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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5
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4answers
121 views

Some Questions regarding preparing for Math Olympiads (searched but didn't get answers)

Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a ...
0
votes
1answer
39 views

Solving $\int\sqrt{1+(-2ax+b)^2}\;dx$

List item What solution $$\int\sqrt{1+(-2ax+b)^2}\;dx$$Unable to develop anything ...$~$:'( I tried completing squares, but can not move much.
0
votes
0answers
20 views

The radius of a circle grows at a rate of $ 30$ cm/s, that rate increases the area of ​​the circle with respect to time?

I would like to address the question The radius of a circle grows at a rate of $ 30$ cm/s, that rate increases the area of ​​the circle with respect to time? I know I have to derive, but where I ...
4
votes
3answers
56 views

Elementary set theory problem - I get an incorrect result

The problem given is this: $\bigcap_{i \in I}(A_i \cup B_i)$ and $(\bigcap_{i \in I}A_i) \cup(\bigcap_{i \in I}B_i)$ I am asked if they are the same. Here is the reasoning I used: for the first ...
-2
votes
1answer
48 views

What is the next letter in the series? [closed]

What is the next letter in the series? O-T-T-F-F-S-S-E-N-? Answer option: A. T B. E C. O D. N Please describe your solution. Thanks for your help.
0
votes
1answer
30 views

How many smallest number moves need to measure 6 liter of water?

You are given two (unmarked) containers of capacity 9 liter and 4 liter and a huge tank of water. Need is to get measure of exactly 6 liter, of water. A move is either filling a container completely ...
-2
votes
3answers
52 views

How to know number of eggs in this problem?

A women took a certain number of eggs to the market and sold some of them. The next day through her poultry industry, the number left over had been doubled, and she sold the same number as the ...
0
votes
0answers
44 views

Matheletics '13 challenges

I was trying to solve the challenges proposed on Matheletics '13. I'm having trouble solving Hockey Classics, Special Arrangement and Permutation. Can anyone point out the idea I can't see, pls?
0
votes
1answer
35 views

Combinations with multiple kids

In a certain country, it has been found over many years that $55$% of the babies born there are males. For a family in that country with five children, what is the probability that (i) the two ...
0
votes
2answers
44 views

Arithmetic sequence problem

Company A pays \$23,000 yearly with raises of \$1200 per year. Company B pays \$26,000 yearly with raises of \$800 per year. Which company will pay more in year 10? How much more?
1
vote
0answers
46 views

When does a ball in a game of brick breaker never hit the remaining breaks?

I have a block size 2N*2N and some squares are filled with bricks and some aren't. I have a ball that travels distance 1 in the x and y direction and bounces off with perpendicular direction if it ...
0
votes
2answers
23 views

Using plant to find depth of water (triangles)

John and Chris were out in their row boat one day, and Chris spied a water lily. Knowing that Pat liked a mathematical challenge, Chris announced that, with the help of the plant, it was possible to ...
1
vote
2answers
34 views

2 states, 2 interarrival distribution Renewal Process.

Karlin and Taylor (1975): 18. Consider a stochastic process $X(t)$, $t \geq 0$, which alternates in 2 states $A$ and $B$. Denote by $\xi_1, \eta_1, \xi_2, \eta_2, \ldots,$ the successive ...
0
votes
3answers
61 views

Proving this inequality

I am having trouble with proving an inequality. Assume we have two positive real numbers $a$ and $b$ such that $a+b=1$ and numbers $x > 0$ and $y > 0$. Prove: $$\frac{2}{\frac{a}{x} + ...
1
vote
1answer
25 views

Finding F(x) given any reals x and y

I have a problem and I think I know how to solve it so here it is: Determine $F(x)$ if, for all real $x$ and $y$, $F(x)F(y)-F(xy) = x+y$. I tried a couple of cases and these were my results: When ...
0
votes
1answer
33 views

Linking 5 communities by plane, train, and bus

Every pair of communities in a country is linked directly by exactly one mode of transportation: bus, train or airplane. All three modes of transportation are used in the country; no community is ...
2
votes
2answers
29 views

Based on census data and namm data, how many musicians are there?

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there? Any help would be appreciated...
16
votes
12answers
5k views

MENSA IQ Test and rules of maths

In a Mensa calendar, A daily challenge - your daily brain workout. I got this and put a challenge up at work. The Challenge starts with.. ...
0
votes
3answers
47 views

Problem Solving

Here the question on my daughter's 4th grade homework assignment: Sarah is decorating a mosaic board it is 12 inches wide and 16 inches long. Sarah is using square tiles all the same size. What size ...
1
vote
3answers
38 views

Permutations of numbers

Given the five digits $1,3,4,6,$ and $7$. In the following question, it should be understood that repition of a digit is not allowed. (i) How many three-digit numbers can be formed from the ...
2
votes
1answer
55 views

Every point of the interval $(0,1)$ is an interior point of that interval. Thus $(0,1)^0 = (0,1)$.

This is a question I found here (on pg.2 example 1.2.2): http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf Definition of interior and interior point: Let $A \subseteq \mathbb{R}$. The point $a$ is ...
1
vote
1answer
91 views

How to learn problem solving (IMO and IPhO)

I'm not interested in IMO and IPhO actually, but one of the most prestigious universities in my country admits students using a test which is composed by 5 IMO and IPhO questions (or slighly lower). ...
0
votes
1answer
22 views

Problem solving question with average

Johnny had to take a test a day late. His 96 raised the class average from 71 to 72. How many students, including Johnny, took the test? I tried to do trial and error to see how many students there ...
1
vote
1answer
61 views

How many ordered triples $(x,y,z)$ of positive integers satisfy $xyz=4000$

How would I find this out? Is there an equation or summation?
0
votes
3answers
55 views

no positive roots for $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$

Hint for showing that $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$ has no positive roots thanks
0
votes
1answer
74 views

Show that the union and the intersection of any two $\epsilon$-neighborhoods which overlap is itself an $\epsilon$ neighborhood.

I want to check if my reasoning and mathematical language is correct here. There's only two cases to check for. One where one of the neighborhoods is inside the other, and the other where the two ...
0
votes
1answer
44 views

Solve equation of form $(d_B - 0.32)^{0.8} (d_B + 1.45)^{1.1} = exp(0.8)$ for the term $d_B$

I have the following equation: $$ \left(\frac{\sqrt{d_B}-\sqrt{d_{Beq}}}{\sqrt{d_{Bmin}}-\sqrt{d_{Beq}}} \right)^{1-\frac{c1}{c2}}\left(\frac{\sqrt{d_B}+\sqrt{c3}}{\sqrt{d_{Bmin}}+\sqrt{c3}} ...
-1
votes
2answers
106 views

How to solve this “$\frac{28x}{56x}$” [closed]

How to solve this "$\frac{28x}{56x}$" using properties. Question from maths of class 8 book thank you in advance regards jonathan
4
votes
8answers
226 views

Evaluating $\int \frac{1}{\sqrt{x^2 + a^2}}\, dx$ without resorting to trigonometric $u$-substitution

I am looking for a quick and intuitive way to evaluate this indefinite integral without resorting to any trigonometric functions. I'm not sure if it is at all possible to do so, but I was just ...
1
vote
2answers
68 views

Can someone help out with this geometry problem plase?

I have a pyramid $P$ that has a square pyramid and each of its 4 triangles is equilateral.I also have cuboid $C$ with height 25 and width 50, something like this: So the volume of $C$ is $25 . 50 . ...
0
votes
2answers
21 views

Define variable value - General Math

I met a little problem in one of my Math - tasks. Its quite simple: I get to cases = case 1: $(476\cdot x)+220$ case 2: $(278\cdot x)+675$ The variable x have to be a value, so case 1 and case 2 ...
0
votes
1answer
46 views

What kind of formula would I use to get all possible outcomes?

I am into a CCG, and I got a question come to mind "how many possible out comes are there for deck combinations?" The game is broken into three: Main Character (6 cards available, only one deck), ...
0
votes
1answer
62 views

How many number of buses that the car encounter?

A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of ...
-8
votes
2answers
46 views

Problem Solving [closed]

can you guyz help me ..i think 77 is the answer .. if 10 men can do a job in 48days in how many days 6 men can do the job ? 80 82 81 90 94 It is multiple choice question of my college.
0
votes
1answer
23 views

Solving the following equation

What is the easiest way to solve the following equation for g in terms of x? I seem to be going in circles, and don't know how exactly to deal with the $\pm$ symbol. Equation: $$\pm \sqrt{2}x + ...
1
vote
2answers
94 views

Prove that for any integer $k>1$ and any positive integer $n$, there exist $n$ consecutive odd integers whose sum is $n^k$

Found these problems in a problem book and got stuck. The book doesn't have solutions to I've come here for help. (1) Prove that for any integer $k>1$ and any positive integer $n$, there exist $n$ ...
2
votes
3answers
92 views

Where is the lost dollar?

Somebody explained me this problem, but I am not sure to understand what is wrong. ...
0
votes
1answer
26 views

Proof of transformations to find an approximate value

I have no idea what this questions is asking, or how to go about solving.. can someone please help? Answer:
0
votes
1answer
25 views

formula to apportion cost of transport among three people in a liftshare

I share lifts with Sed and Awk to work every day. We tally journeys owed on a spreadsheet. A week might look like this: ...
1
vote
2answers
75 views

Linear Algebra and a cube

I am currently working no a linear algebra question and do not understand how to solve it. The questions gives: ...
1
vote
2answers
42 views

Solving Abstract Problems

I'm doing this Solving Abstract Problem but I'm not sure which one it is. I mean from the Series I can see there's a pattern but in the Options I don't see images that link with the Series. Do you ...
1
vote
2answers
98 views

Question about the “master theorem” of recurrences - no “$b$” term

I'm using the master theorem to find the asymptotic run time of recurrences. For example, for a $T(n) = 4 T(n/5) + n^1$ I find that $T(n)$ is $\Theta(n^1)$, or, simply, constant time, via the set of ...
2
votes
0answers
70 views

Is this graph problem already solved

I would like to solve the following: Let $G=(V,E)$ be a directed graph such as $\forall (x,y) \in E, x \neq y$. Find any (all would be even better) graphs $S$ such that: $S \subset V$ $\#\{(x,y) ...
1
vote
1answer
47 views

Is there an analitical solution for such ODE $$ \frac{d y(x)}{dx}=\frac{a*y(x)^3+b}{c* y(x)^3+ d} $$

I have an ODE $$ \frac{d y(x)}{dx}=\frac{a*y(x)^3+b}{c* y(x)^3+ d} $$, $$a,b,c,d - const$$ And I would love to solve it analitically. I tred maple 15 and 17 and got $$ y \left( x \right) =1/2\,{ ...
0
votes
1answer
66 views

Velocity and distance problem

From city A, car a sets on it's road towards city B. 9 Hours later, car b, sets from city B towards city A. The two cars met along the way. At the point of the meeting, car a, passed 240 km more than ...
0
votes
4answers
56 views

How can I solve these equations? [closed]

I can't figure it out, please help :S $$\begin{array}{rcl} 2x + 2xz &=& 0\\ -2y + 2yz &=& 0\\ x^2 + y^2 &=& 4 \end{array}$$ Thanks in advance!
3
votes
3answers
380 views

Magic Trick to Read your Mind

I am a student in High School. My math professor made a magic trick the other day in my class and he read our minds. I knew a similar trick which was based on mathematics, that's why I am asking here. ...
0
votes
1answer
42 views

Solving a tough system of linear equations

I have three equations and have to solve for $x, y, z$. $$ l_1l_2 + m_1m_2 + n_1n_2 = 0 $$ $$ xl_1 + ym_1 + zn_1 = 0 $$ $$ xl_2 + ym_2 + zn_2 = 0 $$ After eliminating a variable (from the last two), ...
0
votes
0answers
26 views

MinMax Tree data structure problem

Let vector (x,y,z) be a "Tree Node" where x,y,z are integers. Each node (x,y,z) has 3 parents which are (x-1,y,z), ...
2
votes
2answers
95 views

Show that if $z = e^{i\theta}$ is a solution to $0 = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0$, …

Show that if $z = e^{i\theta}$ is a solution to $0 = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0$ [1] where all $a_i$ are real, then $0 = a_{n-1}\sin\theta + a_{n-2}\sin2\theta + \cdots + a_0 \sin ...