Assignment 27

"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty" -- (Archimedes, ca 287 B.C. - 212 B.C.)

Math History Tidbit:

Hrotswitha of Gandersheim (935 - 1000): The first British woman mathematician of record, Hrotswitha was a Benedictine nun. She made efforts to educate women in mathematics and science. Hrotswitha's ideas about astronomy predated those of Nicholas Copernicus and Isaac Newton by about 500 years. She developed ideas relating to the concept of gravity and did not hold the popular belief that Earth was the center of the universe. Hrotswitha was well-read and very creative, and she wrote original, poetic moral dramas, along with local history. She is associated with the following quote:

"It is not knowledge which is dangerous, but the poor use of it."

Herkimer's Corner

When Herkimer was a school principal, what was his rule regarding miniskirts?

Answer: The thighs the limit.

Herky's friends:

AUNT CHOVIE... a relative who likes fish on her pizza.

ELLA VADER...she likes to go up and down between floors in tall buildings.

ASSIGNMENT #27

Reading: Section 5.3, pages 264-267.

Written: Pages 267-268/51-67 (odds), 71.

Items for reflection:

Mathematical word analysis:
ACUTE: Derived from the Latin word acus (needle, or something that is pointed or sharp). In a manner of speaking, an acute angle does have a sharp point.

Quadratic equations that do not contain a linear term are relatively easy to solve:

Example:

3x2 = 48 ==> x2 = 16 ==> x = 4 or x = -4.

NOTE: x2 = 16 ==> x = 4 is a false statement.

x = 4 ==> x2 = 16 is a true statement.

Example:

(x - 33)2 = 25 ==> x - 33 = 5 or x - 33 = -5 ==> x = 38 or x = -28.

Example:

Solve x2 -4x - 12 = 0.

OK, we can get a bit clever here. Follow the mathematical logic:

x2 - 4x - 12 = 0

==> x2 - 4x + 4 = 16

==> (x - 2)2 = 16

==> x - 2 = 4 or x - 2 = -4

==> x = 6 or x = -2.

MATH IS A LANGUAGE. YOU SHOULD BE ABLE TO READ WHAT IS WRITTEN ABOVE, AND FOLLOW THE SOLUTION PROCESS I HAVE OUTLINED WITH NO DIFFICULTY.

Problem: Solve the equation (2x - 7)2 - 21 = 43.

Solution (with communication):

(2x - 7)2 - 21 = 43

==> (2x - 7)2 = 64

==> 2x - 7 = 8 or 2x - 7 = -8

==> 2x = 15 or 2x = -1

==> x = 7.5 or x = -0.5.

 

Problem: The height h (in feet) of a falling object after t seconds can be modeled by the equation

h = -16t2 + h0

where h0 is the object's initial height above the ground. If a rock is dropped from a height of 114 feet, how long will it take to hit the ground?

Solution (with communication):

We have h0 = 114 and we want to know when h = 0.

0 = -16t2 + 114

==> 16t2 = 114

==> t = (114/16) = 2.67 (seconds).

Note: The value t = -2.67 also satisfies the equation, but the domain for t is t > 0.