A mathematician from Baghdad, Alkhwarizimi, worked with π but it was Al-Khashi from Samarkand in 1430 AD that approximated π to 16 decimal places. Then came the European Renaissance with a whole new world of mathematicians. Viete in 1593 AD expressed π as an infinite product by using 2s and square roots. In 1610, Ludolph van Ceulen calculated π to 35 decimal places followed by Snell in 1630 to 39 decimal places. In 1655 Wallis showed the value of π/2=2/1x2/3x4/3x4/5x6/5x6/7x8/7x8/9...
Use the commutative and associative laws to write at least three expressions equivalent to (3x)y. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 94 3C • b Properties of Real Numbers Use the commutative and associative laws to find equivalent expressions. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 95 3C Properties of Real Numbers Use the distributive laws to multiply expressions like 8 and x – y. Consider a multiplication problem from arithmetic: To carry out the multiplication, we actually added two products. That is, Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 96 3C Properties of Real Numbers Use the distributive laws to multiply expressions like 8 and x – y. Compute in two ways: Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 97 3C Properties of Real Numbers The Distributive Law of Multiplication over Addition Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 98 3C Properties of Real Numbers The Distributive Law of Multiplication over
What is the natural exponential function? * The logarithmic function with base e. 3. Evaluate 4–1.5 using a calculator. Round your answer to three decimal places. * .125 4.
Both of these formulas were found on page 225 in Mathematics in Our World (Bluman, 2005). Problem #37 • This sequence is geometric • Ending balance is $814.45 STEPS/CALCULTATIONS YOU PERFORMED TO REACH THE ANSWER: To find the ending balance, the formula of An = a1(rn-1) will be used. The initial balance is $500, the interest is 5%, and the time span is 10 years. 5% will be listed as 1.05 as the initial balance is 100% plus 5% interest, so 105% is written 1.05. The number of terms is n=10, the first term is a1=525, the common ratio is r = 1.05.
Reflection questions about the Drake equation: Equation | Minimum values | Maximum values | R= | 1 | 7 | Fp= | 0.4 | 0.6 | Ne= | 2 | 2.5 | F1= | 0.5 | 1 | Fi= | 0.001 | 1 | Fc= | 0.5 | 0.8 | L= | 10,000 | 200,000 | N= | 2 | 1,680,000 | What value did you get for the number of civilizations? After calculating the maximum and minimum values of the equation through researching them individually, the minimum value of the Drake equation, N = R x fp x ne x f1 x fi x fc x L, was N = 2. The values were as such: * R = 1 * fp = 40 % (0.4) * ne = 2 * f1 = 50% (0.5) * fi = 0.001 * fc = 50% (0.5) * L = 10,000 (1 x 0.4 x 2 x 0.5 x 0.001 x 0.5 x 10000). These figures lead the end of the equation at the number of communicative civilizations at N = 2; meaning there is a minimum of 2 expected communicative civilizations in the galaxy. The maximum value that was proposed for the Drake equation, N = R x fp x ne x f1 x fi x fc x L, was N = 1,680,000.
Mesopotamians wrote down what event happened in cuneiform and wrote the date so they know when it happened. Some extraordinary inventions were the ones the Mesopotamian invented. According to Document 1and 2, both a secondary source, the first document states that Mesopotamia “contributed immensely to industrial technology” by inventing useful objects like the wheel. The second document talks about the ziggurat, a temple built to the gods that looked like huge squares of different size placed on top of each other starting from the largest to the smallest.
includes religion. Around 100 C.E., Confucianism, Daoism, and Legalism, were China’s main religions. However, around 300 C.E., Buddhism started becoming popular, mainly due to Indian missionaries. Yet another cultural change in China revolves around inventions. The invention of paper in 105 C.E.
Five thousand years ago, they had philosphers who attempted to list every known thing in the world. 07. They were using Pythagoras'theorem 700 years before Pythangoras. 08. They invented artificial building materials, some kind of pre-fabricated material used to construct high-rise towers.
They also used native copper, silver and gold for metalworking, in which they used very advanced methods. The period between 250 CE and 650 CE was a time of intense flourishing of Maya civilized accomplishments. While the many Mayans city-states never achieved political unity on the order of the central Mexican civilizations, they exerted a tremendous intellectual influence upon Mexico and Central America. The Mayans built some of the most elaborate cities on the continent, and made innovations in mathematics, astronomy, and calendrics. The Mayans also evolved the only true writing system native to the Americas using pictographs and syllabic elements in the form of texts and codices inscribed on stone, pottery, wood, or highly perishable books made from bark paper.
Teacher Resources * Anton, Howard, Ira Bivens, and Stephen Davis, Calculus: Early Transcendentals, 8th edition, Hoboken, NJ: John Wiley & Sons, Inc., 2005 * Finney, Ross, Franklin D. Demana, Bert Waites, and Daniel Kennedy, Calculus: Graphical,Numerical, Algebraic, 3rd edition, Boston: Pearson: Prentice Halll, 2007 * Forrester, Paul, Calculus: Concepts and Applications, 2nd ed., Emeryville, CA, Key Curriculum Press, 2005 * Hallett, Deborah, Andrew Gleason, and William McCallum, Calculus: Single Variable, 4th edition, Hoboken, NJ: John Wiley & Sons, Inc., 2005 * Larson, Ron Robert, P. Hostetler, and Bruce H. Edwards, Calculus with Analytic Geometry, 8th edition. Boston: Houghton Mifflin, 2006 * Stewart, James, Single Variable Calculus Concepts and Content with Vector Functions, Belmont, CA: Thompson Brooks/Cole,