[Search for users]
[Overall Top Noters]
[List of all Conferences]
[Download this site]
| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
1635.0. "1992 American Invitational Math Exam" by BEING::EDP (Always mount a scratch monkey.) Wed Jul 01 1992 09:30
Here are the last three.
-- edp
13. Triangle ABC has AB=9 and BC:CA=40:41. What is the largest area
that this triangle can have?
14. In triangle ABC, A', B', and C' are on sides BC, AC, and AB,
respectively. Given that AA', BB', and CC' are concurrent at the point
O, and that
AO BO CO
-- + -- + -- = 92,
OA' OB' OC'
find the value of
AO BO CO
-- * -- * --.
OA' OB' OC'
15. Define a positive integer n to be a "factorial tail" if there is
some positive integer m such that the base-ten representation of m!
ends with exactly n zeroes. How many positives integers less than 1992
are not factorial tails?
| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1635.1 | by expressing area as f of x, and make derivative=0 to find x | STAR::ABBASI | i^(-i) = SQRT(exp(PI)) | Wed Jul 01 1992 11:47 | 5 |
| > 13. Triangle ABC has AB=9 and BC:CA=40:41. What is the largest area
> that this triangle can have?
820 square units ?
|
| 1635.2 | 14 | DESIR::BUCHANAN | | Mon Jul 06 1992 06:15 | 14 |
| 14.
AO
Let a = --, and similarly define b & c.
OA
Then by manipulating the obvious vector equations, to eliminate everything
except a,b & c, we can't fail to end up with the pretty:
abc = a+b+c + 2
whence the answer.
Andrew.
|