Idaho Society of Professional Engineers
Friday Update - 05/20/05
WELCOME NEW MEMBERS!
Vance Henry/Boise
UPCOMING EVENTS:
● May 24, 2005 -
ISPE Southwest Chapter May Meeting
● July 7 - 9, 2005 - NSPE
2005 Annual Convention, Chicago, Illinois
● October 28, 2005 - PE and
PLS Examinations - Boise, Idaho
● October 29, 2005 FE (aka
EIT) Examinations - Boise, Idaho, Pocatello, Idaho, Moscow, Idaho
ISPE SOUTHWEST CHAPTER 2005
SPRING GOLF TOURNAMENT
The Southwest Chapter of the ISPE held a fundraiser golf tournament on May 13th
at the Purple Sage Golf in Caldwell. 18 teams participated with a record turnout
of golfers. Over $3200 in profit from the entry fees and hole sponsorships will
go towards the ISPE Southwest Chapter's support of both the MATHCOUNTS and
Future City programs. Thanks to all golfers that turned out for a beautiful
afternoon and hope everyone had a great time. First place went to the foursome
from HP of Jim Reppell, Mike Zortman, Kevin Davis and Doug Holbrook. Second
place went to the top golfers from Washington Group International of Kim
Bissell, Dan Stickney, Kelly Head and Steve Frazier. Third place honors went to
a new team this year from HDR of Kate Welch, Lillian Bowen, Mike Johnson, and
David Statkus with help from Sean Clow of Strata. Long drive honors went to Dan
Stickney and Jared Blades while the closest to the pin honors went to Gordon
Smith and Brett Broadhead.
A special thank you to the corporate sponsors of B&A Engineers, CH2M Hill, Civil
Dynamics, Entranco, Geo Engineers, Geo Tek, HDR, JUB, Land Group, MWH,
RiveRidge, Strata, Terracon, Toothman-Orton, Treasure Valley Engineers, and
Washington Group.
We are thinking of repeating the tournament again in the fall. Please forward
any suggestions to Lynn Olson at
lolson@toengrco.com on how we can make the next tournament bigger and
better!
NSPE DISCUSSION FORUMS
These forums are designed to give NSPE members and others interested in the
engineering profession an opportunity to share ideas and discuss workplace and
professional issues. Forum topics include Licensure, Mentoring, Career
Transition, Professional Liability and Risk Management, Business Development,
and Technical and Emerging Issues. Visit the
NSPE web site to learn more.
TAKE THE JETS CHALLENGE
Can you solve this JETS challenge problem? The answer will appear in next week's
edition of the Friday Update!
The Microwave Challenge
Microwave communication towers can penetrate almost any weather, but the sending
and receiving cones must be able to see each other. No obstructions are allowed
because the signal cannot bend like radio waves do. It is 40 miles across Lake
Ontario between tower cones located in Toronto and Niagara Falls, and the
diameter of the earth is 7,918 miles.
At what height (in feet) must the microwave cones be mounted between these
cities due to the curvature of the earth?
Answer to last week's MATHCOUNTS problem:
If the fractions have positive integer denominators less than or equal to 5,
then our denominator options are 1, 2, 3, 4 and 5. We need the value of the
fraction to be positive and less than or equal to 1, so the numerators must be
positive integers less than or equal to the denominators. Additionally, we’re
looking for distinct values. Note that 1/1 is the same value as 2/2, so we can
only include one value of 1. We also have to be careful to not include both 1/2
and 2/4. There are 10 distinct positive values that meet the conditions: 1/1,
1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5 and 4/5. We’re going to have to put these
in order, so let’s look at their decimal representations instead: 1, 0.5, 0.333,
0.666, 0.25, 0.75, 0.2, 0.4, 0.6, and 0.8. If we put these in order, we have
0.2, 0.25, 0.333, 0.4, 0.5, 0.6, 0.666, 0.75, 0.8 and 1. For the median of ten
terms, we need the average of the fifth and sixth terms, or the average of 0.5
and 0.6 in this case, which is 0.55. As a fraction, this is 55/100, which is
11/20 as a common fraction.
--------------------------------------------------------------------------------
Since a, b and c are consecutive integers, they are all really close to one
another. In fact, we could use b – 1, b and b + 1. Substituting these values
into (a + b + c) leaves us with (b – 1 + b + b + 1) = 3b. Without finding it
exactly, we can also see that (a ´ b ´ c) is going to be extremely close to (b ´
b ´ b) = b3. Now we have the equation (b3) ¸ (3b) = 341. This simplifies to (b2)
¸ (3) = 341. If we multiply both sides by 3, we have b2 = 1023. You may notice
that 1023 is almost 1024, which is 210 or (25) 2. So we can estimate that b2 =
(25) 2 and b = 25 or 32. Testing out a = 31, b = 32 and c = 33, we see that the
equation is true, and a = 31. This certainly would have been easier with a
calculator, but for the Sprint Round, estimation comes in very handy!
--------------------------------------------------------------------------------
Our original number n must be divisible by 8. Then n – 1 must be divisible by 9
and n – 2 must be divisible by 10. This last fact clues us in that n has a units
digit of 2, so we’re looking for a multiple of 8 that ends in 2 and a multiple
of 9 that is one less and ends in 1. The multiples of 9 might be the easiest to
start with – all of the digits will have to add to a multiple of 9. Some of the
initial ones to try are 81, 171, 261, 351, 441, 531, 621, 711, 801, 891, and
981. Each of these are divisible by 10 when we subtract 1, so we just need to
see if any are divisible by 8 if we add 1. Here would be the new numbers: 82,
172, 262, 352, 442, 532, 622, 712, 802, 892, and 982. The first one on the list
that is divisible by 8 is 352, so he bought 352 trees.
-------------------------------------------------------------------------------
In order to be a multiple of 100, there must be two factors of 2 and two factors
of 5. So let’s rewrite the members of the set in the prime factorization form:
{2, 2 ´ 2, 2 ´ 5, 2 ´ 2 ´ 3, 3 ´ 5, 2 ´ 2 ´ 5, 2 ´ 5 ´ 5}. Any combination of
two members that gives us at least two 2s and two 5s will be a multiple of 100.
There are 7 members, so there are "7C2" = 21 pairs to try. Only the following
seven pairings work: 2&50, 4&50, 10&20, 10&50, 12&50, 15&20 and 20&50. This is
7/21 or 1/3.
If you want to see last week's problem again, click
http://www.mathcounts.org/webarticles/anmviewer.asp?a=663&z=104
Idaho Society of Professional Engineers
PO Box 170239
Boise, ID 83717-0239
208-426-0636
Fax: 208-426-0639
E-Mail: ispe@rmci.net
Web Site: www.Idahospe.org
Idaho
Society of Professional Engineers
