Assignment 31

 "The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worth of rational beings." -- (George Washington, 1732-1799) Benjamin Banneker (1731-1806): An African-American with tremendous mathematical abilities, Banneker lived during a period of United States history when a struggling country had little interest in scholarly pursuits. Banneker was a problem solver and developed considerable skills in the areas of astronomy and surveying. President George Washington and Secretary of State Thomas Jefferson both knew Banneker, and made use of his work. Born in Maryland to a former slave, Banneker sent a letter to Jefferson, a slave owner, criticizing slavery. Banneker became very interested in astronomy. He overcame many hardships to publish a work called the Almanack, which contained detailed observations of the evening sky and many astronomical calculations. Then Secretary of State Thomas Jefferson was so impressed with the publication that he sent it to the French Academy of Science. Banneker published more almanacs, and they were so popular that he continued to published them until 1797. Banneker also worked with a commission appointed by President George Washington to survey the boundaries of what is now the District of Columbia. When Herkimer was a waiter, what did he say to the customer who complained about the mud in his coffee? Answer: What do you expect? It was just ground this morning." Herky's friends: RHODA HORSE... a jockey. PERRY NOID ... this guy gets frightened quite easily. ASSIGNMENT #31 Reading: Section 5.7, pages 299-303. (DO THIS READING. THE WRITTEN ASSIGNMENT IS NOT DIRECTLY RELATED TO THE READING.) Written: Solve some of the quadratic equations on page 287 using the program below. (Check to make sure the program works.)

 Mathematical word analysis:MILE: From the Latin phrase mille passus (one thousand paces). A soldier's pace was usually about five feet, and a thousand paces is about the distance of what we consider to be a mile.

TI-83 PROGRAM TO SOLVE QUADRATIC EQUATIONS:

:Prompt A,B,C
:B^2-4*A*C->D
:If D<0
:Then
:Disp "COMPLEX SOLUTIONS"
:Disp (-B)/(2*A),"+",÷
(-D)/(2*A),"I"
:Pause
:Disp (-B)/(2*A),"-",÷
(-D)/(2*A),"I"
:Else
:(-B+÷(
D))/(2*A)->P
:(-B-÷(
D))/(2*A)->Q
:Disp"REAL ROOTS ARE ",P," AND ",Q
:END

 Problem: "Read" the program above and explain what it actually does. Solution (with communication): A quadratic equation has the form ax2 + bx + c = 0. The program allows the user to input numerical values for a, b, and c. It stores these values in locations called A, B, and C. It then computes the discrimant b2 - 4ac and stores that in a location called D. If D is negative, the program indicates to the user that the solutions are complex numbers, and it displays the roots in complex number form. If D is not negative, the programs indicates to the user that the roots are real numbers, and displays them. Note that if D is zero, the only real root is -B/(2*A). In the case when D = 0, the root is printed out twice.