course Phy121 Ip{᩠F͛Rxassignment #001
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20:35:18 `questionNumber 10000 `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 --> confidence assessment:
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isa|ЀlF` assignment #001 001. typewriter notation qa initial problems 08-26-2008
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20:38:56 `questionNumber 10000 `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 the 2 would be devided by x before x-2 or x+4. confidence assessment: 3
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20:40:40 `questionNumber 10000 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 --> OK self critique assessment:
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21:10:20 `questionNumber 10000 `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 --> In the first equation 2 would be raised to the power of x then 4 would be added. In the second 2 would be raised to the sum of (x+4) confidence assessment: 3
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21:11:41 `questionNumber 10000 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 --> True self critique assessment: 3
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21:31:28 `questionNumber 10000 `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 --> -1 would be the numerator and 19 would be the denominator 13.571 confidence assessment: 0
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21:33:08 `questionNumber 10000 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 --> self critique assessment: 1
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21:51:27 `questionNumber 10000 `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 --> (4-5)^2(4-1)+(3/4)-2 \ / \ / \ / -1^2 * 3 + .75 -2 \ / -1 * 3 +.75 -2 \ / -3 +.75 -2 \ / -2.75 -2 \ / -4.75 confidence assessment: 3
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21:55:41 `questionNumber 10000 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 --> When I expod (-1)^2 I came up with -1 self critique assessment: 2
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21:58:51 `questionNumber 10000 *&*& 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 --> It is equaly important to work equations out on paper and to understand how to enter them on keypad. self critique assessment: 2
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22:03:31 `questionNumber 10000 `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 --> The link explains the difference in the way equations look in standard form as compaired to typewriter form confidence assessment: 3
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22:04:46 `questionNumber 10000 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 --> self critique assessment: 2
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22:06:04 `questionNumber 10000 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 --> OK self critique assessment: 0
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22:06:16 `questionNumber 10000 end program
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RESPONSE --> self critique assessment: 0
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O{y assignment #001 001. typewriter notation qa initial problems 08-27-2008
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23:01:39 `questionNumber 10000 `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 2 would be divided by x first then the 4 would be added and the sum would be subtracted from x. 2/2=1+4=5 then 2-5=-3 In the second the diffrence of x-2 would be divided by the sum of x+4 (2-2)=0 (2+4)=6 0/6=0 confidence assessment: 3
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23:04:40 `questionNumber 10000 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 added before I subtracted when I should have worked from left to right. I understand what I did wrong self critique assessment: 2
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23:11:02 `questionNumber 10000 `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 --> In the first problem the exponet would be done first then add 4. 2^2=4 then + 4 = 8 Parentheses are done fist in this equation then the exponant (2+4)=6 2^6= 2*2*2*2*2*2= 64 confidence assessment: 3
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23:11:30 `questionNumber 10000 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 --> Exactly self critique assessment: 2
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23:33:31 `questionNumber 10000 `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 --> x-3 is the numerator 2 - 3 / [ ( 4 - 5 )^2 * 3 * 2 + 1 ] - 2 + 7 * 2 2-3 / [-1 ^ 2 * 3 * 2+ 1] -2+ 7 * 2 2-3 / [ -1 * 3 * 2+ 1] - 2+ 7 * 2 2 - 3 / [ -3 * 2 + 1] -2 + 7 * 2 2 - 3 / [ - 6 + 1 ] -2 + 7 * 2 2 - 3 / -5 - 2 + 7 * 2 2 - .6 - 2 + 14 1.4 - 2 + 14 -.6 + 14 = 13.4 confidence assessment: 2
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23:38:42 `questionNumber 10000 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 used a calucator for the exponent and was given -1. I now understand that -1*-1= 1. I believe that my order of operations was correct .Thus the rest of the equation was wrong due to that fact. self critique assessment: 2
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23:44:16 `questionNumber 10000 `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 --> ( 4 - 5 ) ^ 2 * 4 - 1 + 3 / 4 - 2 -1 ^ 2 * 4 - 1 + .75 - 2 -1 * 4 -1 + .75 - 2 4 - 1 + .75 -2 3 + .75 - 2 3.75 - 2 = 1.75 confidence assessment: 2
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23:52:51 `questionNumber 10000 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 --> Is it wrong to convert a fraction into a whole number when working an equation that has a fraction? If so do I need to convert my answer back into a fraction to be in simplest form? self critique assessment: 2
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23:55:05 `questionNumber 10000 *&*& 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 --> I understand the order of opperations except why decimals are not used insted of fractions. self critique assessment: 2
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23:58:50 `questionNumber 10000 `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 --> It appears to be a page displaying the work completed. confidence assessment: 2
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23:59:37 `questionNumber 10000 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 --> Ok I think I've been here before self critique assessment: 3
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23:59:56 `questionNumber 10000 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 --> ok self critique assessment: 3
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DKGٙ assignment #001 001. typewriter notation qa initial problems 08-28-2008 ʴkzz_ assignment #004 004. Liberal Arts Mathematics qa initial problems 08-29-2008
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22:38:46 `questionNumber 40000 `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 --> confidence assessment: 2
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22:38:55 `questionNumber 40000 `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 group doesn't have supervision and they do act in an orderly manner. confidence assessment: 2
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22:40:12 `questionNumber 40000 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 --> reasonable self critique assessment: 3
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22:42:18 `questionNumber 40000 `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,acb,bac,bca,cab,cba. All orders were orginized in alphabetical oreder. (ab,ac,ba,bc,ca,cb...) confidence assessment: 1
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22:43:06 `questionNumber 40000 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 --> Exactly self critique assessment: 3
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22:45:36 `questionNumber 40000 `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 --> AD AD E confidence assessment: 2
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22:51:09 `questionNumber 40000 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 --> I considered the first half stoped at C sinc F was the last letter given I could only assume that these 6 letters would be the limit to this alphabet. self critique assessment: 1
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22:54:24 `questionNumber 40000 `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 --> 20; each number plus the last makes the next. 48; each product is multiplied by 2 to get the next. 29; each number is added to the last to get the next. Conductive reasoning confidence assessment: 3
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22:56:19 `questionNumber 40000 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 --> The first problem was a simple addition problem. self critique assessment: 2
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23:03:23 `questionNumber 40000 `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 --> 28( 2 * 2 * 7 ) ( 4 * 7 ) 34 ( 2 * 17 ) confidence assessment: 2
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23:04:41 `questionNumber 40000 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 --> Do I need to give more detail in this sort of question? self critique assessment: 3
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23:07:50 `questionNumber 40000 `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 --> A=7 3 differs by 4 4 "" "" 3 6 "" "" 1 9 "" "" 2 confidence assessment: 3
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23:09:11 `questionNumber 40000 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 --> Opps, I looked at the wrong # on my calucator. self critique assessment: 1
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23:18:13 `questionNumber 40000 `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 --> 7 differs by 1 to 8 8 "" "" 2 "" 10 10 "" "" 1 "" 11 11 "" "" 2 "" 13 894 "" "" 3 "" 897 897 "" "" 5 "" 902 902 "" "" 6 "" 908 908 "" "" 2 "" 910 910 "" "" 2 "" 912 So the biggest difference between any 2 numbers was 6 so the 2 numbers must be 902 and 908 confidence assessment: 3
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23:19:02 `questionNumber 40000 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 --> self critique assessment: 3
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23:22:14 `questionNumber 40000 `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 --> r= 36 / 4 = 9 d= 36 - 4 =32 r = 288 / 9 = 32 confidence assessment: 3
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23:22:42 `questionNumber 40000 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 --> OK self critique assessment: 3
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23:28:14 `questionNumber 40000 `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 --> Pathgrams Theroy would show that 3 square plus 4 square equals 5 square. So the square root of 12 square plus 16 square would give us 20. With a ratio of 4 confidence assessment: 2
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23:28:57 `questionNumber 40000 ** 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 think I have it. self critique assessment: 3
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Ѕ`{]ΊM assignment #002 002. Precalculus I 08-29-2008 IMŷ{ܻ|v assignment #001 001. typewriter notation qa initial problems 08-30-2008 ~~Pʙв assignment #001 001. Rates qa rates 08-30-2008 灄wwcw assignment #001 08-30-2008 qa prelim ֫ʼnќ[zÅ assignment #001 001. Areas qa areas volumes misc 09-01-2008
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21:34:20 `questionNumber 10000 `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 --> 12 m square The length * the width = Area confidence assessment: 3
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21:34:58 `questionNumber 10000 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 --> understood self critique assessment: 3
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21:37:38 `questionNumber 10000 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> a^2 + b^2 = c^2 4^2 + 3^2 = c^2 16 + 9 = 25^2 =5.0 meters confidence assessment: 3
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21:39:10 `questionNumber 10000 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 --> I misunderstood and gave the hypotinouse insteed of the area. self critique assessment: 2
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21:40:52 `questionNumber 10000 `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 --> b * h = a 5 * 2 = 10^2 confidence assessment: 3
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21:41:03 `questionNumber 10000 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 --> ok self critique assessment: 3
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21:44:18 `questionNumber 10000 `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 --> A = 1/2 * b * h A = 1/2 * 5cm * 2cm A = 5^2cm confidence assessment: 2
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21:44:32 `questionNumber 10000 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 --> yes self critique assessment: 3
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21:54:27 `questionNumber 10000 `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 area of a trapezoid is determind b the base1 +base2 divided by 2. Thus more info is needed. confidence assessment: 1
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21:55:42 `questionNumber 10000 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 --> I see. self critique assessment: 1
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21:58:12 `questionNumber 10000 `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 --> A = w * the average of the two sides 5.5 A = 4 * 5.5 = 22 ^2 confidence assessment: 3
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21:58:22 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:02:26 `questionNumber 10000 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> A = 2 * pi * 3 A = 2 * 3.14 * 3 A = 18.84 confidence assessment: 2
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22:07:21 `questionNumber 10000 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 misread the formula and multiplied by 2 instead of ^2 self critique assessment: 1
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22:08:35 `questionNumber 10000 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> P = pi * D P = 3.14 * 6 P = 18.84 cm confidence assessment: 2
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22:08:54 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:10:14 `questionNumber 10000 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> A = pi * r ^ 2 A = 3.14 * 36 A = 113.04meters confidence assessment: 3
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22:11:10 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:14:23 `questionNumber 10000 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> 14 / pi = 4.46 4.46^2 * pi = 62.39^2meters confidence assessment: 2
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22:17:51 `questionNumber 10000 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 --> I see self critique assessment: 2
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22:20:46 `questionNumber 10000 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> 78^2 meters / pi = 24.82817112 = square root of =8.83 confidence assessment: 2
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22:21:53 `questionNumber 10000 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 don't understand self critique assessment: 1
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22:23:51 `questionNumber 10000 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> As a group of squares inside the rectangle. confidence assessment: 3
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22:25:29 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:26:19 `questionNumber 10000 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> As half the area of a rectangle that has the same width and height. confidence assessment: 3
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22:26:34 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:27:13 `questionNumber 10000 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> multiply the base times the height. confidence assessment: 2
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22:27:26 `questionNumber 10000 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 --> ok self critique assessment: 3
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22:28:34 `questionNumber 10000 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> by multipling the base times an average of the two altitudes. confidence assessment: 3
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22:28:47 `questionNumber 10000 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 --> self critique assessment: 3
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22:29:17 `questionNumber 10000 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> radious^2 times pi confidence assessment: 3
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22:29:26 `questionNumber 10000 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> ok self critique assessment: 3
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22:30:53 `questionNumber 10000 `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 --> multiply the diameter by pi confidence assessment: 3
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22:31:44 `questionNumber 10000 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 --> I forgot to add comment about area being in ^2 form self critique assessment: 2
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22:32:33 `questionNumber 10000 `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 made referance notes to formulas that may be needed. confidence assessment: 3
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22:32:43 `questionNumber 10000 This ends the first assignment.
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RESPONSE --> confidence assessment: 3
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`n֩ڞIx assignment #001 001. Timing (pendulum exp and timer program, using pendulum to time things with feedback on accuracy) Physics I 09-01-2008
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22:43:50 `questionNumber 10000 This exercise was to have included a simulation of the pendulum as a timer. However due to delays in the startup of the course this exercise will not be included this semester. Your real first assignment with this program will be #2. The program will exit after you enter your response (you can enter a blank response or any other response you wish). Then click on Quit Program (upper right-hand corner).
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RESPONSE -->
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ْ°Ӵ|Czr assignment #001 001. Timing (pendulum exp and timer program, using pendulum to time things with feedback on accuracy) Physics I 09-02-2008
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18:01:34 `questionNumber 10000 This exercise was to have included a simulation of the pendulum as a timer. However due to delays in the startup of the course this exercise will not be included this semester. Your real first assignment with this program will be #2. The program will exit after you enter your response (you can enter a blank response or any other response you wish). Then click on Quit Program (upper right-hand corner).
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RESPONSE -->
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