  Assignment 46

 "The control of large numbers is possible, and like unto that of small numbers, if we subdivide them." -- (Sun Tze Ping Fa, 5th - 6th century) Evariste Galois (France, 1811-1832): His short and troubled life makes him sound like a fictional character, but he contributed much to algebra and is considered the founder of a branch of mathematics that we now call group theory. Among other things, Galois was the first to realize and demonstrate that general polynomials with degree higher than four cannot be solved by algebraic means. Among other things, Galois had an implacable hatred of tyranny, he was expelled from school, and was twice arrested for allegedly threatening the life of King Louis-Phillippe. He was killed in a duel at age 20. Much of Galois' life's work was scribbled onto a 31 page document the night before he died. What did Herkimer say when he was about to be hanged for rustling cattle and no rope could be found? Answer: "No noose is good noose." Things Herky would like to know: If a glass blower accidentally inhaled, would he get a pane in his stomach? If a monster is seen in a drip-dry suit, can you call him a wash-and-were wolf? ASSIGNMENT #46 Reading: Make sure you understand the properties of rational exponents on page 407. Written: Page 405/57,59,61,64,65,66 Page 411/5-20 (can write answers neatly in book). Mathematical word analysis:DOZEN: The word is a contraction of the Latin duodecim (two plus ten).
OK folks, this definition is important. If m and n are integers, and n is positive, then

xm/n = n÷xm

Here is a financial problem involving rational exponents.

If money doubles after 6 years, what is the annual interest rate?

Response: If i is the annual interest rate, then premise ==> (1+i)6 = 2 ==> (1+i) = 21/6 ==> i = 21/6 - 1 = 0.12246, or about 12.25%.

Here is a geometrical problem involving rational exponents.

The volume of a cubical box is 2.54 sq. ft. What is the length of the side of the box?

Response: If x is the length of a side, then premise ==> x3 = 2.54 ==> x = 2.541/3 = 1.2599, or about 1.26 ft.

Here is another financial problem involving rational exponents.

A loan has an annual yield of 9.25%. What is the equivalent true monthly yield?

Response: If m is the true monthly yield, them (1+m)12 = 1.0925 ==> 1+m = (1.0925)1/12 ==> m = (1.0925)1/12 - 1 = 0.0073996, or approximately 0.74%.

Rational exponents (fractional exponents) are important and extremely useful.

 Problem: Solve x-2/3 = 17. Solution (with communication): x-2/3 = 17 ==> (x-2/3)-3/2 = 17-3/2 ==> x = 17-3/2 = 0.01427. Problem: Solve a = (1/p)1/c - b for p in terms of a, b, and c. Solution (with communication): a = (1/p)1/c - b ==> (1/p)1/c = a+b ==> 1/p = (a+b)c ==> p = 1/(a+b)c.