Idaho Society of Professional Engineers
Friday Update – 05/04/07
UPCOMING EVENTS:
• May 11, 2007 – National
MATHCOUNTS Competition –
Convention Center, Fort Worth, Texas
• May 11, 2007 –
ISPE
Southwest Chapter Spring Fundraiser Golf Tournament - 4-Person Scramble -
1:00 PM - Purple Sage Golf Course
• May 15, 2007 -
ISPE Southwest Chapter Noon Meeting – 12:00
Noon – Washington Group International – Training Room
• July 26 – 29, 2007 –
NSPE 2007 Annual
Conference – Denver, Colorado
NEW! FREE WEB
SEMINARS
•
Becoming a PE shares information on how to advance your career with this
important designation and why you shouldn't wait any longer!
•
Changing the PE Paradigm includes discussion of the initiative to require
engineering education beyond the bachelor’s degree as a prerequisite for
licensure
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MATHCOUNTS PROBLEM OF THE WEEK
Can you solve this MATHCOUNTS problem? The answer will appear in next week's
edition of the Friday Update!
United States Postal Rates
The Forever Stamp features the Liberty Bell image and the word "forever." It
will always be available at the price of a First-Class Mail stamp in effect at
the time of purchase. To introduce the stamp to the public, the Postal Service
began offering the stamp on April 12, 2007 at 41 cents. Customers may use the
stamp as soon as they wish, but stamp prices will not change until May 14. When
prices change in the future, the Forever Stamp will sell at the new one-ounce,
single-piece First-Class Mail price. It has been suggested that you might want
to stock up on these new 41 cent stamps to avoid price hikes in postage in the
future. Let’s see if this is a good idea.
On May 14, 1975 the single-piece First-Class Mail price was 10 cents for the
first ounce. On May 14, 2007 the price will increase to 41 cents for the first
ounce. What is the percent increase in the one-ounce, single-piece First-Class
Mail price during that time period?
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Suppose the United States Postal Service had made available a Forever Stamp on
May 14, 1975 and Juan’s father was trying to decide if he should buy 1000 of the
10-cent stamps to protect against future price increases or invest the same
amount of money. At what percent interest compounded annually would Juan’s
father have had to invest his money on May 14, 1975 so that the amount of
dollars he has in his investment exceeds the value of the postage of the 1000
stamps on May 14, 2007? Express your answer to the nearest tenth.
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Assume the annual increase in the United States Postal Rate fits a linear model
between May 14, 1975 and May 14, 2007. What has been the annual average increase
in cents in the Postal Rate over this time span? Express your answer to the
nearest tenth.
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Juan thinks the United States Postal Rate will increase from 41 cents to 44
cents on May 14, 2008. He sends 30 billing statements for his business through
the United States Mail each month. He plans to buy enough Forever Stamps to
cover sending all of his billing statements for the 12 months beginning May 14,
2008 through May 13, 2009. Assuming that there are no other price increases
during that time, what percent of his postage costs will he save by buying the
Forever Stamps on or before May 13, 2008? Express your answer to the nearest
tenth.
Answer to last week’s MATHCOUNTS problem:
Divide the cost of each size pizza
by its area. C ÷ π r2
Small: 1520 ÷ π 52
= 19 cents
Medium: 1885 ÷ π 62
= 17 cents
Large: 2270 ÷ π 72
= 15 cents
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The surface area of
the outside of the box is the sum of the area of the top, bottom, and the four
sides: top = 14.5 x 14.5, bottom = 14.5 x 14.5, each side = 14.5 x 1. 2(14.5 x
14.5) + 4(14.5 x 1) = 478.5 square inches.
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The bottom of the
box for a circular large pizza is a square whose sides are 14.5 inches. The
area of the square bottom of the box is 14.5 x 14.5 = 210.25 square inches. The
area of the circular large pizza is π 72 = 153.94 square inches.
210.25 – 153.94 = 56.31. The area of the bottom of the box is 56 square inches
greater than the area of the pizza.
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The area of the
circular large pizza is π 72 = 153.938... square inches. Rounding
the area of the circular pizza to the nearest whole number gives the area of the
rectangular pizza, 154 square inches. Possible dimensions for the rectangular
pizza are 1 x 154, 2 x 77, 7 x 22, and 11 x 14. The dimensions of the rectangle
with the least possible perimeter are 11 x 14. The surface area of the outside
of the box is the sum of the area of the top, bottom, and the four sides: top =
11.5 x 14.5, bottom = 11.5 x 14.5, 2 sides = 11.5 x 1, and 2 sides = 14.5 x 1.
The surface area of the outside of the box for the rectangular large pizza is
2(11.5 x 14.5) + 2(11.5 x 1) + 2(14.5 X 1) = 385.5 square inches.
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The surface area of
the (square base) box for the large circular pizza is 478.5 square inches. The
surface area of a rectangular large pizza box is 385.5 square inches. He saves
478.5 − 385.5 = 93 square inches. The percent less material needed is 93 ÷
478.5 X 100% = 19%.
If you want to see last week's problem again, click
http://www.mathcounts.org/webarticles/anmviewer.asp?a=1011&z=110
Idaho Society of Professional Engineers
PO Box 170239
Boise, ID 83717-0239
208-426-0636
Fax: 208-426-0639
E-Mail: ispe@idahospe.org
Web Site: www.Idahospe.org
Idaho
Society of Professional Engineers
