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  1. reenmachine

    Earth-sized exoplanet spotted in star’s habitable zone

    http://www.nasa.gov/ames/kepler/nasas-kepler-discovers-first-earth-size-planet-in-the-habitable-zone-of-another-star/index.html#.U1BUR1csSuQ Don't know if this is the right section to post this , but I'm a sucker for any news on exoplanets so here goes.
  2. reenmachine

    Random question about cones and cylinders volume

    A cone's volume with height ##x## and radius ##y## is ##1/3## of the volume of a cylinder with height ##x## and radius ##y##.I was trying to visualize it in my head and struggled a bit.Take a rectangle triangle with height ##x## and the other side of lenght ##y## which isn't the hypothenuse ...
  3. reenmachine

    Problem with the chat

    A member in the chat has me on ignored , now I know it's been a couple of weeks since he has ignored me and this problem never occured during that time.What happens is that when I enter the chatroom or when he enters the chat room , a window pop-up appears informing me that "XXX is ignoring your...
  4. reenmachine

    Proof Exercise II

    Homework Statement Suppose ##x## and ##y## are positive real numbers.If ##x < y## , then ##x^2 < y^2##. Homework Equations Assume ##x<y## with ##x,y \in ℝ^+##.This implies that ##\exists z \in ℝ^+## such that ##x+z=y##.We have ##y^2 = (x+z)^2 = x^2 + 2xz + z^2## , and this proves that if ##x...
  5. reenmachine

    Proof exercise

    Homework Statement Prove that if ##x \in ℝ## and ##0<x<4## , then ##\frac{4}{x(4-x)}≥1##. (I'm really not sure about that one but managed to attempt something) Homework Equations We first want to prove that ##\forall y \in \mathbb{Z}## , the largest product of any ##a,b \in ℝ## with...
  6. reenmachine

    Just ran over a fox

    Just ran over a fox :( I was bored tonight so I decided to go out for a drive.As I was driving , two running foxes appeared right in front of my car and I ran over one of them.This happened while a police car was following me , so I made a U-turn to go check with them.They told me this happened...
  7. reenmachine

    Binomial Theorem IIII

    Homework Statement Use the binomial theorem to find the coefficient of ##x^6y^3## in ##(3x-2y)^9##. Homework Equations ##1+9+36+84+126+126+84+36+9+1## (I used two lines for the lenght) ##1(3x)^9(-2y)^0+9(3x)^8(-2y)^1+36(3x)^7(-2y)^2+84(3x)^6(-2y)^3+126(3x)^5(-2y)^4##...
  8. reenmachine

    Applying the binomial theorem

    Homework Statement Use the binomial theorem to find the coefficient of ##x^8y^5## in ##(x+y)^{13}##. Homework Equations We know 13 - 5 = 8 , so we have ##\binom{n}{5}x^{n-5}y^5 = \binom{13}{5}x^8y^5## ##\binom{13}{5} = \frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{5!8!} = \frac{13...
  9. reenmachine

    Binomial Coefficient - Factorials Part III

    Homework Statement ##| \ X \in \mathcal P(\{0,1,2,3,4,5,6,7,8,9\}) : |X|= 4 \ | = \ \ ???## Homework Equations There's no wording in the exercise , just what I wrote above.If I understood correctly , they asked me to find the cardinality of the set of all subsets of {0,1,2,3,4,5,6,7,8,9}...
  10. reenmachine

    Binomial Coefficient - Factorials Part II

    Homework Statement This one is trickier than the problem in my other thread in my opinion.Twenty-one people are to be divided into two teams , The Red Team and the Blue Team.There will be 10 people on Red Team and 11 people on Blue Team.How many ways to do this? I am not sure how to solve...
  11. reenmachine

    Set Theory - Counting - Binomial Coefficient - Factorials

    Homework Statement A department consists of 5 men and 7 women.From this department you select a committee with 3 men and 2 women.In how many ways can you do this? Homework Equations Since the "overall set" (the entire department) is composed of both men and women and each has a specific...
  12. reenmachine

    Highschool mathematics curriculum

    Hi all! I'm a mid-20s guy from Montreal , Quebec , Canada completing his highschool mathematic courses at an highschool for adults with the eventual goal of entering a bachelor program in mathematics (probably either at McGill or Universite de Montreal (UdeM)). Basically I'm worried about the...
  13. reenmachine

    Factorials and lists/subsets counting

    1.1 Homework Statement Using only pencil and paper , find the value of ##\frac{120!}{118!}## 2.1 Relevant equations ##\frac{120 \cdot 119 \cdot 118!}{118!} = 120 \cdot 119 = 14280## 1.2 Homework Statement Compute how many 9-digit numbers can be made from the digits...
  14. reenmachine

    Laws of Exponants II

    Homework Statement Simplify this expression and express the result with only positive exponants. Homework Equations The expression: ##\left( \frac {(-49^4 \ c^{-2} \ d)^3}{14^6 \ c^{-1} \ d^2} \right)^{-1}## The Attempt at a Solution ##\left( \frac {(-49^4 \ c^{-2} \...
  15. reenmachine

    Laws of exponants

    Homework Statement Simplify the following expression: ##\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}## ÷ ##\left( \frac{-10^2}{100^\frac{1}{2}} \right)^3## Homework Equations Start with this side: ##\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}##...
  16. reenmachine

    Proof attempt - Basic Set Theory

    Homework Statement Prove that if A and B are sets , then ##A \subseteq B \ \ \leftrightarrow \ \ A - B = \varnothing## The Attempt at a Solution Let ##A \subseteq B## be arbitrary.The definition of ##A \subseteq B## implies that ##\forall x \in A## , ##x \in B##.This implies that ##A - B...
  17. reenmachine

    Wondering about prison sentences

    My knowledge of the justice system is close to none-existant.I have no criminal record and it's not something that normally interests me.Still , I was wondering about a specific aspect of prison sentences and I wanted to have some feedback on the issue.Why does the justice system , from my...
  18. reenmachine

    Set Notation , Set Theory

    Homework Statement Build a notation for the set: ##\{ ... , -8 , -3 , 2 , 7 , 12 , 17 ,...\}## Homework Equations ##2+5(0) = 2## ##2+5(1) = 7## ##2+5(-1) = -3## etc... The Attempt at a Solution ##\{ \ 2+5y \ | \ y \in \mathbb{Z} \ \}## Take note that you could replace ##2## by any...
  19. reenmachine

    Alcohol and acetaminophen

    Edit: sorry for the typo in the title , can't edit I looked around on google quite a bit and it's very hard to find precise information on the issue.All I can find is vague warnings like "acetaminophen and alcohol is bad for the liver". Anybody have knowledge on just how dangerous the mix can...
  20. reenmachine

    Set Theory , building a set notation

    Homework Statement Build a set notation for $$\bigcup_{i \in N}R × [i , i + 1]$$ The Attempt at a Solution ##\{(x,y) \in R : x \in R \ \ \exists z \in N \ \ z ≤ y ≤ (z+1)\}## Last time I tried one of these kind of sets I struggled quite a bit , so I'm interested in knowing how much...
  21. reenmachine

    Building a set notation part II

    Homework Statement As an exercise , the book I'm reading ask me to build a set notation for the following set: ##\{... \ , \frac{1}{27} \ , \frac{1}{9} \ , \frac{1}{3} \ , 1 \ , 3 \ , 9 \ , 27 , \ ...\}## The Attempt at a Solution After playing with the numbers a couple of minutes , I came...
  22. reenmachine

    Building a set notation

    Homework Statement The book I'm reading ask me to build a set notation for the following set: ##\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}##. The Attempt at a Solution I attempted to build a set notation and came with the result: ##\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}## My...
  23. reenmachine

    Listening to music while doing math

    I still remember a long time ago one of my teachers told me ''Discman(LOL) are forbidden in class , if you are coming to class you should be able to concentrate and music ruins your concentration''.I then proceeded to explain to her that I thought music could actually help me concentrate even...
  24. reenmachine

    Question about proof from a guy with a highschool education

    Hi everyone , I was trying to understand what a math proof is or more specifically how it is presented. Suppose I want to prove that if A , B and C are real numbers and that (A + B) = C , then (A - B) = (C - 2B). How would I present a proof for this? Would this be good?: If (A + B) = C , then...
  25. reenmachine

    26 years old , never went to college , too late for a math career?

    I'm 26 years old , been thinking about going back to school for the last 2 years to pursue a career in mathematics. Never went to college , stopped my education at the end of highschool where I had multiple personal problems that are now more or less solved.Always been strong at math since I...
  26. reenmachine

    Percentage and probability problem

    Homework Statement Suppose I play a game and have a 8,33% chance to lose and a 5,7% chance to win (with the additionnal 85,97% forcing me to play again until I win or lose) does this mean I have a 40,6% chance to win? Homework Equations 8.33 + 5.7 = 14.03 8.33/14.03*100 = 59,4% chance to...
  27. reenmachine

    Percentage question (probability , game)

    Suppose you throw a dice and on the first throw you win if you score 1 , you lose if you score 2 & 3 and have to throw the dice again if you hit 4 , 5 or 6.If you have to throw the dice again the rules changes and you win if you hit 1 but lose if you hit 2.If you hit any other number , you...
  28. reenmachine

    Question about a probability problem

    Hi all , here's hoping someone could help me with this problem. :) The problem is basically as follow: You have 7 balls in your pocket , 3 are whites and 4 are blacks.If you take out 3 balls out of your pocket , what are the odds that you'll have 2 white balls and 1 black ball in your hand ...
  29. reenmachine

    Need Help to understand a simple way to solve this problem

    If Joe produce 16 A everytime he produce 30 K , receives 7 additionnal A everytime he produce 40 K and receive 2 additionnal K everytime he produce 30 A , how many A will he have in total when he's gonna have 180 K? More clearly: 16 A every 30 K +7 A every 40 K + 2 k every 30 A...
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