Assignment 17

 "I was gratified to be able to answer promptly. I said I don't know." -- (Mark Twain) The Pythagoreans (cult whose leader was Pythagoras, founded around 500 B.C.) were number mystics, not scientific sages. Long after the death of Pythagoras, the cult split into two distinct schools. Those who continued with mysticism and rituals became the akousmatikoi (translated "those who hear") school. The other school drifted away from the mystic approach to numbers and used them for what we would call scientific purposes. This group represented the mathematikoi (translated "those interested in science") school. Ah, do you see where our modern word mathematics comes from? What does Herkimer call a headache that one gets from drinking too much wine? Answer: The Wrath of Grapes. Herky 's friends: DAFFY DILL ...she's crazy about flowers. M. T. HEAD ...this guy isn't too smart. Reading: Section 3.2, pages 148-152. Written: Pages 152-153/12-48 (multiples of 3). Solve by any efficient method.

 Mathematical word analysis:COMMUTATIVE: From the Latin word commutare (to exchange). The mathematical operation of addition is commutative. In the sum 7 + 5, you can "exchange" the 7 and the 5 and not change the value of the represented number.

This is an excellent time to practice communicating on paper. If you just slop around and get an answer, this assignment will be relatively useless as far as learning.

Suppose I want to solve the linear system:

(a): -6x + 5y = 4

(b): 7x - 10y = -8

Solution:

Here's a strategy: Multiply (a) by 2, then calculate (a) + (b) to eliminate the variable y.

(c) = 2(a): -12x + 10y = 8.

(d) = (b) + (c): -5x = 0 ==> x = 0.

(a) ==> -6(0) + 5y = 4 ==> y = 4/5.

The lines intersect at the point (0,4/5).

To repeat: This is an excellent assignment to practice organization, neatness, and communication.

MATH IS A LANGUAGE. LEARN TO READ AND WRITE IT WELL.

 Problem: Solve the system 2x - y = 54x - 2y = 20 Solution (with communication): Dividing both sides of the second equation by 2 yields 2x - y = 10. The system represents two parallel lines. Since parallel lines do not intersect, the system has no solution. Problem: Solve the system 2x - y = 54x - 2y = 10 Solution (with communication): Dividing both sides of the second equation by 2 yields 2x - y = 5. Both equations represent the the same line, namely y = 2x - 5. The system solution consists of all points on the line y = 2x - 5. Problem: Solve the system 2x - y = 54x + y = 25 Solution (with communication): Adding the equations as represented yields 6x = 30 ==> x = 5. Substituting x = 5 into the first equation yields 10 - y = 5 ==> y = 5. The system solution is the point (5,5).