  Assignment 16

 "Learning is the only thing the mind never exhausts, never fears, and never regrets." -- (Leonardo Da Vinci) Mathematical Drought in Western World (500 - 1200): The Islamic world was mathematically active during this period, as was the Hindu world. Perhaps the greatest of the Hindu mathematicians was Bhaskara (1114 - 1185), who, among many other things, produced several approximations for the number pi, including the frequently used 22/7. Bhaskara's major work, the Siddantasiromani , was an astronomy text that contained two chapters on mathematics: the Vija-Ganita , on algebra, and the Lilavati , on arithmetic. "It is remarkable to what extent Indian mathematics enters the science of our time. Both the form and the spirit of the arithmetic and algebra of modern times are essentially Indian and not Grecian." -- (Florian Cajori) What does Herkimer call an individual who has to cough every time he tells a joke? Answer: A practical choker. Herky 's friends: PATTY O'FURNITURE ... young lady who sells chairs that are used outside the house. BILL DING ... a contractor. Reading: Section 3.1, pages 139-142. Written: Pages 142-143/20-31. Solve the systems algebraically, and be able to show the solutions graphically. Mathematical word analysis:COEFFICIENT: From the Latin words co and efficiens, meaning "to effect together." [In an expression such as 5x, the numerical coefficient 5 effects the variable x.]

Communication will help you considerable when you are solving systems of linear equations. For example, suppose we are to solve the system:

(a) -3x + y = 4

(b) 7x + 2y = -5

Solution:

(a) ==> y = 3x + 4.

Substituting into (b) yields 7x + 2(3x + 4) = -5 ==> 7x + 6x + 8 = -5 ==> 13x = -13 ==> x = -1.

(a) ==> -3(-1) + y = 4 ==> y = 1.

The lines intersect at the point (-1,1).

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What is below represents a review of the very important concept of a function.

A function is a collection of ordered pairs such that each x-value has a unique y-value.