course Mth 152 I thought that I was sending this as I completed it, however during the final step of the orientation it asks you to go to your access page and make sure all assignments are there and I had none. I am not sure what I did wrong. Please let me know how you think I am doing based upon everything I am sending. Also if you notice anything that I have missed please let me know. I also sent you a request to get the checkmark dvd. I have my dvds but that particular one was not included in my set. Also somewhere on our course website I saw where I should have a matrices dvd as well. I also do not have that one. Thanks Kristie Roark }K~؇R}a
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22:34:00 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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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. OK
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22:40:44 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> I located SEND file.
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22:45:07 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> If I enter a response to a question here and click enter response my response is immediately set to the SEND file where it is stored safely. Even if my computer crashes all my stored information in the SEND file will still be there.
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22:47:30 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> OK
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22:49:00 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> I understand how to email myself a copy but I do not know what a key drive is.
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23:04:16 Once more, locate the SEND file in your c:\vhmthphy folder, and open the file. Copy its contents to the clipboard (this is a common operation, but in case you don't know how, just use CTRL-A to highlight the contents of the file and CTRL-C to copy the contents to the clipboard). Then return to the form that instructed you to run this program, and paste the contents into the indicated box (just right-click in the box and select Paste). You may now click on the Quit button, or simply close the program.
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RESPONSE --> }K~؇R}a assignment #001 001. Only assignment: prelim asst qa prelim
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22:34:00 `q001. Part 1 includes six activities. If you have completed an activity, just enter the answer 'completed'. This question is appearing in the Question box. The box to the right is the Answer box, where you will type in your answers to the questions posed here. To use this program you read a question, then enter your answer in the Answer box and click on Enter Answer. In your answers give what is requested, but don't go into excruciating detail. Try to give just enough that the instructor can tell that you understand an item. After entering an answer click on Next Question/Answer above the Question box. Do you understand these instructions?
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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. OK
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22:40:44 This program has created the folder c:\vhmthphy on your hard drive. Browse to that folder and locate the file whose name begins with SEND. The name of this file will also include your name, as you gave it to the program, and the file will show as a Text file. Never tamper with a SEND file in any way. It contains internal codes as if these codes are tampered with you won't get credit for the assignment. However you are welcome to copy this file to another location and view it, make changes, etc. Just be sure that when requested to do so you send the instructor the original, tamper-free file. State in the Answer box whether or not you have been able to locate the SEND file. Don't send the SEND file yet. Note that more questions/instructions remain in the q_a_prelim.
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RESPONSE --> I located SEND file.
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22:45:07 `q002. Note that every time you click on Enter Answer the program writes your response to your SEND file. Even if the program disappears all the information you have entered with the Enter Answer button will remain in that file. This program never 'unwrites' anything. Even if this program crashes your information will still be there in the SEND file. Explain this in your own words.
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RESPONSE --> If I enter a response to a question here and click enter response my response is immediately set to the SEND file where it is stored safely. Even if my computer crashes all my stored information in the SEND file will still be there.
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22:47:30 Any time the instructor does not post a response to your access site by the end of the following day, you should resubmit your work using the Submit Work form, and be sure at the beginning to indicate that you are resubmitting, and also indicate the date on which you originally submitted your work. If you don't know where your access site is or how to access it, go to http://www.vhcc.edu/dsmith/_vti_bin/shtml.dll/request_access_code.htm and request one now. You can submit the q_a_prelim without your access code, but other assignments should contain your code.
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RESPONSE --> OK
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22:49:00 `q003. If you are working on a VHCC computer, it is probably set up in such a way as to return to its original configuration when it is rebooted. To avoid losing information it is suggested that you back up your work frequently, either by emailing yourself a copy or by using a key drive or other device. This is a good idea on any computer. Please indicate your understanding of this suggestion.
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RESPONSE --> I understand how to email myself a copy but I do not know what a key drive is.
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REyɥ`Oб assignment #001 001. typewriter notation qa initial problems 01-18-2009
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13:35:59 `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 expression there are no parentheses and in the second expression there are. According to the order of operations (parentheses, exponents, multiply, divide, add, subtract), in an expression, you must complete each step of a problem in the above mentioned order. Therefore, this means that in these two particular expressions, although they look similar, the second expression must be done in a different step by step order than the first. x-2/x+4 2-2/2+4 2-1+4 5 (x-2)/(x+4) (2-2)/(2+4) 0/6 0 confidence assessment: 3
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13:41:53 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 --> In your answer to the second expression (x-2)/(x+4) you have written (x-2)/(x-4), I think that it should have been (x+4) which would have given you the answer (2-2)/(2+4)=0/6=0. Please let me know. self critique assessment: 2
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13:52:04 `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 difference between 2^ x+4 and 2^(2+4) is the parentheses present in the second expression. These parentheses indicate that the expression inside the parentheses (2+4) should be completed prior to the exponentiation of the 2. 2^x+4 2^2+4 4+4 8 2^(x+4) 2^(2+4) 2^(6) 2^6 64 confidence assessment: 3
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13:53:01 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 --> Critique not necessary. self critique assessment: 3
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14:20:39 `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 x-3. The denominator is [(2x-5)^2*3x+1]-2+7x. x-3/[(2x-5)^2*3x+1}-2+7x 2-3/[(2)(2)-5)^2*3(2)+1]-2+7(2) 2-3/[(4-5)^2*6+1]-2+7(2) 2-3/[(-1)^2*7]-2+7(2) 2-3/[1*7]-2+7(2) 2-3/[7]-2+14 2-3/{7}-16 2-3/-9 -1/-9 1/9 confidence assessment: 2
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14:57:59 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 --> x is not part of the numerator and -2+7x is not part of the denominator because it was not included in the bracekets and parentheses in the original expression. I correctly aswered the problem through the step 2-3/7-2+14. At this point I did not follow the order of operations and therefore missed the problem. When the order of the terms were changed to 2-2+14-3/7 the 2s cancel out and the 14 is converted into a fraction with a denominator matching 3/7 and then subtraction can be easily performed. self critique assessment: 2
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15:24:48 `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 --> (x-5)^2x-1+3/x-2 for x=4 Order of operations: Parentheses (4-5)=(-1) (-1)^2(4)-1+3/4-2 Exponents (-1)^2=1 1(4)-1+3/4-2 Division (reorder problem) 4-1+3/4-2 4-1-2+3/4 convert to fraction and then add 1+3/4=4/4+3/4=7/4 confidence assessment: 2
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15:27:19 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.
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RESPONSE --> Remembering order of operations is key to these problems. self critique assessment: 3
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15:29:37 *&*& 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 --> Notation is very important in working problems, without the use of the correct notation problems would be worked incorrectly every time. self critique assessment:
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16:28:24 `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 --> Many extra practice problems that will help me to be firmiliar with and understand the difference between ""standard"" and ""typewriter"" notation. This page also helps with remembering order of operations. confidence assessment: 3
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16:30:12 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 --> This is what I read and understand. self critique assessment: 3
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16:30:48 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 saw that link. self critique assessment: 3
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16:31:08 end program
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RESPONSE --> ok self critique assessment: 3
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Ԫ՛Hՠ assignment #004 004. Liberal Arts Mathematics qa initial problems 01-18-2009 Tϸ·rGlŎ䂑\ assignment #004 004. Liberal Arts Mathematics qa initial problems 01-18-2009
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20:15:44 `q001. Consider the statement 'If that group of six-year-olds doesn't have adult supervision, they won't act in an orderly manner.' Under which of the following circumstances would everyone have to agree that the statement is false? The group does have supervision and they do act in an orderly manner. The group doesn't have supervision and they don't act in an orderly manner. The group doesn't have supervision and they do act in an orderly manner. The group does have supervision and they don't act in an orderly manner.
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RESPONSE --> The statement "" If that group of six-year-olds doesn't have adult supervision, they won't act in an orderly manner"" would have to be considered false if the following two circumstances were true: ""The group doesn't have supervision and they do act in an orderly manner."" and ""The group does have supervision and they don't act in an orderly manner."" The initial statement implies that if the group of children had supervision they would act in an orderly manner and also that children lacking adult supervision do not act in an orderly manner. Therefore both statements listed above prove the opposite reaction to the implied information given in the original statement. confidence assessment: 3
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20:17:16 The statement says that if the group doesn't have supervision, they will not act in an orderly manner. So if they don't have supervision and yet do act in an orderly manner the statement is contradicted. If the group does have supervision, the statement cannot be contradicted because condition of the statement, that the group doesn't have supervision, does not hold. The statement has nothing to say about what happens if the group does have supervision. Of course if the group doesn't have supervision and doesn't act in orderly manner this is completely consistent with the statement. Therefore the only way to statement can be considered false is the group doesn't have supervision and does act in an overly manner. Note that what we know, or think we know, about childrens' behavior has nothing at all to do with the logic of the situation. We could analyze the logic of a statement like 'If the Moon is made of green cheese then most six-year-olds prefer collard greens to chocolate ice cream'. Anything we know about the composition of the Moon or the tastes of children has nothing to do with the fact that the only way this statement could be shown false would be for the Moon to be made of green cheese and most six-year-olds to prefer the ice cream.
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RESPONSE --> I over inferred information that was not explicitly given about what happens when the group has supervision. self critique assessment: 2
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22:16:22 `q002. List the different orders in which the letters a, b and c could be arranged (examples are 'acb' and 'cba'). Explain how you know that your list contains every possible order.
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RESPONSE --> abc bac cba cab acb bca I know that I have listed all the different possible answers to the different orders in which the letters a, b and c could be arranged because there are 3 letters involved in the arrangement and each of those three letters could be first in 2 different arrangements because the second and third letters can be switched in order. Therefore 3 letters * 2 different first letter arrangements= 6 total different letter arrangements. confidence assessment: 3
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22:18:26 The only reliable way to get all possible orders is to have a system which we are sure the list every order without missing any. Perhaps the simplest way to construct all possible orders is to list then alphabetically. We start with abc. There is only one other order that starts with a, and it is obtained by switching the last two letters to get acb. The next alphabetical order must start with b. The first possible listing starting with b must follow b with a, leaving c for last. The orders therefore bac. The only other order starting with b is bca. The next order must start with c, which will be followed by a to give us cab. The next order is obtained by switching the last two letters to get cba. This exhausts all possibilities for combinations of the three letters a, b and c. Our combinations are, in alphabetical order, abc, acb, bac, bca, cab, cba.
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RESPONSE --> My method was very similiar. self critique assessment: 3
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22:24:39 `q003. One collection consists of the letters a, c, d and f. Another collection consists of the letters a, b, d and g. List the letters common to both collections. List the letters which appear in at least one of the collections. List the letters in the first half of the alphabet which do not appear in either of the collections.
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RESPONSE --> Collection #1 of letters: a,c,d,f Collection #2 of letters: a,b,d,g The letters that are common to both collections are: a and d. The letters which appear in at least one of the collections are: a,b,c,d,f,g. The letters in the first half of the alphabet that do not appear in either of these collections are: e,h,i,j,k,l and m. confidence assessment:
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22:26:28 To letters a and d each appear in both collections. No other letter does. The letters a, c, d, and f appear in the first collection, so they all in at least one of the collections. In addition to letters b and g appear in the second collection. Therefore letters a, b, c, d, f and g all appear in at least one of the collections. We consider the letters in the first half of the alphabet, in alphabetical order. a, b, c and d all appear in at least one of the collections, but the letter e does not. The letters f and g also appear in at least one of the collections, but none of the other letters of the alphabet do. The first half of the alphabet ends at m, so the list of letters in the first half of the alphabet which do not occur in at least one of the collections is e, h, i, j, k, l, m.
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RESPONSE --> My answer is correct. self critique assessment: 3
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22:36:21 `q004. Give the next element in each of the following patterns and explain how you obtained each: 2, 3, 5, 8, 12, ... 3, 6, 12, 24, ... 1, 3, 4, 7, 11, 18, ...
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RESPONSE --> The next element in the pattern 2,3,5,8,12... is17 because each new element in the pattern is one more in quantity away from the last number than the previous one. 3-2=1, 5-3=2, 8-5=3,12-8=4, 17-12=5 and so on. The next element in the pattern 3,6,12,24... is 48 because each new element is double the last number. The next element in the pattern 1,3,4,7,11,18... is 29 because if you add the two previous numbers in the pattern you obtain the next new number in the pattern. confidence assessment: 3
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22:37:11 The pattern of the sequence 2, 3, 5, 8, 12, ... can be seen by subtracting each number from its successor. 3-2 = 1, 5-3 = 2, 8-5 = 3, 12-8 = 4. The sequence of differences is therefore 1, 2, 3, 4, ... . The next difference will be 5, indicating that the next number must be 12 + 5 = 17. The pattern of the sequence 3, 6, 12, 24, ... can be discovered by dividing each number into its successor. We obtain 6/3 = 2, 12/6 = 2, 24/12 = 2. This shows us that we are doubling each number to get the next. It follows that the next number in the sequence will be the double of 24, or 48. The pattern of the sequence 1, 3, 4, 7, 11, 18, ... is a little obvious. Starting with the third number in the sequence, each number is the sum of the two numbers proceeding. That is, 1 + 3 = 4, 3 + 4 = 7, 4 + 7 = 11, and 7 + 11 = 18. It follows that the next member should be 11 + 18 = 29.
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RESPONSE --> My answer is correct. self critique assessment: 3
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22:46:28 `q005. The number 18 can be 'broken down' into the product 9 * 2, which can then be broken down into the product 3 * 3 * 2, which cannot be broken down any further . Alternatively 18 could be broken down into 6 * 3, which can then be broken down into 2 * 3 * 3. Show how the numbers 28 and 34 can be broken down until they can't be broken down any further. Show that there at least two different ways to break down 28, but that when the breakdown is complete both ways end up giving you the same numbers.
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RESPONSE --> The number 28 can be ""broken down"" into the product 14*2, which can be broken down into the product 7*2*2, which cannot be broken down any further. Another way to ""break down"" 28 is to breakdown into the products 7*4, which can be broken down into the product 7*2*2, which cannot be broken down any further. The number 34 can be ""broken down"" into the product 17*2, which cannot be broken down any further. confidence assessment: 3
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22:46:59 A good system is to begin by attempting to divide the smallest possible number into the given number. In the case of 34 we see that the number can be divided by 2 give 34 = 2 * 17. It is clear that the factor 2 cannot be further broken down, and is easy to see that 17 cannot be further broken down. So the complete breakdown of 34 is 2 * 17. To breakdown 28 we can again divide by 2 to get 28 = 2 * 14. The number 2 cannot be further broken down, but 14 can be divided by 2 to give 14 = 2 * 7, which cannot be further broken down. Thus we have 28 = 2 * 2 * 7. The number 28 could also the broken down initially into 4 * 7. The 4 can be further broken down into 2 * 2, so again we get 28 = 2 * 2 * 7. It turns out that the breakdown of a given number always ends up with exactly same numbers, no matter what the initial breakdown.
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RESPONSE --> I got the correct answer. self critique assessment: 3
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22:53:52 `q006. Give the average of the numbers in the following list: 3, 4, 6, 6, 7, 7, 9. By how much does each number differ from the average?
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RESPONSE --> The average of the numbers 3,4,6,6,7,7 and 9 is 7. To get the average of a group of numbers you obtain the sum of the group of numbers, which in this case is 42 and divide that number by the number of numbers in the group, which in this case was 7. Therefore, 42/7=6 which is the average of these numbers. Each of these numbers in this list differ from the average by these amounts: 6-3=3 6-4=2 6-6=0 6-6=0 7-6=1 7-6=1 9-6=3 confidence assessment: 3
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22:54:31 To average least 7 numbers we add them in divide by 7. We get a total of 3 + 4 + 6 + 6 + 7 + 7 + 9 = 42, which we then divide by 7 to get the average 42 / 7 = 6. We see that 3 differs from the average of 6 by 3, 4 differs from the average of 6 by 2, 6 differs from the average of 6 by 0, 7 differs from the average of 6 by 1, and 9 differs from the average of 6 by 3. A common error is to write the entire sequence of calculations on one line, as 3 + 4 + 6 + 6 + 7 + 7 + 9 = 42 / 7 = 6. This is a really terrible habit. The = sign indicates equality, and if one thing is equal to another, and this other today third thing, then the first thing must be equal to the third thing. This would mean that 3 + 4 + 6 + 6 + 7 + 7 + 9 would have to be equal to 6. This is clearly not the case. It is a serious error to use the = sign for anything but equality, and it should certainly not be used to indicate a sequence of calculations.
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RESPONSE --> I got the correct answer. self critique assessment: 3
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23:00:15 `q007. Which of the following list of numbers is more spread out, 7, 8, 10, 10, 11, 13 or 894, 897, 902, 908, 910, 912? On what basis did you justify your answer?
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RESPONSE --> Between the two lists of numbers: List #1-7,8,10,10,11,13 and List #2-894,897,902,908,910,912 the list 894, 897,902,908,910,912 is spread out more. I determined the spread by finding the difference between the smallest and largest number in each list. In list #1 13-7=6 which is the spread of this list. In list #2 912-894=18 which is the spread of this list. 18 is larger than 6 which means that list #2 has the larger spread. confidence assessment: 3
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23:01:15 The first set of numbers ranges from 7 to 13, a difference of only 6. The second set ranges from 894 to 912, a difference of 18. So it appears pretty clear that the second set has more variation the first. We might also look at the spacing between numbers, which in the first set is 1, 2, 0, 1, 2 and in the second set is 3, 5, 6, 2, 2. The spacing in the second set is clearly greater than the spacing in the first. There are other more sophisticated measures of the spread of a distribution of numbers, which you may encounter in your course.
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RESPONSE --> I got the answer correct. self critique assessment: 3
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23:05:08 `q008. 12 is 9 more than 3 and also 4 times 3. We therefore say that 12 differs from 3 by 9, and that the ratio of 12 to 3 is 4. What is the ratio of 36 to 4 and by how much does 36 differ from 4? If 288 is in the same ratio to a certain number as 36 is to 4, what is that number?
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RESPONSE --> The ratio of 36 to 4 is 9 and 36 differs from 4 by 32. If 288 is in the same ratio to a certain number as 36 to 4, which was 9, the number is 72. I obtained this number by dividing 288 by 4 to equal 72. confidence assessment: 3
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23:09:12 Just as the ratio of 12 to 3 is 12 / 3 = 4, the ratio of 36 to 4 is 36 / 4 = 9. 36 differs from 4 by 36 - 4 = 32. Since the ratio of 36 to 4 is 9, the number 288 will be in the same ratio to a number which is 1/9 as great, or 288 / 9 = 32. Putting this another way, the question asks for a 'certain number', and 288 is in the same ratio to that number as 36 to 4. 36 is 9 times as great as 4, so 288 is 9 times as great as the desired number. The desired number is therefore 288/9 = 32.
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RESPONSE --> When I arrived at my answer I divided 288 by 4 rather than 9. I did not read the question carefully and therefore made a careless error. self critique assessment: 2
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23:15:17 `q009. A triangle has sides 3, 4 and 5. Another triangle has the identical shape of the first but is larger. Its shorter sides are 12 and 16. What is the length of its longest side?
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RESPONSE --> Triangle #1 has sides 3,4, and 5 and triangle #2 has the identical shape of the first but is large. Its shorter sides are 12 and 16 and the length of its longest side is 20. I obtained the length of triangle #2's longest side by comparing the relationship of both triangles two shorter sides. I found that both shorter sides of the two triangles were 4* larger on the triangle #2 than on triangle #1, therefore I estimated that 4*5=20. confidence assessment: 3
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23:15:38 ** You need to first see that that each side of the larger triangle is 4 times the length of the corresponding side of the smaller. This can be seen in many ways, one of the most reliable is to check out the short-side ratios, which are 12/3 = 4 and 16/4 = 4. Since we have a 4-to-1 ratio for each set of corresponding sides, the side of the larger triangle that corresponds to the side of length 5 is 4 * 5 = 20. **
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RESPONSE --> I got the answer correct. self critique assessment: 3
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23:15:51 end program
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RESPONSE --> Ok self critique assessment: 3
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oㅒLٽ assignment #001 001. Areas qa areas volumes misc 01-18-2009
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23:18:36 `q001. There are 11 questions and 7 summary questions in this assignment. What is the area of a rectangle whose dimensions are 4 m by 3 meters.
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RESPONSE --> The area of a rectangle with dimensions 4m*3m=12m confidence assessment:
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23:20:04 A 4 m by 3 m rectangle can be divided into 3 rows of 4 squares, each 1 meter on a side. This makes 3 * 4 = 12 such squares. Each 1 meter square has an area of 1 square meter, or 1 m^2. The total area of the rectangle is therefore 12 square meters, or 12 m^2. The formula for the area of a rectangle is A = L * W, where L is the length and W the width of the rectangle. Applying this formula to the present problem we obtain area A = L * W = 4 m * 3 m = (4 * 3) ( m * m ) = 12 m^2. Note the use of the unit m, standing for meters, in the entire calculation. Note that m * m = m^2.
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RESPONSE --> I forgot to square my units but I got the correct quanity by the formula of a rectangle. self critique assessment: 2
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23:28:48 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> The area pf a right triangle whose legs are 4.0m and 3.0 m is 6 m. I calculated this area by using the formula for area of a triangle which is A=1/2bh, where, b and h are the base and altitude of the triangle. confidence assessment: 3
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23:29:46 A right triangle can be joined along its hypotenuse with another identical right triangle to form a rectangle. In this case the rectangle would have dimensions 4.0 meters by 3.0 meters, and would be divided by any diagonal into two identical right triangles with legs of 4.0 meters and 3.0 meters. The rectangle will have area A = L * W = 4.0 m * 3.0 m = 12 m^2, as explained in the preceding problem. Each of the two right triangles, since they are identical, will therefore have half this area, or 1/2 * 12 m^2 = 6.0 m^2. The formula for the area of a right triangle with base b and altitude h is A = 1/2 * b * h.
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RESPONSE --> Again I arrived at the correct numberical answer and forgot to square the units. self critique assessment: 2
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23:32:48 `q003. What is the area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters?
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RESPONSE --> The area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters is 10 meters^2. I calculated this area by using the formula for area of a parallelogram, which is A=bh, wher b is base and h is altitutde. confidence assessment: 3
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23:33:19 A parallelogram is easily rearranged into a rectangle by 'cutting off' the protruding end, turning that portion upside down and joining it to the other end. Hopefully you are familiar with this construction. In any case the resulting rectangle has sides equal to the base and the altitude so its area is A = b * h. The present rectangle has area A = 5.0 m * 2.0 m = 10 m^2.
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RESPONSE --> I got the answer correct and I did not forget to square my units. self critique assessment: 3
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23:35:54 `q004. What is the area of a triangle whose base is 5.0 cm and whose altitude is 2.0 cm?
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RESPONSE --> The area of a triangle whose base is 5.0cm and whose altitude is 2.0cm is 5cm^2. I calculated this area by using the formula A=bh, where b=base of triangle and and h=altitude. confidence assessment: 3
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23:36:09 It is possible to join any triangle with an identical copy of itself to construct a parallelogram whose base and altitude are equal to the base and altitude of the triangle. The area of the parallelogram is A = b * h, so the area of each of the two identical triangles formed by 'cutting' the parallelogram about the approriate diagonal is A = 1/2 * b * h. The area of the present triangle is therefore A = 1/2 * 5.0 cm * 2.0 cm = 1/2 * 10 cm^2 = 5.0 cm^2.
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RESPONSE --> I got the anser correct. self critique assessment: 3
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23:41:03 `q005. What is the area of a trapezoid with a width of 4.0 km and average altitude of 5.0 km?
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RESPONSE --> The are of a trapezoid with a width of 4.0km and average altitude of 5.0km is 20.0km^2. I calculated this are b using the formula A=1/2(a+b)h, where a and b=bases of width and h=altitude. confidence assessment: 3
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23:41:18 Any trapezoid can be reconstructed to form a rectangle whose width is equal to that of the trapezoid and whose altitude is equal to the average of the two altitudes of the trapezoid. The area of the rectangle, and therefore the trapezoid, is therefore A = base * average altitude. In the present case this area is A = 4.0 km * 5.0 km = 20 km^2.
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RESPONSE --> My answer is correct. self critique assessment: 3
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23:45:18 `q006. What is the area of a trapezoid whose width is 4 cm in whose altitudes are 3.0 cm and 8.0 cm?
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RESPONSE --> The area of a trapezoid whose width is 4.0 cm and whose altitudes are 3.0 cm and 8.0 cm is 12.0 cm^2. Based upon the formula A=1/2(a+b)h, where a and b are the widths and h is the altitude of the triangle. confidence assessment: 3
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23:48:23 The area is equal to the product of the width and the average altitude. Average altitude is (3 cm + 8 cm) / 2 = 5.5 cm so the area of the trapezoid is A = 4 cm * 5.5 cm = 22 cm^2.
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RESPONSE --> I missed this question because I used measurements in the incorrect places within the formula. I also did not get the average of the altitutde by adding the two lengths and then dividing by2. I do understand the correct method of obtaining this answer know. self critique assessment: 2
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23:53:15 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> The area of a circle whose radius is 3.00cm is 88.8264396098 cm. I calculated this area based on the formula A=pi(3.14)r^2, where r=3.14. confidence assessment: 3
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23:57:55 The area of a circle is A = pi * r^2, where r is the radius. Thus A = pi * (3 cm)^2 = 9 pi cm^2. Note that the units are cm^2, since the cm unit is part r, which is squared. The expression 9 pi cm^2 is exact. Any decimal equivalent is an approximation. Using the 3-significant-figure approximation pi = 3.14 we find that the approximate area is A = 9 pi cm^2 = 9 * 3.14 cm^2 = 28.26 cm^2, which we round to 28.3 cm^2 to match the number of significant figures in the given radius. Be careful not to confuse the formula A = pi r^2, which gives area in square units, with the formula C = 2 pi r for the circumference. The latter gives a result which is in units of radius, rather than square units. Area is measured in square units; if you get an answer which is not in square units this tips you off to the fact that you've made an error somewhere.
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RESPONSE --> I incorrectly used the ^2. I see my mistake I should have only raised 3cm^2 instead of pi*3cm^2. self critique assessment: 2
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00:07:59 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> The circumference of a circle whose radius is exactly 3 cm is 18.84cm. I calculated the circumference of this circle by using the formula C=(pi)(d), where d=diameter. Since I know the radius of the circle I can multiply the radius by 2 to obtain the diameter, which would be 6cm. 6*3.14=18.84cm confidence assessment: 3
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00:08:20 The circumference of this circle is C = 2 pi r = 2 pi * 3 cm = 6 pi cm. This is the exact area. An approximation to 3 significant figures is 6 * 3.14 cm = 18.84 cm. Note that circumference is measured in the same units as radius, in this case cm, and not in cm^2. If your calculation gives you cm^2 then you know you've done something wrong.
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RESPONSE --> My answer is correct. self critique assessment: 3
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00:12:40 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> The area of a circle whose diameter is exactly 12 meters is 113.04. I calculated this measurement by using the formula A=(pi)r^2, where r is the radius. The diameter is twice the radius therefore 12/2=6 meters=radius. 6^2=36 36*3.14=113.04 meters confidence assessment: 3
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00:13:58 The area of a circle is A = pi r^2, where r is the radius. The radius of this circle is half the 12 m diameter, or 6 m. So the area is A = pi ( 6 m )^2 = 36 pi m^2. This result can be approximated to any desired accuracy by using a sufficient number of significant figures in our approximation of pi. For example using the 5-significant-figure approximation pi = 3.1416 we obtain A = 36 m^2 * 3.1416 = 113.09 m^2.
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RESPONSE --> My answer was correct, however iused 3.14 as pi and the instructors answer used a more precise pi=3.1416. self critique assessment: 2
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00:20:37 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> To obtain the area of a circle the formula is A=3.14r^2, where r=radius. In q010 the information given about the circle is the circumference which is 14 pi meters. With this information I am not sure how to obtain the requested information. confidence assessment: 0
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00:28:03 We know that A = pi r^2. We can find the area if we know the radius r. We therefore attempt to use the given information to find r. We know that circumference and radius are related by C = 2 pi r. Solving for r we obtain r = C / (2 pi). In this case we find that r = 14 pi m / (2 pi) = (14/2) * (pi/pi) m = 7 * 1 m = 7 m. We use this to find the area A = pi * (7 m)^2 = 49 pi m^2.
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RESPONSE --> In this problem we must use the information provided to see the relationship between the circumference and radius. c=2 pi r I do not follow the instructors explaination of solving r to obtain r=C/2(2 pi) which shows then that r=14 pi m / (2 pi)=(14/2) * (pi/pi) m =7 *1 m =7m. Which is then used to find the area A = pi* (7m)^2 = 49 pi m^2. self critique assessment: 1
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00:40:28 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> confidence assessment: 2
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00:50:12 Knowing that A = pi r^2 we solve for r. We first divide both sides by pi to obtain A / pi = r^2. We then reverse the sides and take the square root of both sides, obtaining r = sqrt( A / pi ). Note that strictly speaking the solution to r^2 = A / pi is r = +-sqrt( A / pi ), meaning + sqrt( A / pi) or - sqrt(A / pi). However knowing that r and A are both positive quantities, we can reject the negative solution. Now we substitute A = 78 m^2 to obtain r = sqrt( 78 m^2 / pi) = sqrt(78 / pi) m.{} Approximating this quantity to 2 significant figures we obtain r = 5.0 m.
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RESPONSE --> I am not following the use of the formulas when they are used to obtain reverse information. This question and the last question have confused me. I don't understand how I can use a formula to obain information that I need to use in another formula to obtain the desired answer. self critique assessment: 1
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00:54:05 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> The area of a triangle is visualized as 1/2 of a parallelogram, base * altitude * 1/2. confidence assessment: 3
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00:55:12 We visualize the rectangle being covered by rows of 1-unit squares. We multiply the number of squares in a row by the number of rows. So the area is A = L * W.
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RESPONSE --> This question asked about the visualization of a triangle not a rectangle. Please clarify. self critique assessment: 1
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00:56:20 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> We visualize the area of a right triangle as a square because two right triangles would equal a square. confidence assessment: 3
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00:59:48 We visualize two identical right triangles being joined along their common hypotenuse to form a rectangle whose length is equal to the base of the triangle and whose width is equal to the altitude of the triangle. The area of the rectangle is b * h, so the area of each triangle is 1/2 * b * h.
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RESPONSE --> Instead of a square, a rectangle would be visualized because 2 righgt triangles would equal a rectangle if joined by their hypotenuse. This is because the area of a rectangle is b*h, and therefore the area of a right triangle is 1/2*b*h. self critique assessment: 2
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01:01:09 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> We calculate the area of a parallelogram by multiplying the base and altitude together. confidence assessment: 3
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01:01:27 The area of a parallelogram is equal to the product of its base and its altitude. The altitude is measured perpendicular to the base.
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RESPONSE --> My answer is correct. self critique assessment: 3
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01:05:08 We think of the trapezoid being oriented so that its two parallel sides are vertical, and we multiply the average altitude by the width.
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RESPONSE --> The area of a trapezoid is calculated by adding the two length bases of the trapezoid together and then dividing them by 1/2 and then multiplying that answer by the altitude of the trapazoid. 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. self critique assessment: 2
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01:06:45 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> We calculate the area of a circle by multiplying pi by the radius of the circled squared. confidence assessment: 3
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01:07:04 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> My answer is correct. self critique assessment: 3
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01:10:02 `q017. Summary Question 6: How do we calculate the circumference of a circle? How can we easily avoid confusing this formula with that for the area of the circle?
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RESPONSE --> The circumference of a circle is calculated by pi times the diameter. We can avoid confusing the circumference formula with the area formula by remembering that circumferenc deals with the diameter of a circle and area deals with the radius of a circle. confidence assessment: 3
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01:11:05 We use the formula C = 2 pi r. The formula for the area involves r^2, which will give us squared units of the radius. Circumference is not measured in squared units.
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RESPONSE --> The instructors explanation is clear. self critique assessment: 3
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01:15:27 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I have organized my knowledge of the principles illustrated by the exercises in this assignment by memorizing the formulas for obtaining the areas and perimeters of the shpaes in these exercises. confidence assessment: 3
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01:15:43 This ends the first assignment.
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RESPONSE --> ok confidence assessment: 3
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`wMYMzQߪSӍ assignment #002 002. Volumes qa areas volumes misc 01-19-2009
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16:04:00 `q001. There are 9 questions and 4 summary questions in this assignment. What is the volume of a rectangular solid whose dimensions are exactly 3 cm by 5 cm by 7 cm?
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RESPONSE --> The volume of a rectanglar solid whose dimensions are exactly 3cm by 5cm by 7cm is 105 cm^3. I calculated this dimension using the formula V= lwh or volume =length*width*height. confidence assessment: 3
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16:06:44 If we orient this object so that its 3 cm dimension is its 'height', then it will be 'resting' on a rectangular base whose dimension are 5 cm by 7 cm. This base can be divided into 5 rows each consisting of 7 squares, each 1 meter by 1 meter. There will therefore be 5 * 7 = 35 such squares, showing us that the area of the base is 35 m^2. Above each of these base squares the object rises to a distance of 3 meters, forming a small rectangular tower. Each such tower can be divided into 3 cubical blocks, each having dimension 1 meter by 1 meter by 1 meter. The volume of each 1-meter cube is 1 m * 1 m * 1 m = 1 m^3, also expressed as 1 cubic meter. So each small 'tower' has volume 3 m^3. The object can be divided into 35 such 'towers'. So the total volume is 35 * 3 m^3 = 105 m^3. This construction shows us why the volume of a rectangular solid is equal to the area of the base (in this example the 35 m^2 of the base) and the altitude (in this case 3 meters). The volume of any rectangular solid is therefore V = A * h, where A is the area of the base and h the altitude. This is sometimes expressed as V = L * W * h, where L and W are the length and width of the base. However the relationship V = A * h applies to a much broader class of objects than just rectangular solids, and V = A * h is a more powerful idea than V = L * W * h. Remember both, but remember also that V = A * h is the more important.
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RESPONSE --> I understand the concept bewteen both the formulas: V=lwh and v=Bh and also the the relationship bewteen the two. self critique assessment: 2
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16:12:28 `q002. What is the volume of a rectangular solid whose base area is 48 square meters and whose altitude is 2 meters?
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RESPONSE --> The volume of a rectangular solid whose base area is 48m^2 and whose altitude is 2m is 96m^3. Using the formula V=Bh, where B=base area and h=altitude I inserted the values and multiplied. confidence assessment: 3
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16:14:14 Using the idea that V = A * h we find that the volume of this solid is V = A * h = 48 m^2 * 2 m = 96 m^3. Note that m * m^2 means m * (m * m) = m * m * m = m^2.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:17:38 `q003. What is the volume of a uniform cylinder whose base area is 20 square meters and whose altitude is 40 meters?
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RESPONSE --> The volume of a uniform cylinder whose base area is 20m^2 and whose altitude is 40 meters is 800m^2. I calculated this measurement using the formula V=Bh or Voolume=base area *height or altitude. confidence assessment: 3
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16:18:05 V = A * h applies to uniform cylinders as well as to rectangular solids. We are given the altitude h and the base area A so we conclude that V = A * h = 20 m^2 * 40 m = 800 m^3. The relationship V = A * h applies to any solid object whose cross-sectional area A is constant. This is the case for uniform cylinders and uniform prisms.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:25:47 `q004. What is the volume of a uniform cylinder whose base has radius 5 cm and whose altitude is 30 cm?
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RESPONSE --> The colume of a unifrom cycliner whose base has a radius of 5cm and whose altitude is 30cm is 2356.19449019cm^2. I calculated this measurement by using the formula A=pi r^2 to obtain the base area of the circle=78.5398163397 and then using this measurement in the formula V=Bh, where B=base area and h=altitude. confidence assessment: 3
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16:28:11 The cylinder is uniform, which means that its cross-sectional area is constant. So the relationship V = A * h applies. The cross-sectional area A is the area of a circle of radius 5 cm, so we see that A = pi r^2 = pi ( 5 cm)^2 = 25 pi cm^2. Since the altitude is 30 cm the volume is therefore V = A * h = 25 pi cm^2 * 30 cm = 750 pi cm^3. Note that the common formula for the volume of a uniform cylinder is V = pi r^2 h. However this is just an instance of the formula V = A * h, since the cross-sectional area A of the uniform cylinder is pi r^2. Rather than having to carry around the formula V = pi r^2 h, it's more efficient to remember V = A * h and to apply the well-known formula A = pi r^2 for the area of a circle.
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RESPONSE --> My answer is correct, however I went one step farther and multiplied out 750*pi. Which would you perfer? self critique assessment: 2
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16:31:56 `q005. Estimate the dimensions of a metal can containing food. What is its volume, as indicated by your estimates?
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RESPONSE --> The area of the circular base of a juice can is pi(2.75 cm)^2=7.5625 pi cm^2. The height is h=9.5 cm, so the colume V=Bh=71.84375 pi cm^3, or about 226 cm^3. confidence assessment: 3
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16:32:34 People will commonly estimate the dimensions of a can of food in centimeters or in inches, though other units of measure are possible (e.g., millimeters, feet, meters, miles, km). Different cans have different dimensions, and your estimate will depend a lot on what can you are using. A typical can might have a circular cross-section with diameter 3 inches and altitude 5 inches. This can would have volume V = A * h, where A is the area of the cross-section. The diameter of the cross-section is 3 inches so its radius will be 3/2 in.. The cross-sectional area is therefore A = pi r^2 = pi * (3/2 in)^2 = 9 pi / 4 in^2 and its volume is V = A * h = (9 pi / 4) in^2 * 5 in = 45 pi / 4 in^3. Approximating, this comes out to around 35 in^3. Another can around the same size might have diameter 8 cm and height 14 cm, giving it cross-sectional area A = pi ( 4 cm)^2 = 16 pi cm^2 and volume V = A * h = 16 pi cm^2 * 14 cm = 224 pi cm^2.
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RESPONSE --> My answer is very similar. self critique assessment: 3
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16:34:46 `q006. What is the volume of a pyramid whose base area is 50 square cm and whose altitude is 60 cm?
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RESPONSE --> The volume of a pyramid whose base area is 50 cm^2 and whose altitude is 60 cm is 100cm^3. I calculated this dimension using the formula V=1/3Bh confidence assessment: 3
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16:35:11 We can't use the V = A * h idea for a pyramid because the thing doesn't have a constant cross-sectional area--from base to apex the cross-sections get smaller and smaller. It turns out that there is a way to cut up and reassemble a pyramid to show that its volume is exactly 1/3 that of a rectangular solid with base area A and altitude h. Think of putting the pyramid in a box having the same altitude as the pyramid, with the base of the pyramid just covering the bottom of the box. The apex (the point) of the pyramid will just touch the top of the box. The pyramid occupies exactly 1/3 the volume of that box. So the volume of the pyramid is V = 1/3 * A * h. The base area A is 30 cm^2 and the altitude is 60 cm so we have V = 1/3 * 50 cm^2 * 60 cm = 1000 cm^3.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:37:17 `q007. What is the volume of a cone whose base area is 20 square meters and whose altitude is 9 meters?
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RESPONSE --> The volume of a cone whose base area is 20m^2 and whose altitude is 9m is 60m^3. I calculated this measurement using the formula V=1/3Bh. confidence assessment: 3
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16:37:40 `q008. What is a volume of a sphere whose radius is 4 meters?
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RESPONSE --> My answer is correct. 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. confidence assessment: 3
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16:39:32 The volume of a sphere is V = 4/3 pi r^3, where r is the radius of the sphere. In this case r = 4 m so V = 4/3 pi * (4 m)^3 = 4/3 pi * 4^3 m^3 = 256/3 pi m^3.
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RESPONSE --> I understand the formula for volume of a sphere and feel comfortable calulating thie measurement. self critique assessment: 3
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16:45:50 `q009. What is the volume of a planet whose diameter is 14,000 km?
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RESPONSE --> The volume of a planet whose diameter is 14,000km is calculated with the formula V=4/3 pi r^3. We were given the value for the diameter of the planet and therefore must divide the diamter by2=7,000km=radius. We can know insert the values into the formula:v=4/3 pi (7000)km^3. confidence assessment: 3
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16:46:12 The planet is presumably a sphere, so to the extent that this is so the volume of this planet is V = 4/3 pi r^3, where r is the radius of the planet. The diameter of the planet is 14,000 km so the radius is half this, or 7,000 km. It follows that the volume of the planet is V = 4/3 pi r^3 = 4/3 pi * (7,000 km)^3 = 4/3 pi * 343,000,000,000 km^3 = 1,372,000,000,000 / 3 * pi km^3. This result can be approximated to an appropriate number of significant figures.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:47:11 `q010. Summary Question 1: What basic principle do we apply to find the volume of a uniform cylinder of known dimensions?
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RESPONSE --> Volume=base area*height or altitude. confidence assessment: 3
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16:47:31 The principle is that when the cross-section of an object is constant, its volume is V = A * h, where A is the cross-sectional area and h the altitude. Altitude is measure perpendicular to the cross-section.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:48:41 `q011. Summary Question 2: What basic principle do we apply to find the volume of a pyramid or a cone?
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RESPONSE --> We find the volume of a pyramid or cone using formula volume=1/3*base area*height or altitude. confidence assessment: 3
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16:48:56 The volumes of these solids are each 1/3 the volume of the enclosing figure. Each volume can be expressed as V = 1/3 A * h, where A is the area of the base and h the altitude as measured perpendicular to the base.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:49:39 `q012. Summary Question 3: What is the formula for the volume of a sphere?
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RESPONSE --> The formula for the volume of a sphere is V=4/3 pi r^3. confidence assessment: 3
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16:49:56 The volume of a sphere is V = 4/3 pi r^3, where r is the radius of the sphere.
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RESPONSE --> My answer is correct. self critique assessment: 3
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16:50:52 `q013. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I have recorded all formulas and are comfortable in using each of the formulas to calculate the volume of an object. confidence assessment: 3
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16:51:02 This ends the second assignment.
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RESPONSE --> ok confidence assessment: 3
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