course Mth 173 çä¢ìž®€¸–¬Ó¯ûÛóЧ~¡F…Â{ã„X̃assignment #001
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12:17:26 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
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RESPONSE --> In the first example, 2 is divided by x then subtracted from x and finally added to 4. In the second example, 2 is subtracted from x then divided by the addition of x and 4. Equation 1: First process division: 2 / 2 = 1. Then proceed from left to right and doing any addition or subtraction: 2 - 1 + 4 = 5. Equation 2: First process inside parentheses: 2 - 2 = 0 (numerator) and 2 + 4 = 6 (denominator). Then process division: 0 / 6 = 0 confidence assessment: 2
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12:25:25 `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation.
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RESPONSE --> Order of operations again. Exponentiation happens first in a standard equation, but parentheses take precedence over that. Equation 1: First raise 2 to the x power: 2 ^ 2 = 4. Then add to 4: 4 + 4 = 8. Equation 2: First evaluate inside the parentheses: 2 + 4 = 6. Then raise 2 to the 6 power: 2 ^ 6 = 64. confidence assessment: 2
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12:34:33 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
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RESPONSE --> The denominator is [ (2x-5)^2 * 3x + 1 ]. Evaluating the expression: First go inside to the deepest level of parentheses and evaluate: 2(2) - 5 = -1. Then evaluate exponents: -1 ^ 2 = 1. Multiply: 1 * 3(2) = 6. Add: 6 + 1 = 7. Next, go outside the parentheses and start with the division: 3/7 = 3/7 (keep in fractional form for accuracy). Multiply: 7(2) = 14. Add: 2 - 3/7 - 2 + 14 = 14 -3/7. Turn into mixed fraction: 95/7 or 13 4/7. confidence assessment: 2
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12:41:20 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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RESPONSE --> First evaluate inside parentheses: (4 -5) = -1. Next evaluate exponents: -1 ^ 2 = 1. Multiply: 1(4) = 4. Divide: 3 / 4 = 3/4. Add or subtract from left to right: 4 -1 + 3/4 - 2 = 1 + 3/4 = 1 3/4. confidence assessment: 2
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12:42:28 *&*& Standard mathematics notation is easier to see. On the other hand it's very important to understand order of operations, and students do get used to this way of doing it. You should of course write everything out in standard notation when you work it on paper. It is likely that you will at some point use a computer algebra system, and when you do you will have to enter expressions through a typewriter, so it is well worth the trouble to get used to this notation. Indicate your understanding of the necessity to understand this notation.
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RESPONSE --> Standard notation is fine for paper, but computers don't read paper too well, so it is better to learn typewriter notation and understand the order of operations. self critique assessment: 2
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12:47:35 `q005. At the link http://www.vhcc.edu/dsmith/genInfo/introductory problems/typewriter_notation_examples_with_links.htm (copy this path into the Address box of your Internet browser; alternatively use the path http://vhmthphy.vhcc.edu/ > General Information > Startup and Orientation (either scroll to bottom of page or click on Links to Supplemental Sites) > typewriter notation examples and you will find a page containing a number of additional exercises and/or examples of typewriter notation.Locate this site, click on a few of the links, and describe what you see there.
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RESPONSE --> This site shows examples of typewriter notation and standard notation and includes explanations about how to switch between the two. It looks like a very valuable resource as the difficulty of the problems increase. confidence assessment: 2
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12:48:23 end program
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RESPONSE --> Is this the end? Thanks! self critique assessment: 2
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