course Phy 121 ???€?????????t?assignment #001001. typewriter notation
......!!!!!!!!...................................
23:01:45 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
......!!!!!!!!...................................
RESPONSE --> there isn't really any difference in the two either way you get the same answer. although the Parenthesis technicaly specify what you should do first. Both ways you still end up whith the answer being 0 confidence assessment: 3
.................................................
......!!!!!!!!...................................
23:05:14 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.
......!!!!!!!!...................................
RESPONSE --> I was mistaking the / as making the problem a fraction instead of a division sign I'm a little rusty. self critique assessment: 2
.................................................
......!!!!!!!!...................................
23:10:54 `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.
......!!!!!!!!...................................
RESPONSE --> there is a big difference in these due to the order of opprations the parenthasis would cause it to be 2^(6) as opposed to 2^(2)+4 giving two completely diff. answers. 2^(2)+4=8 whereas 2^(6)=64. confidence assessment: 3
.................................................
......!!!!!!!!...................................
23:12:22 `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?
......!!!!!!!!...................................
RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.OK confidence assessment:
.................................................
......!!!!!!!!...................................
23:26:18 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 ].
......!!!!!!!!...................................
RESPONSE --> on the last question I didn't type anything in the box because I understood the problem. So when I clicked Enter Response it gave me the message about always entering a response or critique. so I typed OK and clicked enter Response. the it asked how certain I was of my answer. I didn't know what to say to that so I hit cancel and in-turn it skipped this question. but I thought when something whas in front of the / that it was considered to be on top of the fraction or the numerator and what was after the/ was the denomonator? am I wrong? self critique assessment: 2
.................................................
......!!!!!!!!...................................
23:39:57 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
......!!!!!!!!...................................
RESPONSE --> first plug in the 4 for the xs to get (4-5)^2(4)-1+3/x-2 then you follow the order of opperations solving your parenthesis first to get (-1)^8-1+3/4-2 then exponentiate to get 1-1+3/4-2 then devide to get 1-1+.75-2 then add getting 1-1.75-2 and finally subtracting to get -2.75. confidence assessment: 2
.................................................
......!!!!!!!!...................................
23:45:19 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.?......!!!!!!!!................................... RESPONSE --> I made the mistake of multiplying the 2 and 4 before I exponentiated but I see where I went wrong. and I also devided 3/4 instead of leaving it as a fraction which can be easily fixed. self critique assessment: 2
.................................................
......!!!!!!!!...................................
23:46:36 *&*& 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.
......!!!!!!!!...................................
RESPONSE --> This is very important notation and I will probably see it in the future. self critique assessment: 3
.................................................
......!!!!!!!!...................................
23:52:21 `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.
......!!!!!!!!...................................
RESPONSE --> there are alot of different examples of typewriter notation with links to pictures of what they would actually look like on paper. confidence assessment: 3
.................................................
......!!!!!!!!...................................
23:53:18 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,
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
.................................................
......!!!!!!!!...................................
23:53:44 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.
......!!!!!!!!...................................
RESPONSE --> OK self critique assessment: 3
.................................................