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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-2
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0answers
21 views

Equation of a plane equidistant from 3 points

Question: Given 3 point (point A, point B, point C), find an equation to a plane that crosses the axes at points equidistant to the origin P[0,0,0]. Are the following steps the right way to approach ...
0
votes
1answer
18 views

How to know when a line is parallel to the xz-plane

What are some features of the equations of a line that is parallel to the xz plane, but does not lie on the plane, and is not parallel to any of the axes? So far all I got: -dot product of plane's ...
1
vote
2answers
284 views

Problem Solving ( Sequences and series)

After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D\exp^{-at}$ where $t$ represents time in hours and $a$ ...
1
vote
1answer
38 views

Difficult generating function

Prove that the coefficient of $x^i$ for $i=1,2,3,...$ in the expansion of $\prod_{n=0}^{\infty} (1+x^{3^n})(1+x^{4^n})(1+x^{5^n})(1+x^{6^n})$ is greater than $0$.
2
votes
1answer
41 views

Last 7 digits of 7th powers

Alice and Bob play the following game. They alternately select distinct nonzero digits from $1$ to $9$, until they have chosen seven such digits. Consider the resulting seven-digit number by joining ...
2
votes
1answer
62 views

How to see 4th dimension? [on hold]

Anyone has tricks or methods? Great help, thank you. P.S.: Abstractly of course, not actually seeing 4D, which I don't think is possible.
3
votes
1answer
46 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
1
vote
1answer
63 views

Calculating completed percentage of a jigsaw puzzle

At first I thought the solution for this problem was simple…maybe to you it will be, but it evades me at present. I need to figure out how to calculate the completed percentage of a jigsaw puzzle. ...
4
votes
4answers
163 views

Inequalities, when does the sign change here?

I have encountered a problem with inequalities. I have been looking at examples provided by two websites which 'solve' inequalities, however when I try using my own method, the extremely simple ...
1
vote
0answers
56 views

How long should you study Mathematics each day if you want to get into a graduate school? [on hold]

I'm a university student (Junior now!) and I was wondering how many hours fellow undergraduates and graduate students study a day. I hear posts about how time doesn't really matter and that it's about ...
6
votes
2answers
104 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
41
votes
15answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
1
vote
1answer
1k views

Problem Solving Question - A sidewalk being built around a garden

We have a garden that measures 17 feet by 20 feet. We want to pour cement for a 3-foot-wide sidewalk around the garden. To make the forms for the cement, we will need to buy some 2-by-4-inch lumber. ...
-1
votes
0answers
30 views

child custody percentage [on hold]

$1$st parent has custody every Tues $8$ am until Thursday $3:45$ pm and alternate weekends Saturday $8$ am until Tues $8$ am. $2$nd parent has custody every Thursday $3:45$ pm until Saturday $8$ am ...
6
votes
1answer
102 views

Coming up with short “magical” proofs

I was reading the solution to this problem: Prove that $f(n) = 2n$ is the only non-constant solution to $2f (m^2 + n^2 ) = (f (m))^2 + (f (n))^2 .$ The solution used these identities, pulled out of ...
9
votes
1answer
86 views

How could I improve this approximation?

In a computer application, I need to solve trillions of times an equation which can be reduced to $$f(x)=\sin(x)-a x=0$$ Newton methods (quadratic and higher orders) are used for the solution. ...
1
vote
3answers
25 views

Iterative Equation Problem with Constraints

I was given a programming riddle recently. It was eluded to that there is an equation, but I was told that finding the equation was not the goal, and that writing a simple program was the goal. I ...
0
votes
1answer
33 views

Basic Mixture question

Let's say that I have 50 ounces of 100% sugar water solution. If I add 50 more ounces of pure water to that solution. What percentage of sugar water solution would I have left?
1
vote
1answer
64 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
2
votes
3answers
80 views

Trouble with inequalities

I'm a 9th grade student, going into 10th grade. Math has always been a subject I enjoyed and excelled in. I'm writing a schoolboard-wide math contest next year in mid-February I believe. To prepare ...
11
votes
4answers
1k views

How to solve this sequence $165,195,255,285,345,x$

This is a question appeared in a competitive exam. The question is: Find the unknown term in $165,195,255,285,345,x$ 1)375 $\ \ \ \ \ \ \ \ $ 2)420 3)435 $\ \ \ \ \ \ \ ...
5
votes
2answers
53 views

Putting objects in a line.

I'm working on a project outside of school, and I've run into a bit a problem. I thought, maybe there are some problem solvers on the internet who would enjoy this. I have 8 balls, 3 red cubes, and ...
1
vote
2answers
83 views

How to solve for $x$ in the function $y=x\ln(x)$?

I have $y=x\ln(x)$ and I need to solve for x. How am I supposed to do that? Because I get $y=x\ln(x)$ $y=\ln(x^x)$ $e^y=x^x$ and I am stack here... Can somebody help me? EDIT In my case the ...
0
votes
1answer
29 views

Finding the range from standard deviation and Gaussian Curve

The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a ...
-1
votes
0answers
26 views

Splitting a remainder

So let's say i have a thousand pieces. Person 1 gets 350, person 2 gets 100 and person 3 gets 50. Now i have 500 pieces left. What i want to do now is split all the pieces i have left, over the 3 ...
3
votes
2answers
51 views

Sum of square roots of integers

Let $x, y$ be integers and consider the equation $$\sqrt{x}+\sqrt{y}= 8 \sqrt{31}.$$ It is claimed that this implies $\sqrt{x}= a\sqrt{31}$ and $\sqrt{y}=b \sqrt{31}$ for $a,b$ integers. While this ...
2
votes
3answers
679 views

Crossword puzzle- Crossnumber puzzle

The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator. ACROSS: a. A prime ...
26
votes
3answers
450 views

How does one cut onions in a mathematically efficient way?

Perhaps a math degree and cooking don't go hand in hand, but hopefully they do. I have been thinking about this problem for some time when in the kitchen without making any real progress: How does ...
0
votes
3answers
103 views

Unsure how to solve equation

I have the problem. Solve: $x^3 - 3x^2 + 2x - 5 = 0$. I've done similar, simpler ones like this, but in this case I don't know. Can someone at least tell me what you'd even call this exact type of ...
2
votes
2answers
506 views

Proving Holder's inequality using Jensen's inequality

Let $p$ and $q$ be positive reals such that $\frac{1}{p}+\frac{1}{q} = 1$, so that $p,q$ in $(1,\infty)$. For $\vec a$ and $\vec b \in \mathbb{R}^2$ prove that $|\vec a \cdot \vec b | \leq ||\vec ...
0
votes
0answers
31 views

Can I solve this problem with matrices?

So I have some two dimensional data sets thats I want to analyse. They can be viewed in 2D form as below: $M1$: $$\begin{matrix}00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 ...
0
votes
1answer
23 views

LASSO Problem - A matrix structure!

I'm wondering if anybody knows about the structure of $A^{m\times n}$ in real big data LASSO problems. I want to ask if anybody know what is the degree of sparsity and separability(number of nonzero ...
31
votes
9answers
3k views

When to give up on a hard math problem?

I practice olympiad problems from books like Putnam and Beyond. Often I come across a problem that I simply can't solve. After $\sim30$ minutes of deep thinking it feels like I'm ramming my head into ...
42
votes
3answers
809 views

Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?

I understand "transform methods" as recipes, but beyond this they are a big mystery to me. There are two aspects of them I find bewildering. One is the sheer multiplicity of such transforms. Is ...
14
votes
2answers
269 views

Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling?

Post-Bounty Edit: Still no answer; will gladly accept if someone can provide a reference. Earlier Edit: It appears that the answer is "yes," either by an already existent publication or by ...
-1
votes
1answer
48 views

Boats and Stream Problem

Boats and Streams: A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is: ...
1
vote
2answers
45 views

How to solve this simple linear equation

I have the following equation (I personally wrote) $2x + (5+3) = 46 + 3x$ Is the above equation possible at all? If yes, how to solve it? I am new to math, as a free-learner (not associated with my ...
2
votes
2answers
56 views

Elements and Unions [closed]

Need help solving this problem step by step!
2
votes
2answers
59 views

Why does the additive subgroup of $\mathbb{R}$ generated by $1$ and $\sqrt{2}$ contain arbitrary small elements? [duplicate]

Let $G\subset \mathbb{R}$ be the additive subgroup of $(\mathbb{R},+)$ defined by $G=\mathbb{Z}+\sqrt{2}\mathbb{Z}$. I want to prove that for every $\epsilon>0$ there exists an element ...
-2
votes
1answer
27 views

math question im stumped on [closed]

Two race cars are speeding around the racetrack at different speeds. One goes around the track in 2 minutes; the other goes around the track in 1 1/2 minutes. How often does the faster car pass the ...
0
votes
1answer
282 views

Distributions of $X^2$ and $X-1$ when $X$ is geometric

Let$ X$ be a discrete random variable with the probability mass function given by $p_x(x)= 2^{-x}$ for $x=1,2,3,\ldots$ and $0$ otherwise. a) Let $Y=X^2$, find the probability mass function of ...
5
votes
2answers
175 views

How many diamonds did they steal?

There are $7$ thieves. They steal diamonds from a diamond merchant and run away into the jungle. Whilst they're running, night falls and they decided to rest in the jungle. When everybody is ...
1
vote
1answer
56 views

what is wrong in my answer and what will be the correct solution for this probability question ?

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is - ...
0
votes
2answers
51 views

X and Y are independent random variables and their distributions are..

X and Y are independent random variables and their distributions are.. $P(X=1) = 0.1 $ $P(X=2) = 0.2$ $P(X=3) = 0.3 $ $P(X=4) = 0.4 $ $P(Y=4) = 0.4 $ $P(Y=2) = 0.3$ $P(Y=3) = 0.2 $ $P(Y=4) = 0.1$ I ...
0
votes
1answer
23 views

$X $ and $Y$ are continuous $RVs$, such that$ f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$

X and Y are continuous RVs, such that $f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$ I'm trying to find $P(x<1/2,y>1/2)$. So i'm integrating from $\dfrac{1}{2}$ to $1$ for $y$ ...
1
vote
3answers
60 views

Let $U$ be $~U [0,1] $and let $Y = U^{\frac{1}{2}}$

Let $U$ be $\sim \mathcal{U}[0,1]$ and let $Y = U^{1/2}$. I'm having trouble finding the $E(Y)$. How do I go about doing this?
-1
votes
0answers
13 views

Limiting Behaviour Transition Matrix [closed]

If I was given a transition matrix, and I want to know the limiting behaviour(limiting values) is there a "trick" or a quicker way instead of keep squaring my transition matrix? Also, if my only way ...
0
votes
0answers
38 views

Strategy in solving linear equations with 3 unknown variables

I have an equation with this form: $ A x + B y + C z = N$ $A$, $B$, $C$, and $N$ are known. $A$, $B$, $C$, $N$, $x$, $y$, and $z$ are positive integers $>= 0$. I need to find out values of ...
0
votes
1answer
21 views

Uniform Spinner is spun twice..

A fair uniform spinner is spun twice, and the results V and W are noted. V and W are uniform RVs ∼U[0,1]. I'm trying to answer the question what is the joint pdf for V and W. I know that I have to ...
0
votes
1answer
38 views

P(X>Y) Probability Double Integral

$f(x,y) = \frac{12}{7(x^2 + xy)}$ $ 0 \le x \le 1$ and $0 \le y \le 1 $ I want to know the $P(X>Y)$. I believe the correct solution to this is integrating from 0 to 1 for dy and y to 1 for dx ...