course PHY 201 As you can see by how I answered, I had a few questions and I also was not able to see the additional links that were talked about, nor the questions and examples. }¦ß¯áœ®üM˦Ïíë~͈ÓñëÞ¤rÙ^††v‰assignment #001
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11:06:08 `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 --> For these expressions, how the problem is read and subsequently answered for each is very different. The first expression: In this problem the value ""x"" is to be subtracted from the nuber 2. The number 2 is divided by the value ""x"". A 4 is then added to the total. This means the problem when simplified would read 2 subtracted by 1 plus 4. 1 subtracted from 2 is 1. 1is then added to 4 which gives the final answer of 5. The second expression: This problem is compound and consists of two smaller problems. The smaller problems are ""x"" minus 2 and ""x"" plus 4, within the greater problem of ""x"" minus two divided by ""x"" plus 4. In order to do the problem correctly,you simplifiy it by doing each of the smaller problems before the larger one. Meaning that you would have 2 minus 2 or 0 and 2 plus 4 or 6. Then, the 0 would be divided by the 6 as in the greater problem. This would then give a value of 0 as the answer. confidence assessment: 2
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11:14:34 The order of operations dictates that grouped expressions must be evaluated first, that exponentiation must be done before multiplication or division, which must be done before addition or subtraction. It makes a big difference whether you subtract the 2 from the x or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract. Substituting 2 for x we get 2 - 2 / 2 + 4 = 2 - 1 + 4 (do multiplications and divisions before additions and subtractions) = 5 (add and subtract in indicated order) If there are parentheses you evaluate the grouped expressions first: (x - 2) / (x - 4) = (2 - 2) / ( 4 - 2) = 0 / 2 = 0.
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RESPONSE --> I got the first expression correct and understand why, as I explained before, however I had down that the second expression was (x-2)/(x+4), which must have been an error on my part. But, if it was (x-2)/(x-4), then shouldn't that make the problem with a value of 2 for x to be: (2-2)/(2-4) which would be (0)/(-2), which would of course still be the vaule of 0? I was always taught that without retaining the appropraite signs, it was not legal to move digits and the negative value of the 4 was not retained.
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11:21:25 `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 --> The first expression reads: 2 raised to the value of x. A 4 is then added to this entire expression. This means with the value of 2 for x the expression would read 2 squared, which would be 4, with a 4 then added to it and would give the total of the expression as 8. The second expression reads: 2 raised to the value of x plus 4 or for a value of 2 for x, 2 raised to the 2+4. This would be 2 raised to the sixth power ( or 2*2*2*2*2*2) which would give the value of 64. confidence assessment: 3
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11:23:56 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 --> After seeing the solutions and comparing them with my own, I see and undstand that I was correct in my earlier beliefs. As in the previous problems from question one, the parentheses make a big difference in how the problem is unsderstood and solved. self critique assessment: 2
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11:37:01 `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 (on the top of the division line) is 3. There is no other value on this line. The denominator (on bottom of the division line) is ((2x-5)^2 * 3x + 1). You can know for cerain the -2+7x, is not part of the section of the expression within this group because it falls outside the parenthenses. For the expression, with the value of 2 as x is: 2- 3 / ((2(2)-5^2 * 3(2) +1) - 7(2), which simplified is 2- 3/7 -16. This then equals -101/7. confidence assessment: 2
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11:48:48 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 understand how the correct solution was obtained. It has been along time since I have done the whole order of operations thing. I also see now that I made a silly mistake anyway (-2+14 does not = 16). If the 3/7 is to be done first, why did the 2-2+14 proceed it when the question was re-written though? You said before it was grouped, exponents, mult. & divis., then add. & subt.- right? If I had gone by this and put the -3/7 out in front and then added 2-2+14 to it, you get the same thing. Is that ok to do?
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12:04:27 `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 --> This one is a little tricky because of the way the nubers are spaced out so I am going to explain it to different ways. If the spacing is to be a hint, then I think it shoudl read and be completed as such for x=4: (4-5)^2(4)-1 + 3/ 4-2, which would be -1 raised to the 7 + (3/2) simplified which would be (1/2). If the spacing is just an accident, then for x=4 it would be: (4-5)^2(4) minus 1 plus 3/4 minus 2, which when simplified by order of operatoins would be 1-1+(3/4)-2, but it appears as if the spacing does in fact attempt to provide a hint as to how the problem is broken down. confidence assessment: 2
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12:20:16 `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 --> I have compared my answer with the correct one, but I do not understand how to get from step one to step two.
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12:24:34 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 --> The only instructions I see are the ones that tell me I should see over 30 numbered examples. I also do not see any links to Examples or Pictures because I do not have these instructions, nor do I have any explanations.
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12:25:35 while students in other courses should understand the notation and should understand the more basic simplifications. There is also a link to a page with pictures only, to provide the opportunity to translated standard notation into typewriter notation.
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RESPONSE --> I still do not see these links. self critique assessment: 2
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12:26:22 end program
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RESPONSE --> I hope it is ok, but I am going to email you about seeing these links since they are so important. self critique assessment: 2
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