# Tagged Questions

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1answer
28 views

### What are some ways to find the minimum of an expression?

I don't get how people solve these types of questions. If you have a single variable expression then I guess you could differentiate it, but how would you find the extreme values of an expression ...
1answer
32 views

### Solve the equation by putting new variable

I want to solve the equation $$x^2+(2 x+3) \sqrt{3 x^2+6 x+2}=6 x+5.$$ I tried. Put $t = \sqrt{3 x^2+6 x+2}.$ We have $$x^2+(2 x+3)t - 6x - 5 = 0.$$ Discriminant of this equation (with unknown $x$) ...
2answers
55 views

### How to solve this system of equations?

How to solve this system of equations? $$\begin{cases} 1+\sqrt{2 x+y+1}=4 (2 x+y)^2+\sqrt{6 x+3 y},\\ (x+1) \sqrt{2 x^2-x+4}+8 x^2+4 x y=4. \end{cases}$$
1answer
38 views

### Imperfect digit-to-digit invariants in Base $10$

$3435 = 3^3 + 4^4 + 3^3 + 5^5$ is an example of a perfect digit-to-digit invariant. Fact: The number of PDDIs is finite for any given base; in particular, for base $10$. Question: Working over base ...
1answer
45 views

### Story Problem: Algebra

A teacher gave a test, and most of his students did poorly. The teacher decided to let the students correct the questions they got wrong for 70% credit. One student corrected 80% and received a final ...
0answers
50 views

### Arbitrary ratio sequences on a partition of $\mathbb{R}$ (Partition regularity of fixed ratio sequences)

Background: This question arose purely recreationally and doesn't really fit into any context that I know of. Let $A \sqcup B = \mathbb{R}$ be a partition of the ...
1answer
78 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 ...
2answers
48 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" ...
1answer
76 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 + ...
0answers
34 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 ...
1answer
96 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 $1,2,...,10$ ...
2answers
62 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 ...
1answer
29 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 ...
3answers
76 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? ...
1answer
83 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 ...
1answer
182 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 $b$ ...
2answers
51 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 ...
3answers
136 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 $x = 3.$
2answers
37 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 ...
0answers
94 views

### geometry, problem solving!

A friend gave me this problem but I have no idea how to approach it. Suppose you are given a triangle $ABC$. Pick points $P$ inside or on perimeter, such that the perimeter of the triangle ...
0answers
83 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 ...
2answers
60 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, ...
4answers
465 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 ...
1answer
82 views

### Worded problems.

There are 9 chocolates in a selection box: 3 white, 3 milk & 3 dark chocolates. There are 3 soft centres, 3 truffles & 3 pralines. Each chocolate is different. Using the clues below, arrange ...
1answer
80 views

### Word problem: List all acceptable possibillities

Ingrid, Jean, Karen, Philippa and Shirley are sharing a box of chocolates. There are 5 chocolates left in the box: a Coffee Cream a Orange Fondant, a Hazelnut Praline a Toffee Crunch a Nougat ...
2answers
178 views

### a word problem algebra

Fred and George are to share a chocolate bar made up of an 8 by 6 square rectangular array. The top-left top-right squares each contain a visible nut. They take it in turns, starting with Fred, to ...
4answers
320 views

### solving $\sqrt{3-\sqrt{3+x}}=x$.

Can we solve the following equation in $\mathbb{R}$ without expanding it into a fourth degree equation : $$\sqrt{3-\sqrt{3+x}} = x.$$ squaring both sides and squaring again is the only thing I ...
4answers
85 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.
1answer
54 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 ...
2answers
85 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 ...
1answer
75 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.
6answers
330 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, ...
1answer
109 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, ...
2answers
99 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 + ...
1answer
91 views

### I really need help on this question… Please help… [closed]

Mickey, as well as being a very clever mathematician, is also a keen gardener and has a fenced allotment which has a square shed placed in one of its corners. In order to celebrate his wife Gilly’s ...
3answers
156 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: ...
3answers
84 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 ...
1answer
43 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 ...
2answers
50 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. ...
1answer
46 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 ...
4answers
69 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 ...
2answers
106 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 ...
2answers
530 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 ...
2answers
48 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 ...
1answer
21 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 ...
2answers
160 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 ...
1answer
167 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 ...
3answers
429 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 ...
1answer
64 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 ...
3answers
56 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
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