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.
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 ...
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...
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...
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...
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...
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##...
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...
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}...
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...
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...
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...
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...
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} \...
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}}##...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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 ...
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...