# Tagged Questions

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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### 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 ...
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### 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....
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 '...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 : ...
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### 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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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### Elements and Unions [closed]

Need help solving this problem step by step!
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 $g_\epsilon\... 2answers 252 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 sleeping, ... 1answer 212 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 - a)1/... 2answers 57 views ### X and Y are independent random variables and their distributions are.. X and Y are independent random variables and their distributions are..$P(X=1) = 0.1 P(X=2) = 0.2P(X=3) = 0.3 P(X=4) = 0.4 P(Y=4) = 0.4 P(Y=2) = 0.3P(Y=3) = 0.2 P(Y=4) = 0.1$I ... 1answer 32 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$y$... 3answers 92 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)$. How do I go about doing this? 0answers 175 views ### Strategy in solving linear equations with 3 unknown variables I have an equation with this form:$ A x + B y + C z = NA$,$B$,$C$, and$N$are known.$A$,$B$,$C$,$N$,$x$,$y$, and$z$are positive integers$>= 0$. I need to find out values of$x$,... 1answer 452 views ### P(X>Y) Probability Double Integral$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 ... 1answer 46 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 ... 1answer 32 views ### Probability “average” understanding This is more of a problem understanding probabilities than an actual question. In a game I am playing I can use a certain item to try to unlock different levels. The item will unlock a new level ... 2answers 72 views ### How many real solutions of this equation? How many real solutions of this equation $$\sqrt{x}+\sqrt{1-x^2}=\sqrt{2-3 x-4 x^2}?$$ I posted my question at here http://mathematica.stackexchange.com/questions/51316/how-can-i-get-the-exact-real-... 2answers 433 views ### Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling? 8/18/14 Edit: If anyone has a copy of a related reference, then I would be happy to see it. For now, I am accepting the answer below and considering the question answered in the affirmative: Yes. ... 1answer 199 views ### How is this card/paper plate magic trick done? There are 3 paper plates, in which A is written on one, B on the 2nd, and C on the third. Now the person performing the trick knows the initial order of the paper plates. He then asks an audience ... 1answer 52 views ### Ehrenfest's urns have been loaded with a total of 6 balls… Ehrenfest's urns (two of them) have been loaded with a total of 6 balls. If the first urn now contains 1 ball, what is the probability that it will contain 2 balls after the next transition? My ... 1answer 76 views ### Probability - A trial consists of tossing a fair coin twice and noting H = number of heads observed… A trial consists of tossing a fair coin twice and noting H = number of heads observed. What is the probability that if 5 trials are performed, we will note H=0 two times, H=1 one time, and H=2 two ... 2answers 378 views ### Advice for self-studying Inequalities and Calculus I'm interested in self-studying the following books over the next year or so: Spivak's Calculus (I'm already in Ch. 5 and it is very slow going) The Cauchy-Schwarz Master Class by J. Michael Steele ... 2answers 114 views ### How can I solve this problem without having to do it by hand? I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ... 1answer 78 views ### How can I solve this problem without doing it by hand? [duplicate] I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ... 2answers 106 views ### Is there any way to solve this problem without having to do it by hand? [duplicate] I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement. Is there any way to group ... 2answers 68 views ### Guess the right permutation game Consider the following game (somewhat similar to Bulls and Cows): player A selects a permutation of$n$different numbers, say$1$to$n$. Player B then has to guess the permutation: he suggests some ... 2answers 994 views ### Concept of Probability in math first level I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ... 1answer 1k views ### Mean and Standard Deviation self thought problem I am 13 years old trying to teach myself about standard deviation and was wondering how this problem would look like. I know I am young to be learning this but I was reading about this and got ... 0answers 37 views ### Difficult Integral in functional basis Let $$g(x)=\int f\prime(x)\left[\frac{4}{3}x^2+4x^3+(2x^2+4x^3)f(x)+6x^2f^2(x)+xf^3(x)\right]dx$$ express$g(x)$in terms of$\{1,x,x^2,x^3,....\}$and$\{f(x),f^2(x),f^3(x),...\}$. Is there a clever ... 2answers 61 views ### Divisibility of sum of squares I'm currently working through an olympiad problem book that uses the following fact:$3 \mid a^2 + b^2 \implies 3 \mid a$and$3 \mid b$. I don't see how to show this. I know for that a prime$p$... 1answer 41 views ### Special equation solving I would like to get x from the following function when the y is known and which + means If$...
I have a function for that I want to find the minimum. The function calculates the distance between two sets where a set is defined as matix of row vectors $D = [ d_1, d_2, ..., d_n]$, $d_n$ is a \$m \...