course Phy 121
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13:18:42 `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 --> The difference is that x-2/x+4 means that 2/x would be subtracted from x, then 4 would be added, and (x-2)/(x+4) means that the difference of x-2 would be divided by the difference of x-4. When x=2, x-2/x+4 means 2-2/2+4. PEMDAS states that after Parentheses & Exponents, that Multiplcation and Division must folloe before adding and subtracting. So 2/2=1, therefore 2-1+4=5. For (x-2)/(x+4) with x=2, (2-2)/(2+4). You would once again follow the rules of PEMDAS, doing the subtraction in the parentheses first, then dividing. So (2-2)/(2+4)= 0/6, or 0. confidence assessment: 3
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Á͍Tåլ assignment #001 001. typewriter notation qa initial problems 06-04-2008
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13:25:49 `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 --> The difference is x-2/x+4 is an addition and subtraction problem that includes division, while (x-2)/(x+4) is a divsion problem that includes addition and subtraction. For x=2, following the rules of PEMDAS. 2-2/2+4=> 2-1+4=5. (2-2)/(2+4)=> 0/6=0 confidence assessment: 3
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13:28:32 2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64.
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RESPONSE --> One indicates a number with an exponent, and then addition, the other indicated a number with an exponent that requires addition. self critique assessment: 3
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13:37:00 `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 numerator is 3 and the denominator is ((2x-5)^2*3x+1) . x=2 means: 2-3/(([2*3]-5)^2*3(2)+1)-2+7(2) => 2-3/((6-5^2*6+1)-2+14 => 3-3/7+12 = 15-3/7 = (105/7)-(3/7)= 102/7 confidence assessment: 2
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13:40:54 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7. COMMON STUDENT QUESTION: ok, I dont understand why x isnt part of the fraction? And I dont understand why only the brackets are divided by 3..why not the rest of the equation? INSTRUCTOR RESPONSE: Different situations give us different algebraic expressions; the situation dictates the form of the expression. If the above expression was was written otherwise it would be a completely different expression and most likely give you a different result when you substitute. If we intended the numerator to be x - 3 then the expression would be written (x - 3) / [(2x-5)^2 * 3x + 1 ] - 2 + 7x, with the x - 3 grouped. If we intended the numerator to be the entire expression after the / the expression would be written x - 3 / [(2x-5)^2 * 3x + 1 - 2 + 7x ].
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RESPONSE --> I think I see where I made my mistake, as I tried to do most of it in my head as opposed to writing it out. My mistake, and I learned a lesson. self critique assessment: 2
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13:47:22 `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 I would substitute x with 4 as given in the problem, and re-write it so it is easy to understand. So we have (4-5)^2(4)-1+3/4-2. Next, parentheses (4-5) =-1 and exponents ^(2*4) (-1)^8=1 =>1-1+3/4-2=> then division, so 1-1+.75-2= .75-2= -1.25 confidence assessment: 2
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13:49:56 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first. Exponentiation precedes multiplication. Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4). Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power. -1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.
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RESPONSE --> Just a bit of notation confusion. self critique assessment: 2
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13:52:01 *&*& 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 easier to see and comprehend, but since computers are a widely used form of communcation, it is necessary to understand the notation in the computer algebra system. self critique assessment: 2
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13:54:33 `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 --> Examples and explanations of standard and typewriter notation, with links to pictures of the examples as well. confidence assessment: 3
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13:55:40 You should see a brief set of instructions and over 30 numbered examples. If you click on the word Picture you will see the standard-notation format of the expression. The link entitled Examples and Pictures, located in the initial instructions, shows all the examples and pictures without requiring you to click on the links. There is also a file which includes explanations. The instructions include a note indicating that Liberal Arts Mathematics students don't need a deep understanding of the notation, Mth 173-4 and University Physics students need a very good understanding,
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RESPONSE --> I see it, and I guess since I am in PHY 121 I need something in between not needing a deep understanding and a very good understanding. self critique assessment: 2
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