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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0
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0answers
27 views

trigonometry problem solving question!!

Crystal is organizing the seating arrangements for a concert in her local park. The first row's seats are modeled by the function f(x) = 12. To give everyone a good view, each row must have three more ...
0
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0answers
29 views

$\sum$ of binomial coefficients inequality

Let $m,n$ be positive integers with $m>n$. When is it true that $$m\cdot 5^{m-1}\cdot 3+\binom{m}{3}\cdot 5^{m-3}\cdot 3^3\cdot 2+\cdots +\binom{m}{2k+1}\cdot m^{m-2k-1}\cdot 3^{2k+1}\cdot ...
1
vote
1answer
128 views

Comparing $\pi^e$ and $e^\pi$

Comparing $\pi^{e}$ and $e^{\pi}$ I read the answer there but I didn't understand one thing. How I should know to put $\dfrac{π}e-1$ instead of $x$? If I had this question on a test, I had no idea ...
1
vote
2answers
20 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
3
votes
0answers
47 views

How to find $f$ and $g$ if $f\circ g$ and $g\circ f$ are given?

The question is: Let $f:\mathbb R\rightarrow \mathbb R$ and $g:\mathbb R\rightarrow \mathbb R$ be two functions such that $(f\circ g)(x)=4x^2+4x+1$ and $(g\circ f)(X)=x^2+2x+2$. Find $f(x)$ and ...
2
votes
1answer
62 views

Prove that $\sqrt{n} \le \sum_{k=1}^n \frac{1}{\sqrt{k}} \le 2 \sqrt{n} - 1$ is true for $n \in \mathbb{N}^{\ge 1}$

I'm trying to solve these induction exercises proposed by the department of mathematics of Oxford University. I don't know how to give a valid proof for the third one which says the following: ...
2
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0answers
28 views

Fermat pseudo primes

Is it possible for a number of the form $2^p-1$ with $p\in \mathbb{P}$ (the primes) to satisfy $3^{2^p-2}\equiv 1\pmod {2^p-1}$ and not be a prime? In other words, can a Mersenne number be a Fermat ...
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2answers
219 views

Can't solve this trignometric equation, why am I wrong?

There is this trig equation: $$ 5\tan x - 2\tan 2x = 0 \text{ for 0 < 0 < 360 } $$ So far I've gotten $$\tan x = \text{0, 180}$$ and all I have to solve now is $$\tan ^2x = 0.2$$ which gives ...
0
votes
1answer
42 views

Best approach or algorithm to solve equation with multiple variables?

I have an equation : $A^6x_1 + A^5x_2 + A^4x_3 + A^3x_4 + A^2x_5 + A^1x_6 + x_7 = B$ What can be the best algorithm/approach I can use to crack this? $A$ and $B$ are constants. $x_1,x_2...x_7$ are ...
1
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1answer
92 views

If one plays $132$ games in $77$ days, there is a span of consecutive days with exactly $21$ games

This is a high school contest question. Simple answers are required A chess player has $77$ days to prepare for a tournament. During this time he wants to have a match everyday and to have $132$ ...
1
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2answers
33 views

(What is the formula to find) What is the probability that the sum of the numbers on the tickets chosen is at least 7?

Senario: Box A contains four equal-sized tickets, numbered 1, 2, 3 ,4 Box B contains three tickets of the same size, numbered 4, 5, 6 An experiment consists of selecting one ticket from the box A ...
1
vote
2answers
47 views

How can I solve this puzzle using equations?

There's a hall with 100 seats. I want to fill up these seats with men, women and children; they're going to purchase seat positions. The cost per seat for men is 5 USD, women 1 USD, and children 0.05 ...
0
votes
1answer
15 views

How to find plane that's equidistant from the origin

Objective: Give the equation of a plane that crosses the axes at points equidistant from the origin. How do I make sure that the points $A(1,2,-2)$, $B(-5,1,1)$, $C(4,-3,1)$ are equidistant from the ...
7
votes
3answers
192 views

Calculate $\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$

I'm an eight-grader and I need help to answer this math problem. Problem: Calculate $$\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$$ This one is very hard for me. It ...
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0answers
36 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
23 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 ...
4
votes
2answers
105 views

Difficult generating function

Define a beautiful number to be an integer of the form $a^n$, where $a\in\{3,4,5,6\}$ and $n$ is a positive integer. Prove that each integer greater than $2$ can be expressed as the sum of pairwise ...
3
votes
1answer
82 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
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1answer
74 views

How to see 4th dimension? [closed]

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
53 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 ...
4
votes
4answers
167 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
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0answers
67 views

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

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
126 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 ...
6
votes
1answer
108 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
99 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. ...
0
votes
1answer
43 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
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1answer
65 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 ...
0
votes
3answers
11 views

How to find 2 data point in Bezier satisfy the condition the Chord Length Method?

Suppose bezier curve have 4 control point $P0$, $P1$, $P2$, $P3$. How to find 2 data point $D1$, $D2$ satisfy the condition the Chord Length Method? The Chord Length Method : ...
2
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3answers
91 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 ...
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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 : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
5
votes
2answers
54 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
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1answer
32 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
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3answers
28 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 ...
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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
54 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 ...
0
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0answers
32 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 ...
0
votes
2answers
126 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 ...
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votes
1answer
53 views

Find the speed of stream from rowing speeds with and against the stream

Problem 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: (A) 1 ...
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
64 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 ...
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1answer
30 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 ...
5
votes
2answers
177 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
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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
24 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
62 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?
0
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0answers
40 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 ...