Community

Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.
Login Register Memberlist Search AoPS Blogs Contests Galleries Forum Index
The time now is Wed Dec 02, 2009 3:06 pm
All times are UTC - 8
 		View posts since last visit
View unanswered posts
Home » Mathematics » Middle School Contests (MATHCOUNTS, AMC 8, MOEMS, Ages 10-13)
 
Middle School Marathon
Moderators: AIME15, frost13, isabella2296, LadyKn1ght, nebula42, rcv, solafidefarms
Post new topic   Reply to topic View previous topicView next topic
629 Posts • Page 30 of 32 • Previous 1, 2, 3, ..., 28, 29, 30, 31, 32 Next
Author Message
AceOfDiamonds
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 06 May 2009
Posts: 447
Location: Charlotte, North Carolina
To rate posts you must be logged in
#581
ban him Sad he's pissing me off and being a retard.

PostPosted: Thu Sep 24, 2009 2:33 pm  Back to top 
  ProfilePM
Maybach
Navier-Stokes Equations
Navier-Stokes Equations


Offline
Joined: 06 Jun 2009
Posts: 1684
Location: NW Indiana
United States
To rate posts you must be logged in
#582
Solution
The numbers are 18 and 21, 1+8+2+1=12.

_________________
Goals: Make MC Nats, get 25 on AMC8, get 40/40 on Math League, 120 AMC10
Name Change: maybach to Maybach! :rofl:

PostPosted: Thu Sep 24, 2009 3:11 pm  Back to top 
  ProfilePM
$LaTeX$
Riemann Hypothesis
Riemann Hypothesis


Online
Joined: 11 Jul 2009
Posts: 480
Location: Why Are You Looking At This STALKER??? Say NO to Stalkers!
ChinaUnited States
To rate posts you must be logged in
#583
UMMMMM......

NEW PROBLEM

A cube has a volume of 343 cubic cm. What is the number of square centimeters in the surface area of the cube?

_________________
I,^{{\LaTeX}^{{Shall}^{{Pwn}^{ALL!}}}}
Wallbash Red DOPE!!! I FAIL AT EVERYTHING!!!
I hope this isn't Spam !!!!! Please rate this post at least a 4. If not, please pm me and tell me why.

PostPosted: Thu Sep 24, 2009 3:14 pm  Back to top 
  ProfilePM
basketball9
Hodge Conjecture
Hodge Conjecture

Offline
Joined: 30 Jul 2009
Posts: 92
Location: ....
United States
To rate posts you must be logged in
#584
solution
solution
A cube has equal side lengths so we need to find what cubed equals 343 and that is 7. The surface area of a cube is the side length to the sixth power and 7^6=117649

np what is the 100th term in 2/7

PostPosted: Thu Sep 24, 2009 3:44 pm  Back to top 
  ProfilePM
batteredbutnotdefeated
Yang-Mills Theory
Yang-Mills Theory


Online
Joined: 21 Mar 2009
Posts: 553
Location: probably near my laptop
IndiaUnited States
To rate posts you must be logged in
#585
ummmm... your new problem makes no sense.
_________________
"Signature are things that allow you to express the most blatant of thoughts in the most cryptic of ways." ~ BBND Liked my quote? it's original! RATE THIS POST A 6-cube. you know you want to. Smile

PostPosted: Thu Sep 24, 2009 4:42 pm  Back to top 
  ProfilePMBlog
Erdong171
P versus NP
P versus NP


Offline
Joined: 05 Sep 2008
Posts: 27
Location: Somewhere near Springfield, United States
ChinaAntarctica
To rate posts you must be logged in
#586
I think he means the 1000th digit after the decimal of the decimal representation of 2\7.

PostPosted: Thu Sep 24, 2009 6:37 pm  Back to top 
  ProfilePMBlog
randomtext
Hodge Conjecture
Hodge Conjecture

Offline
Joined: 13 Nov 2008
Posts: 70
To rate posts you must be logged in
#587
Erdong171 wrote:
I think he means the 1000th digit after the decimal of the decimal representation of 2\7.
Ok then, but he said 100th digit xD

Solution
I honestly can't find a way to do this without a calculator without memorizing the decimal representation of \frac {2}{7}, which is 0.285714... repeating... (anyone know how to do overbar in \LaTeX? After that, it's pretty easy, just do 100 mod 6 (the number of repeating digits), which is 4. The 4th digit in 285714 is \boxed{7}.


NP
What is .7823\overline{624} as a fraction?

EDIT: changed my NP
Last edited by randomtext on Mon Sep 28, 2009 10:26 am; edited 1 time in total 
PostPosted: Sun Sep 27, 2009 7:22 pm  Back to top 
  ProfilePM
cgyao15
Navier-Stokes Equations
Navier-Stokes Equations


Offline
Joined: 08 Nov 2007
Posts: 1166
Location: STALKER!!! >:(
To rate posts you must be logged in
#588
Code:
 $\overline {}$
i would think shows up like this
\overline {.45}
_________________
Check out my new avatar made by Izzy. PM her to get one!

PostPosted: Mon Sep 28, 2009 5:14 am  Back to top 
  ProfilePMBlog
randomtext
Hodge Conjecture
Hodge Conjecture

Offline
Joined: 13 Nov 2008
Posts: 70
To rate posts you must be logged in
#589
Thanks, changed my NP. Smile

PostPosted: Mon Sep 28, 2009 10:26 am  Back to top 
  ProfilePM
goldenboy1.618
Poincare Conjecture
Poincare Conjecture

Offline
Joined: 14 Mar 2009
Posts: 147
Location: USA
To rate posts you must be logged in
#590
Solution
Ughh...Such an ugly number...Anyway, here it is:
If we call the number x = 0.7823\overline{624}, then we can say 1000x = 782.3624\overline{624}.
Now we can line these up and subtract without any repeating decimals to get 999x = 781.5801\implies 9990000x = 7815801.
Dividing gives us x = \frac{7815801}{9990000} = \boxed{\frac{2605267}{3330000}}. Seriously, such a nasty number...


NP
Given p + q = 2 and p^2 + q^2 = 2, what is the largest possible real value of p^{2009} + q^{2009}?
_________________
i to pi: "Be rational!" Very Happy
pi to i: "Get real!" Mr. Green

PostPosted: Tue Sep 29, 2009 10:11 am  Back to top 
  ProfilePM
Erdong171
P versus NP
P versus NP


Offline
Joined: 05 Sep 2008
Posts: 27
Location: Somewhere near Springfield, United States
ChinaAntarctica
To rate posts you must be logged in
#591
Solution
Solving the system of equations, p+q=2 and p^2+q^2=2, gets p=1 and q=1. Substituting, p^{2009}+q^{2009}=\boxed{2}


NP
Given that x^2-x+1=0, find x^6+\frac{1}{x^6}.


PostPosted: Tue Sep 29, 2009 6:13 pm  Back to top 
  ProfilePMBlog
AwesomeToad
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 25 Apr 2009
Posts: 808
Location: West Lafayette, IN (Rating: 1337)
United States
To rate posts you must be logged in
#592
Solution
Since x^2-x+1=0,x+\frac{1}{x}=1 so x^3+\frac{1}{x^3}=-1 and (x^3+\frac{1}{x^3})^2=x^6+\frac{1}{x^6}+2 and x^6+\frac{1}{x^6}=-3

NP
If x^2+\frac{1}{x^2}=14 and x>0 find x^5+\frac{1}{x^5}

PostPosted: Wed Sep 30, 2009 8:29 am  Back to top 
  ProfilePMBlog
AndrewTom
Navier-Stokes Equations
Navier-Stokes Equations

Offline
Joined: 13 Dec 2006
Posts: 1641
To rate posts you must be logged in
#593
Solution


(x+\frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} +2 = 14+2 = 16

x+\frac{1}{x}=4

(x^{2} + \frac{1}{x^{2}})(x+\frac{1}{x}})= x^{3} + \frac{1}{x^{3}}+x + \frac{1}{x}

14\times4=x^{3} + \frac{1}{x^{3}} + 4

x^{3} + \frac{1}{x^{3}} = 52

(x^{2} + \frac{1}{x^{2}})(x^{3} + \frac{1}{x^{3}})= x^{5} + \frac{1}{x^{5}}+x+\frac{1}{x}

14\times52=x^{5}+\frac{1}{x^{5}} + 4

x^{5} + \frac{1}{x^{5}} = 724



NP


Which is larger 2^{85} or 3^{53}?



PostPosted: Wed Sep 30, 2009 10:46 am  Back to top 
  ProfilePM
goldenboy1.618
Poincare Conjecture
Poincare Conjecture

Offline
Joined: 14 Mar 2009
Posts: 147
Location: USA
To rate posts you must be logged in
#594
Solution
Taking the base-ten logarithm of each number gives the number of digits it has.
2^{85} has \lfloor85\log2\rfloor digits, which is approximately 85\times0.3 = 25.5.
3^{53} has \lfloor53\log3\rfloor digits, which is approximately 53\times0.48 = 25.44.
Thus, they both have 25 digits, but 25.5 is slightly larger, so the larger number is \boxed{2^{85}}.


NP
How many zeroes are at the end of 2009!_{10}?
_________________
i to pi: "Be rational!" Very Happy
pi to i: "Get real!" Mr. Green

PostPosted: Wed Sep 30, 2009 12:40 pm  Back to top 
  ProfilePM
cgyao15
Navier-Stokes Equations
Navier-Stokes Equations


Offline
Joined: 08 Nov 2007
Posts: 1166
Location: STALKER!!! >:(
To rate posts you must be logged in
#595
base ten? Huh?
isn't that just \ 2009! technically.
And hint

Blah i'm lazy 2009/5=a a/5=b b/5=c etc,
Smile
_________________
Check out my new avatar made by Izzy. PM her to get one!

PostPosted: Wed Sep 30, 2009 5:14 pm  Back to top 
  ProfilePMBlog
goldenboy1.618
Poincare Conjecture
Poincare Conjecture

Offline
Joined: 14 Mar 2009
Posts: 147
Location: USA
To rate posts you must be logged in
#596
I guess I'll have to post a solution.
There are \lfloor\frac{2009}{5}\rfloor = 401 factors of 5^1.
Similarly, we find \lfloor\frac{401}{5}\rfloor = 80 factors of 5^2.
Next there are \lfloor\frac{80}{5}\rfloor = 16 factors of 5^3 and
\lfloor\frac{16}{5}\rfloor = 3 factors of 5^4.
Now our sum is 401 + 80 + 16 + 3 = \boxed{500} zeroes.


NP
In square MNOP, I draw arc MQO centered at N, and I draw arc NQP centered at M.
Given that these arcs intersect at Q, find the measure of QNM. (Source: Practice test for the NYC SSHSAT)
_________________
i to pi: "Be rational!" Very Happy
pi to i: "Get real!" Mr. Green

PostPosted: Sat Oct 10, 2009 4:33 am  Back to top 
  ProfilePM
AwesomeToad
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 25 Apr 2009
Posts: 808
Location: West Lafayette, IN (Rating: 1337)
United States
To rate posts you must be logged in
#597
New Problem
If 22^2\cdot55^2 = 11^2N^2 and N > 0, what is N?
_________________
Join Mock AMC! Participation encouranged and appreciated!

PostPosted: Mon Oct 12, 2009 8:17 am  Back to top 
  ProfilePMBlog
gauss1181
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


Offline
Joined: 08 Sep 2007
Posts: 2603
Location: IMSA
United States
To rate posts you must be logged in
#598
22^255^2=11^22^255^2=11^2110^2

So N=\boxed{110}

NP:

Heather and Brooke are playing a game in which each player is to remove 1, 2, 3, 4, or 5 stones from a pile of 30 stones on her turn. They take turns, and whoever picks up the last stone wins. Heather goes first. How many stones should she take from the pile to guarantee winning?
_________________
My Olympiad Compilation! (plus some bits of randomness too)
Latest Problems Typed: 1979 ISL number theory problem

PostPosted: Mon Oct 12, 2009 8:26 am  Back to top 
  ProfilePMWWWAIMYMBlogAlbum
vliu
P versus NP
P versus NP

Offline
Joined: 16 Jan 2008
Posts: 25
Location: hmm SOMEWHERE OVER THE RAINBOW
To rate posts you must be logged in
#599
No vertex means the lowest or highest point of a parabola
THE SOLUTION:The vertex is usually located where x is 0 so the point would be (0,47) and i think that is the solution

New Problem: A point inside a square is positioned so that the distances to the four vertices are 27, 21, 6 and x. If x is a whole number , what is the value of x

PostPosted: Mon Oct 12, 2009 7:16 pm  Back to top 
  ProfilePM
AIME15
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


Offline
Joined: 24 Mar 2008
Posts: 8594
Location: Pleasanton, TX
United States
To rate posts you must be logged in
#600
Wait, I fail to see how she should take (0,47) stones to guarantee winning...?
_________________
GOALS: MC School: 46 | Chapter: 46 | State: 46 | National: 46 | AMC 8: 25 | AMC 10: 150 | AMC 12: 150 | AIME: 15 | USAMO: 42 | TST: 63 | IMO: 42 |

PostPosted: Mon Oct 12, 2009 8:04 pm  Back to top 
  ProfilePMAIMBlog
Display posts from previous:   Sort by:   
629 Posts • Page 30 of 32 • Previous 1, 2, 3, ..., 28, 29, 30, 31, 32 Next
Post new topic   Reply to topic View previous topicView next topic
Home » Mathematics » Middle School Contests (MATHCOUNTS, AMC 8, MOEMS, Ages 10-13)
 
Jump to:  


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You can download files in this forum
You cannot post calendar events in this forum


© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us