# Search results

1. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...