentages and this sum is confusing me a bit. If the question was " 380 is what percent of 600" , I would have converted it to an equation as follows.. 380 = ?% × 600 'n then I could ...
2
votes
0answers
29 views

expectation half-normal distribution or expectation Truncated Normal Distribution [duplicate]

I want to calculate integrals $$ \begin{split} \int_0^\infty x \exp\{ ax-b x^2\} dx &= \int_0^\infty x\exp\{-b(x^2-\frac{a}{b}x)\}dx\\ &= \exp\left\{\frac{a^2}{4b}\right\}\frac{\sqrt{\pi}...
1
vote
4answers
71 views

how to find $t$ from $2t^2-0.01t^4=100$?

how to find $t$, from $2t^2-0.01t^4=100$? I was guessing may be I can take $t^2$ common but if it is so so why cannot we take $t$ common in other cases? I mean, for example: $t^2+4t=-4$ why can we ...
0
votes
0answers
47 views

How to simplify a problem with two variables?

I am trying to solve this problem. Let $\Delta$ be a positive number. I would like to find the values of $x$ and $y$ such that: $$ \left(1+\dfrac{x}{1+y}\right)\cdot\left(1+\dfrac{y}{1+x}\right) \...
4
votes
4answers
335 views

Can you find the treasure??

My big bro gave this problem one week ago. I could not still solve it.Please HELP. STORY A man was just looking for items in his store room. Suddenly he found a map , which showed then it stated ...
13
votes
0answers
114 views

Every natural number in binary can be cut and added so that it is a power of $2$? [duplicate]

I was watching a google techtalk with Donald Knuth and he mentions for every binary number $\overline{a_1a_2a_3\dots a_n}$ there exists $c_1<c_2<\dots <c_r=n$ so that: $\overline{a_1a_2\...
0
votes
2answers
23 views

Regarding a Markov chain example state space $\{0,1\}$

I have trouble formulating a question. The set up is $(X_n)$ is a Markov chain with the state space $\mathcal{S} = \{0,1\}$. We know $X_0 =1$ and $X_2=1$ and the transition probability matrix, $p$. ...
0
votes
1answer
19 views

Finding other point's values on a line knowing one point and distance between two others

So I have a normal line that has points $A, B, C$ and $D$ on it (same order). The distance between $A$ and $D$ is $392$. Point $B$ is equal to $293$. $$CD = 2AB = 4BC$$ Picture of the problem (drawn ...
3
votes
1answer
148 views

Prove that $(a-b)^n\mid (a^n-b^n) \iff n=1$ under given conditions

Suppose that $a,b,(a-b)$ are pairwise co-prime (i.e. $a\perp b\perp (a-b)\perp a$), and that $\frac{a}{2}<b<a$, where $a$ and $b$ are both positive integers greater than $2$. Let $n$ be odd. ...
0
votes
1answer
67 views

Paradox of Random Natural Numbers

I've got a question about a game taken from a book called Rachunek prawdopodobieństwa dla (prawie) każdego by Jacek Jakubowski and Rafał Sztencel. Adam and Bolek have a machine that generates a pair ...
0
votes
2answers
26 views

Cuboid room, hooks and strings proof

I'm trying to do the following problem: In a cuboid shaped room a hook is placed in the centre of each wall, the floor, and the ceiling. Every pair of hooks has either a piece of red or blue ...
0
votes
0answers
30 views

How to invert a transformation

I've come across a recursive equation involving vectors. You basically have one starting point $P = (x, y)$ and you transform it to another point $P'=(x', y')$ with the following equations $$ x' = x ...
2
votes
3answers
71 views

Where did two dollars go?? [duplicate]

One of my school friends gave me this sum.Its basically a story formated into a sum STORY There were 3 friends. They each gave 20 dollars to buy a radio. They bought the radio for 60 dollar. Later ...
1
vote
0answers
53 views

How to solve even/odd divide-and-conquer problems?

I am looking into something called the Josephus problem, which seems to be popular, so I am sure there are lots of explanations online, but I want to do the work myself, but I do need a small push to ...
2
votes
1answer
63 views

Sum of squares using generating functions

I tried using generating functions to solve the sum of squares formula based on the recurrence $a_n = a_{n-1} + n^2$ with $a_0 = 0$. $$G(x) = \sum_{n=0}^{\infty} a_n x^n \\ G(x) - 0 = \sum_{n=1}^{\...
0
votes
1answer
30 views

Need to solve for t but can not work out how to get t on one side

I have a object in free fall with $g$ = acceleration, $y$ is the position above the ground and $t$ = time. I worked out that to find the speed at and $t$ is $dy = g . t$ So to get the position $py$ ...
-3
votes
2answers
45 views

Find numbers that fit each riddle look for more than one answer [closed]

There are two $2$ digits numbers. The first number is greater than $50$ and ends in $0$. When you subtract one number from the other number the difference is $29$
2
votes
2answers
90 views

A quicker generalized method to finding a curve tangent to another curve?

Let's say we have a curve of $\sin(x)$ and we have to find a curve tangent to this in form of $c(x-d)^{1/3}$. This curve should have the same tangent line as $\sin(x)$ at any point around $(a,\sin(a))$...
1
vote
1answer
47 views

Solving a Chessboard problem using the Invariance principle

Problem Statement There is an integer in each square of an 8 x 8 chessboard. In one move, you may choose any 4 x 4 or ...
9
votes
4answers
543 views

Optimization-like question

Let's say I have a formula like $ax + by + cz = N$. $a, b, c$, and $N$ are known and cannot be changed. $x, y$, and $z$ are known and can be changed. The problem is that the equation is not true! My ...
3
votes
0answers
37 views

What could be examples at calculus or introductory analysis level for the idea contained in the statement by David Hilbert?

I read the following quote in the book "As opposed to abstraction the art of doing mathematics consists in finding special cases which contain all the germs of generality. --David Hilbert", however ...
1
vote
3answers
48 views

How is a general case equivalent to a special case and how showing a special case demonstrates a general case, in the proof of pythagoras theorem?

"The general theorem expressed by $\lambda a^2 = \lambda b^2 + \lambda c^2 $ is equivalent not only to the special case $a^2 = b^2 + c^2 $ but to any other special case. Therefore, if any such ...
2
votes
0answers
33 views

Where can I find a lot of good exercises on the wave equation?

I find myself in the situation of needing to understand the wave equation inside and out -- I've studied it, obviously, and have been looking for resources for some time. So far in my search I'm ...
0
votes
1answer
31 views

Solving problems of the form $x^c - c^x = d$ in the complex plane.

Is there a known procedure for solving for $x$ in $x^c - c^x = d$ with known $c, d \in \mathbb C$?
-4
votes
3answers
95 views

Publishing journals in mathematics. [closed]

I want to ask if I am to publish any research paper on trigonometric function. Where is the best place to do that and what field of mathematics can it be categorized?
0
votes
1answer
35 views

Applying invariance principle on a problem on sequence of positive integers

The problem statement: Start with the positive integers 1,...,4n-1. In one move you may replace any two integers by their difference. Prove that an even integer ...
2
votes
3answers
115 views

How to solve an irrational equation?

I want to solve this equation $$2 (x-2) \sqrt{5-x^2}+(x+1)\sqrt{5+x^2} = 7 x-5.$$ I tried The given equation equavalent to $$2 (x-2) (\sqrt{5-x^2}-2)+(x+1)(\sqrt{5+x^2}- 3)=0$$ or $$(x-2)(x+1)\left [\...
2
votes
1answer
38 views

Find all sets of N addends equal to a given total W

How many distinct combinations of N natural numbers sum to a given natural number W? For example; for $W=16, N=4$ two of the combinations are $(4,4,4,4)$ and $(5,4,4,3)$ Note: Combination not ...
1
vote
1answer
41 views

Sum of $n$ positive real numbers is 1. Estimate subsums of k elements.

Sum of $n$ positive real numbers $a_1, ...,a_n$ is $1$. Let $S_k$ be maximal sum of k distinct elements of $a_n$. (they can be equal but must have different indexes). What is $\sup S_k$ and $\inf S_k$ ...
3
votes
3answers
99 views

Applying trigonometry in solving quintic polynomials?

So I came across the unsolvable quintic polynomial noticing that solutions can be found by connections with ellipses and such here. But more importantly, I was considering methods we use (or at least ...
0
votes
1answer
64 views

Clock Problem, Number of Chimes

An old fashioned clock chimes as many times as the number of hours it is when it hits a new hour. For example, the clock ticks two times when the clock reads two or the clock ticks 12 times when the ...
8
votes
2answers
98 views

Solution to $e^{e^x}=x$ and other applications of iterated functions?

While trying to solve $e^{e^x}=x$, I ran into the simple solution $x=-W(-1)$. I found it by using the equation $$e^x=x$$Then powering both sides with a base $e$.$$e^{e^x}=e^x$$Now note that the left ...
0
votes
1answer
43 views

Problem solving rolling dice

You are rolling two fair dice, and you are blindfolded, after a certain roll, your partner tells you that you have rolled at least 9. What is the probability that you have rolled at least 11? ...
2
votes
2answers
22 views

Problem involving counting about marbles

Five red cards and four blue cards are blaced in a bag, five cards are selected blind from the bag, what is the probablity that they are all red?
4
votes
2answers
57 views

The chart-problem; problem solving

In how many ways can we construct a $6\times 6$ chart with only $1$ and $-1$ such that in every row and column, the product is always positive?
0
votes
1answer
20 views

Showing properties of the kernal and range of a linear transformation.

Let $T:\mathbb{R}^3\to V$. Show directly that the Ker($T$) is a subspace of $\mathbb{R}^3$ and that dim(Ker($T$)) $\leq 3$. Show that $R(T)$ is a subspace of $V$ and that dim$(R(T)) \leq 3$...
2
votes
1answer
40 views

Finding the formula for a linear transformation given the transformation of the basis vectors.

Consider the basis $\{\vec{p},\vec{q}\}$ where $\vec{p}=(1,1)$ and $\vec{q}=(-1,0)$. Let $T:\mathbb{R}^2\to\mathbb{R}^2$ be the linear operator such that $T(\vec{p})=(1,-2)$ and $T(\vec{q})=(4,1)$....
2
votes
3answers
76 views

Finding roots of Equation involving trig. functions.

In a problem of classical mechanics, I encounter the following equation: $$\mu \sin^4 \theta + \cos \theta = 0 \qquad \mu > 0 \qquad \frac{\pi}{2} < \theta < \pi,$$ where $\mu$ is some ...
2
votes
2answers
56 views

Determine the angle of 3 drawn lines from each corner of 3 congruent squares

Three squares are drawn next to each other. Three lines are drawn from a corner as illustrated. Determine the sum of the three angles exposed (the exact number of degrees or radians):
1
vote
1answer
36 views

Problem solving: How far is the maximum distance?

The tires located on the front of the car wears out after $25000$ km, while the tires on the back wears out after $15000$ km. How far can you maximum ride with new tires if you can swap the tires ...
-1
votes
5answers
64 views

Christmas problem, the salesman with the nuts [closed]

At the Christmas market, a man was selling nuts in a market stall. The first person bought one nut, the next customer bought two nuts, the next bought four, and so on. That is, every new ...
3
votes
0answers
98 views

Chess tournament problem

$12$ chess players took part in a tournament. Each played against each other exactly once. After the tournament every chess player did $12$ lists of names. On the first list, the player only wrote ...
0
votes
2answers
86 views

A coin is tossed if a dice is rolled

I was given this question yesterday. A dice is rolled. If the number is even, a coin is tossed. If it is odd, the dice is rolled exactly once again and results are recorded. Find the probability ...
1
vote
1answer
95 views

Prove that 012345678910111213 etc is not a periodic sequence.

Prove that the sequence $012345678910111213...$ (all non-negative integers written one by one in natural order) is not periodic. I want to know the shortest and most elegant way to prove it. Can you ...
3
votes
0answers
35 views

Green's Theorem with respect to a given polar region.

Using Green's Theorem, compute the counterclockwise circulation $I$ of $\vec{F}=\langle-\sqrt{x^2+y^2},\sqrt{x^2+y^2}\rangle$ around the region defined by the polar coordinate inequalities $7 \leq ...
2
votes
1answer
64 views

Solve matrix vector equation

Let $A$ be a real $n\times n$ matrix and $w,x$ real $n\times 1$ vectors. For fixed $A$ and $w$ solve the following for $x$: $(x^\top A x)w - (x^\top w) (A+A^\top) x = 0$ Any hints? I do not really ...