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
107 views

creating a more complex sudoku (69x6)

I would like to know if its possible to create a "sodoku" with this rule: in a table $69\times 6$ i want to put in the numbers from $1$ to $46$ repeated $9$ times, each numbers HAS to stay in the same ...
8
votes
2answers
57 views

Having $A_1=a+b+c$,$A_2=a^2+b^2+c^2$, $A_3=a^3+b^3+c^3$ - how to get $a,b,c$?

Perhaps I'm just a bit dense at the moment - I've re-read some of my notes from monthes ago concerning elementary symmetric polynomials, and I find that I've no idea how to approach the "inverse" ...
5
votes
1answer
89 views

How to solve this inequality with another way?

I want to solve this inequality $$x^3-3 x^2+2 \sqrt{(x+2)^3}-6 x\geqslant 0.$$ I tried. Put $t = \sqrt{x + 2}$. Then, we get $$t^6+2t^3-9t^4+18t^2-8\geqslant 0.$$ Equavalent to $$(-2 + t)^2 (1 + ...
3
votes
0answers
49 views

Dividing planes with lines and spheres

What is the greatest number of parts a plane can be divided into using $n$ infinite straight lines? What about $n$ circles? Can you generalise this into 3-dimensional space, planes and spheres? For ...
3
votes
2answers
403 views

Permutation of 1…9 with no ascending or descending subsequence of length 4

Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order. Show that there is no arrangement of the numbers $1,2,...,10$ ...
4
votes
2answers
115 views

How to isolate x in this equation?

Suppose we have this equation: $y = 1 + x + \lceil \log_2(x)\rceil$ where $x$ is an integer > $0$. How can we get $x$ as a function of $y$ (basically isolate $x$)? I don't understand how to handle ...
0
votes
1answer
47 views

Concavity intervals

My second derivative is $$\frac{(250-64 x^3)}{(3 x (-125+8 x^3))^\frac{5}{3}} $$ I know that function is undefined if $x = 0$ and $x=5/2$. What would be concavity intervals? Why not ...
2
votes
3answers
169 views

Tricky volume of revolution

So I was trying to find the volume, but I'm always getting wrong answer. $$x=-y^2+6y$$ and the y-axis to rotate about is $y=-7$. $$V = \pi*\int_0^6 (-y^2+6y)^2-49 \;dy$$ But answer doesn't much? ...
3
votes
1answer
118 views

$0 = \left(\sqrt{p^2+m^2}-\sqrt{k^2+p^2+2\cdot k\cdot p\cos(\theta)}\right)^2 -k^2-m^2$ solving for $k$

This question is related to $\delta(f(k))$ concerning the Dirac-delta. OK I know this might seem trivial but the result is very very important to me so I want to check with you if my logic seems ...
1
vote
1answer
927 views

Solving a quadratic diophantine equation in two variables

I have an equation in the following form: $$6mn+m+n=x$$ $$m,n,x\in\Bbb Z; \qquad0 < m,n$$ If I were given a value for $x$, how would I go about finding solutions to this equality for $a$ and $b$ ...
3
votes
2answers
69 views

How to solve the non homogeneous equations

I am looking for the proof of the following I have the following equations $x_1^2+x_2^2+x_3^2+....+x_n^2=1$, $x_1+x_2+x_3+........+x_n=1$ $0 \leq x_i\leq 1$ for-all $i$ I believe that the only ...
8
votes
3answers
316 views

How to solve this irrational equation?

How to solve this equation in the set real numbers $$\sqrt{8x + 1} - \sqrt{6x - 2} - 2x^2 + 8x - 7 = 0.$$ Using Mathematica, I know, this equation has two solutions $x = 1$ and $x = 3.$
1
vote
2answers
222 views

Calculating the same exchange rate to make an investor indifferent

If we consider an American investor in 2009 with 160 million Dollars to place in a bank deposit in either America or the UK. The (1 yr) interest rate on bank deposits is 6 percent in the UK and 1 ...
1
vote
0answers
93 views

Whats the purpose : Hilbert's problems in measure space

This may sound a very newbie question, anyway I would like to ask here and to make it more clear for me. I've got an assignment to consider boundary problems in space of finite measures W, where the ...
1
vote
2answers
75 views

Prove $|A| + |B| \ge |A \cup B|$ if $A$ and $B$ are finite sets

I have a question like this: Prove $|A| + |B| \ge |A \cup B|$ if $A$ and $B$ are finite sets. Here is the solution but I don't agree with it: Let $A = \{a_1, \dots, a_n\}$ and $B = \{b_1, \dots, ...
12
votes
5answers
2k views

Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially

I have to give a combinatorial proof of $$\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}.$$ I find it difficult to solve such problems. I'm not a brilliant person and never will be so I need to have ...
2
votes
4answers
433 views

Filling a swimming pool with two hoses

Hose A can fill a pool in 4 days. You add a second hose B, now both A and B can fill it in 3 days. How many days will it take to fill the pool with just hose B? I would like to see a formula.
0
votes
1answer
251 views

Sequence Question from past post

I recently saw a post about sequences. This made me remember some other post someone had posted here on Math.SE. He did not want answers but wanted general ways to tackle them. I did spend an hour or ...
3
votes
2answers
131 views

Sequence and series problems with slick group theoretic solutions.

So I'm trying to get this unmotivated student in my class interested in learning group theory. I've recently ascertained that he likes analysis a bit better than algebra, and that sequences and ...
4
votes
1answer
109 views

How to solve this nonstandard trigonometric equation?

I want to solve this equation $$\sin(\sin(\sin(\sin x)))=\cos(\cos(\cos(\cos x))),$$ but I don't know how to solve.
15
votes
7answers
3k views

List of problem books in undergraduate and graduate mathematics

I would like to know some good problem books in various branches of undergraduate and graduate mathematics like group theory, galois theory, commutative algebra, real analysis, complex analysis, ...
7
votes
1answer
261 views

A good book for short problems

What is a good book for problems which can be done without much mathematical background? I don't mean IMO-level, since those questions generally require a fairly big amount of mathematical knowledge, ...
3
votes
2answers
270 views

Solving a cubic system of equations

I have the following equation system: $A_1 x + B_1 y + C_1 z + D_1 xy + E_1 xz + F_1 yz + G_1 xyz = M_1$ $A_2 x + B_2 y + C_2 z + D_2 xy + E_2 xz + F_2 yz + G_2 xyz = M_2$ $A_3 x + B_3 y + C_3 z + ...
2
votes
3answers
1k views

Linear independence and dependence of vectors

I am really stuck in this problem, I have only 2 days to learn matrix's base, and its generator. My problem is that I know definitions but I don't understand intuitively what they mean. What I know: ...
5
votes
3answers
114 views

Closed formula for linear binomial identity

I have the following identity: \begin{equation} m^4 = Z{m\choose 4}+Y{m\choose 3}+X{m\choose 2}+W{m\choose 1} \end{equation} I solved for the values and learned of the interpretation of W, X, Y, and ...
0
votes
1answer
105 views

Ratios and projections

Let's say a company manages two types of projects A and B. A type projects are more complex than B type projects. A study found that the ideally, a project manager can handle at the same time 2 type A ...
2
votes
2answers
150 views

Problem Solving Methods

My problem solving strategy involves looking at the problem and collecting as much relevant information as possible, elaborating the given information and waiting for a general strategy to develop. ...
2
votes
1answer
47 views

asymptotics of a solution for equation

I want to solve the equation $$\frac{x^{17/6}}{a^{17/6}} - \frac{x^2}{a} -1 = 0$$ where I assume $a \gg1$ and $x$ is the unknown. How do I compute the dependence of $x$ on $a$ as $a \rightarrow ...
2
votes
4answers
95 views

rewrite $2ie^{i\pi}+i^3$

i am asked to rewrite $2ie^{i\pi}+i^3$ into $x+iy$ form. i just tried all what i know so far, but couldnot come to solution. i said: $2ie^{i\pi}+i^3=2ie^{i\pi}-i$ but further i am stuck really. i am ...
2
votes
2answers
260 views

which problems do you recommend it to me to solve it? [closed]

i study abstract algebra from dummit and foote . i started to solve some problems in section 3 in chapter 4 there is 36 problems i study the subject myself , so there is no proffesor to ...
1
vote
2answers
5k views

Solving equations that contain summations

My previous algebra course did not go over summation at all, and now that I'm in my new course, Discrete Math for Information Technology, we have been introduced to summation. I understand summation ...
2
votes
2answers
708 views

Combinatorial restriction on choosing adjacent objects

I am having trouble understanding an approach to the following problem. Suppose 14 books are aligned in a bookcase. How many ways can we choose 5 books so that no adjacent books are chosen? I think my ...
1
vote
1answer
59 views

Counting Card hands with various restrictions

I would like to know if my solutions are correct for the following three combinatorial card questions. In each question, assume we have a standard deck of cards (13 ranks, and 4 suits). How many ...
1
vote
2answers
536 views

Need help with an integration word problem. This appears to be unsolvable due to lack of information.

I'm not sure I understand what to do with what's given to me to solve this. I know it has to do with the relationship between velocity, acceleration and time. At a distance of 45m from a traffic ...
9
votes
1answer
2k views

Finding the general term of a sequence

I would like to find an expression for the sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots,\;$ $$-\frac{1}{6},\,\frac{2}{7},\,\frac{5}{8},\,\frac{8}{9},\,\frac{11}{10},\,\ldots$$ So by trial and ...
11
votes
3answers
536 views

Arc sums for a circle of $k$ positive integers whose total sum is $n$

This problem got me thinking about the following more general scenario: Suppose you have $k$ positive integers with total sum $n$, and you arrange them in a circle. Given such an arrangement, you ...
-1
votes
1answer
216 views

How many students like all the three subjects?

Among 64 students, 28 of them like Science, 41 like Mathematics and 20 like English. 24 of them like both Math and English. 12 students like both Science and English. 10 students like both science and ...
0
votes
3answers
68 views

what is the value of the digit in the ones place of the following?

1×3×5×7×9×11×13×...×2007×2009 what is the value of the digit in the ones place of the following? I can't find the solution for this problem. Please give me some hints
2
votes
3answers
46 views

At what speed should it be traveling if the driver aims to arrive at Town B at 2.00 pm? [closed]

A car will travel from Town A to Town B. If it travels at a constant speed of 60 km/h, it will arrive at 3.00 pm. If travels at a constant speed of 80kh/h, it will arrive at 1.00 pm. At what speed ...
1
vote
1answer
231 views

Modular arithmetic word problem

We are buying a total of 12 fruits (apples and bananas) for 132 dollars. If the apples are 3 dollars more expensive than the bananas, and we bought more apples than bananas, how many bananas we ...
-2
votes
2answers
536 views

Change parabolic equation to canonical form

I have equation $y = -x^2 + 2x + 7$. How can I change it to canonical form, which looks like $y^2 = 2px$ ? ($p$ will be parameter) What i ve tried so far: $$\begin{align} y &= -x^2 + 2x + 7\\ y ...
0
votes
2answers
86 views

Area of a function is the same as the area of the inverse function

The area of between the function $f(x)=x^2$ and the $x$-axis from $1\to a$ is the same as the area between $f^{-1}(x)$ and the $y$-axis from $1 \to b$ when $f(a)=b$ It says write two equations of $a$ ...
4
votes
2answers
402 views

prove the divergence of cauchy product of convergent series $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$

i am given these series which converge. $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$ i solved this with quotient test and came to $-1$, which is obviously wrong. because it must be $0<\theta<1$ so ...
0
votes
1answer
252 views

How many eggs are there in the basket?

There is a basket of an eggs. The remainder is 1 When we put the eggs into the group of 2. The remainder is 2 when put the eggs in the group of 3. The remainder is 3 when we put eggs in the group of ...
1
vote
1answer
93 views

How can I solve for $x\,$? $:\;\;x-x_r=(x-x_1)e^{\large -(x-x_1)^2}$

I want to find $x$ for given values of $x_r$ and $x_1\,$ (domain $\mathbb{R}$): $$x-x_r=(x-x_1)e^{\large -(x-x_1)^2}$$ Thanks
1
vote
0answers
103 views

Find total number of sets of integers which satisfy a given equality and inequality

Compute the total number of different sets of integers a1, a2,..,an which satisfy the following equality and constraints: $$ ...
0
votes
1answer
28 views

How far could the plane travel before it made its return?

A fighter plane had enough fuel to last a 6-hour flight. The speed of the wind and the speed of the plane made up a total of 1500km/h when the plane was flying in the direction of the wind during its ...
1
vote
1answer
126 views

what is the ratio of their speed?

Jonathan and Cindy run on a circular track where AB is the diameter of the track, as shown below. If Jonathan and Cindy run towards each other at the same time from Point A and Point B respectively, ...
1
vote
4answers
459 views

In how many ways can he form a rectangle using all the tiles each time?

A contractor has exactly $1088$ square tiles. In how many ways can he form a rectangle using all the tiles each time?
1
vote
3answers
84 views

How old was the teacher in 2008?

Julie ask her teacher, "how old were you in 2008?" "My age in 2008 was the sum of all the digits of my year of birth,' replied the teacher. How old was the teacher in 2008?