The problem-solving tag has no wiki summary.
1
vote
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 ...
2
votes
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 $x$) ...
1
vote
2answers
55 views
How to solve this system of equations?
How to solve this system of equations?
$$\begin{cases}
1+\sqrt{2 x+y+1}=4 (2
x+y)^2+\sqrt{6 x+3 y},\\
(x+1) \sqrt{2 x^2-x+4}+8 x^2+4
x y=4.
\end{cases}$$
2
votes
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 ...
0
votes
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 ...
4
votes
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 ...
3
votes
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 ...
8
votes
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" ...
5
votes
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
$$(-2 + t)^2 (1 + ...
3
votes
0answers
34 views
Dividing planes with lines and spheres
What is the greatest number of parts a plane can be divided into using $n$ infinite straight lines? What about $n$ circles?
Can you generalise this into 3-dimensional space, planes and spheres?
For ...
3
votes
1answer
96 views
Permutation of 1…9 with no ascending or descending subsequence of length 4
Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order.
Show that there is no arrangement of the numbers $1,2,...,10$ ...
4
votes
2answers
62 views
How to isolate x in this equation?
Suppose we have this equation:
$y = 1 + x + \lceil \log_2(x)\rceil$
where $x$ is an integer > $0$.
How can we get $x$ as a function of $y$ (basically isolate $x$)? I don't understand how to handle ...
0
votes
1answer
29 views
Concavity intervals
My second derivative is
$$\frac{(250-64 x^3)}{(3 x (-125+8 x^3))^\frac{5}{3}}
$$
I know that function is undefined if $x = 0$ and $x=5/2$.
What would be concavity intervals? Why not ...
2
votes
3answers
76 views
Tricky volume of revolution
So I was trying to find the volume, but I'm always getting wrong answer.
$$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$$
But answer doesn't much? ...
3
votes
1answer
83 views
$0 = \left(\sqrt{p^2+m^2}-\sqrt{k^2+p^2+2\cdot k\cdot p\cos(\theta)}\right)^2 -k^2-m^2$ solving for $k$
This question is related to $\delta(f(k))$ concerning the Dirac-delta.
OK I know this might seem trivial but the result is very very important to me so I want to check with you if my logic seems ...
1
vote
1answer
182 views
Solving a quadratic diophantine equation in two variables
I have an equation in the following form:
$$6mn+m+n=x$$
$$m,n,x\in\Bbb Z; \qquad0 < m,n$$
If I were given a value for $x$, how would I go about finding solutions to this equality for $a$ and $b$ ...
3
votes
2answers
51 views
How to solve the non homogeneous equations
I am looking for the proof of the following
I have the following equations
$x_1^2+x_2^2+x_3^2+....+x_n^2=1$,
$x_1+x_2+x_3+........+x_n=1$
$0 \leq x_i\leq 1$ for-all $i$
I believe that the only ...
8
votes
3answers
136 views
How to solve this irrational equation?
How to solve this equation in the set real numbers $$\sqrt{8x + 1} - \sqrt{6x - 2} - 2x^2 + 8x - 7 = 0.$$ Using Mathematica, I know, this equation has two solutions $x = 1$ and $x = 3.$
1
vote
2answers
37 views
Calculating the same exchange rate to make an investor indifferent
If we consider an American investor in 2009 with 160 million Dollars to place in a bank deposit in either America or the UK. The (1 yr) interest rate on bank deposits is 6 percent in the UK and 1 ...
0
votes
0answers
94 views
geometry, problem solving!
A friend gave me this problem but I have no idea how to approach it.
Suppose you are given a triangle $ABC$. Pick points $P$ inside or on perimeter, such that the perimeter of the triangle ...
1
vote
0answers
83 views
Whats the purpose : Hilbert's problems in measure space
This may sound a very newbie question, anyway I would like to ask here and to make it more clear for me.
I've got an assignment to consider boundary problems in space of finite measures W, where the ...
1
vote
2answers
60 views
Prove $|A| + |B| \ge |A \cup B|$ if $A$ and $B$ are finite sets
I have a question like this:
Prove $|A| + |B| \ge |A \cup B|$ if $A$ and $B$ are finite sets.
Here is the solution but I don't agree with it:
Let $A = \{a_1, \dots, a_n\}$ and $B = \{b_1, \dots, ...
12
votes
4answers
465 views
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
I have to give a combinatorial proof of
$$\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}.$$
I find it difficult to solve such problems. I'm not a brilliant person and never will be so I need to have ...
1
vote
1answer
82 views
Worded problems.
There are 9 chocolates in a selection box: 3 white, 3 milk & 3 dark chocolates. There are 3
soft centres, 3 truffles & 3 pralines. Each chocolate is different. Using the clues below,
arrange ...
-1
votes
1answer
80 views
Word problem: List all acceptable possibillities
Ingrid, Jean, Karen, Philippa and Shirley are sharing a box of chocolates.
There are 5 chocolates left in the box:
a Coffee Cream
a Orange Fondant,
a Hazelnut Praline
a Toffee Crunch
a Nougat ...
2
votes
2answers
178 views
a word problem algebra
Fred and George are to share a chocolate bar made up of
an 8 by 6 square rectangular array. The top-left top-right
squares each contain a visible nut.
They take it in turns, starting with Fred, to ...
8
votes
4answers
320 views
solving $\sqrt{3-\sqrt{3+x}}=x$.
Can we solve the following equation in $\mathbb{R}$ without expanding it into a fourth degree equation :
$$ \sqrt{3-\sqrt{3+x}} = x.$$
squaring both sides and squaring again is the only thing I ...
2
votes
4answers
85 views
Filling a swimming pool with two hoses
Hose A can fill a pool in 4 days. You add a second hose B, now both A and B can fill it in 3 days. How many days will it take to fill the pool with just hose B?
I would like to see a formula.
0
votes
1answer
54 views
Sequence Question from past post
I recently saw a post about sequences. This made me remember some other post someone had posted here on Math.SE. He did not want answers but wanted general ways to tackle them. I did spend an hour or ...
3
votes
2answers
85 views
Sequence and series problems with slick group theoretic solutions.
So I'm trying to get this unmotivated student in my class interested in learning group theory. I've recently ascertained that he likes analysis a bit better than algebra, and that sequences and ...
4
votes
1answer
75 views
How to solve this nonstandard trigonometric equation?
I want to solve this equation $$\sin(\sin(\sin(\sin x)))=\cos(\cos(\cos(\cos x))),$$ but I don't know how to solve.
5
votes
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, ...
5
votes
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, ...
3
votes
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 + ...
0
votes
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 ...
2
votes
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: ...
5
votes
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 ...
0
votes
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 ...
0
votes
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. ...
2
votes
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$$
where I assume $a \gg1$ and $x$ is the unknown. How do I compute the dependence of $x$ on $a$ as $a \rightarrow ...
2
votes
4answers
69 views
rewrite $2ie^{i\pi}+i^3$
i am asked to rewrite $2ie^{i\pi}+i^3$ into $x+iy$ form. i just tried all what i know so far, but couldnot come to solution. i said: $2ie^{i\pi}+i^3=2ie^{i\pi}-i$ but further i am stuck really. i am ...
2
votes
2answers
106 views
which problems do you recommend it to me to solve it? [closed]
i study abstract algebra from dummit and foote .
i started to solve some problems in section 3 in chapter 4
there is 36 problems
i study the subject myself , so there is no proffesor to ...
1
vote
2answers
530 views
Solving equations that contain summations
My previous algebra course did not go over summation at all, and now that I'm in my new course, Discrete Math for Information Technology, we have been introduced to summation. I understand summation ...
2
votes
2answers
48 views
Combinatorial restriction on choosing adjacent objects
I am having trouble understanding an approach to the following problem. Suppose 14 books are aligned in a bookcase. How many ways can we choose 5 books so that no adjacent books are chosen? I think my ...
1
vote
1answer
21 views
Counting Card hands with various restrictions
I would like to know if my solutions are correct for the following three combinatorial card questions. In each question, assume we have a standard deck of cards (13 ranks, and 4 suits).
How many ...
1
vote
2answers
160 views
Need help with an integration word problem. This appears to be unsolvable due to lack of information.
I'm not sure I understand what to do with what's given to me to solve this. I know it has to do with the relationship between velocity, acceleration and time.
At a distance of 45m from a traffic ...
8
votes
1answer
167 views
Finding the general term of a sequence
I would like to find an expression for the sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots,\;$ $$-\frac{1}{6},\,\frac{2}{7},\,\frac{5}{8},\,\frac{8}{9},\,\frac{11}{10},\,\ldots$$
So by trial and ...
11
votes
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 ...
0
votes
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 ...
0
votes
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
