Assignment 6

 "The advancement and perfection of mathematics are intimately connected with the prosperity of the state." -- (Napoleon Bonaparte, 1769-1821) Archimedes (c. 287-212 B.C.): Considered one of the greatest mathematicians of all time, he produced a very accurate computation of pi and was the first to determine the volume of a sphere. He also developed laws of hydrostatics that included mathematical analysis related to pressure on bodies placed in water. He discovered many principles of physics, including those relating to levers and pulleys. He is credited with this quote: "Give me a place to stand I and shall move the earth." Where did Herkimer put his noisy dogs while he strolled around the big city? Answer: In a barking lot. Herky's friends: DENTON FENDER...guy who works in an auto body repair shop. KAREN A. LOTT... nice lady who is always concerned about the welfare of others. Reading: Section 1.7, pages 50-53. Written: Pages 53-54/33-51(odds)

 Mathematical word analysis:CENTER: From the Greek word kentrus, meaning "spur" or "sharp pointed object." In creating circles, the ancients had a sharp pointed object to fix the center, and then another object was dragged around it to form the circle.

Don't make the concept of absolute value difficult. The absolute value of a number is either the number itself, or its opposite. If x is a positive number, or 0, then |x| = x. If x is a negative number, then |x| = -x. OK, let's be careful here, and let's think! The algebraic expression -x does not necessarily represent a negative number. For instance, if x = -5, then -x = 5. In general, it is a good idea to read -x as "the opposite of x." instead of "minus x" or "negative x." Note that on your calculator, there are two distinct keys with the "-" symbol. One references subtraction (a binary operation performed with two numbers), and the other is used to represent the opposite of a single number.

Here are some problem examples from pages 53 and 54. Note the communication, and the use of the words and and or.

Problem #36.

|8x + 1| = 23

==> 8x + 1 = 23 or 8x + 1 = -23

==> 8x = 22 or 8x = -24

==> x = 11/4 or x = -3.

Problem # 42.

|4n - 12| > 16

==> 4n - 12 > 16 or 4n - 12 < -16

==> 4n > 28 or 4n < -4

==> n > 7 or n < -1.

Summary: The conditional statement is true if n is a number that is greater than 7 or less then -1.

Problem #54.

|4x + 10| < 20

==> -20 < 4x + 10 and 4x + 10 < 20

==> -30 < 4x and 4x < 10

==> -7.5 < x and x < 2.5.

Summary: The conditional statement is true if x is a number between -7.5 and 2.5.

Math is a language. Math is power!

 Problem: Solve | 4 - 2x | < 52. Solution (with communication): | 4 - 2x | < 52 ==> -52 < 4 - 2x < 52 ==> -56 < -2x < 48 ==> 28 > x > -24 ==> -24 < x < 28. Conclusion: Any number between -24 and 28 will make the conditional statement true. Problem: Solve | 1 - 2x | > 13. Solution (with communication): | 1 - 2x | > 13 ==> 1 - 2x > 13 or 1 - 2x < -13 ==> -2x > 12 or -2x < -14 ==> x < -6 or x > 7. Conclusion: The conditional statement is true for any number less than -6 or greater than 7.