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course Phy 201
6/4/12 around 8:30pm
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
It will take 9 hours to earn $72 because 72 divided by 8 equals 9. For each of the nine hours you earn eight dollars so those nine eights added up equals seventy two.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
Your solution:
(8+3)*5= 55 because due to order of operations you calculate what is in parentheses first then the remaining math. Therefore, 8+3=11 and 11*5=55.
8+3*5= 23 because due to order of operations you calculate multiplication before addition if there are no parentheses. Therefore, 3*5=15 and 15+8=23.
Order of operations is why the results differ for these two problems.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
Your solution:
(2^4)*3= 48 because due to order of operations, parentheses and exponents occur before multiplication. Therefore, 2^4 is first and equals 16. Then 16*3= 48.
2^(4*3)= 4,096 because due to order of operations, parentheses occur before exponents. Therefore, 4*3 is first and equals 12, then 2^12 equals 4,096.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
3*5-4*3^2 = -21 because first, I equated the exponent 3^2 which equals 9. Then multiplication is proceeded, but there are two multiplications, so 4*9= 36 and 3*5=15. Then the subtraction of the two sides comes last so 15-36=-21.
3*5-(4*3)^2 = -129 because first, I equated the parentheses (4*3) which equals 12. Then the exponent 12^2=144. Then multiplication of 3*5=15. Then subtraction of the two sides comes last so 15-144= -129.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
Y=2x+3 when x=-2 equals -1. First -2*2=-4. Then -4 + 3 = -1
Y=2x+3 when x=-1 equals 1. First 2*-1=-2. Then -2 + 3= 1
Y=2x+3 when x=0 equals 3. First 2*0= 0. Then, 0+3=3
Y=2x+3 when x=1 equals 5. First 2*1=2. Then, 2+3=5
Y=2x+3 when x=2 equals 7. First, 2*2=4. Then, 4+3=7
My graph starts out at the lower left quadrant with points moving upward and to the right for each equation. They form a linear line on the graph.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
Y= x^2+3 when x= -2, y= 7 because -2*-2=4 and 4+3=7
Y= x^2+3 when x= -1, y=4 because -1*-1=1 and 1+3=4
Y= x^2+3 when x= 0, y=3 because 0*0=0 and 0+3=3
Y= x^2+3 when x= 1, y= 4 because 1*1=1 and 1+3 =4
Y= x^2+3 when x=2, y=7 because 2*2=4 and 4+3 =7
The graph starts out in the top left hand quadrant and swoops down then up into the top right quadrant. This graph fits the example of the quadratic or parabolic graph.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
Y = 2^x +3 when x = 1, y = 5 because 2^1= 2 and 2+3=5
Y = 2^x +3 when x=2, y=7 because 2^2=4 and 4+3=7
Y = 2^x +3 when x=3, y= 11 because 2^3=8 and 8+3=11
Y = 2^x +3 when x=4, y=19 because 2^4= 16 and 16+3=19
The graph doubles on the right with each point. It continues to get higher and higher with no indication of decreasing. Therefore, we call that graph exponential.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result is equal to the original number.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result will be less than the original number. A number greater than 1 such as 2 means that the result will always be half the original number, which is less than the original number. Therefore, any number greater than 1or 2 will have a smaller result than the original number because it just breaks the original number into smaller and smaller numbers.
confidence rating #$&*:
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Self-critique: OK
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Self-critique rating: OK
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Self-critique Rating:
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result will be greater than the original number. Since dividing a number by 1 always equals the original number then dividing by a number greater than 1 will result in a smaller number. Also, if dividing by greater than 1 results in a number less than the original number then I can relate these ideas. Taking less than itself away from itself will leave more.
Critique rating: 2
####Self critique: Although I understand this problem, I find it hard to actually explain myself. When I read the given solution, it was very understandable but I couldn’t come to that explanation on my own. This helped me realize I need to better understand my answer before giving it and moving on.
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Self-critique rating: 3
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That is so, but you are doing a good job. Naturally of course you want to keep improving.
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Self-critique Rating:
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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.
However, in order to better understand the process, you are asked here to go back and find something in one of the given solutions that you did not address in your solution, and insert a self-critique. You should choose something that isn't trivial to you--something you're not 100% sure you understand.
If you can't find anything, you can indicate this below, and the instructor will point out something and request a response (the instructor will select something reasonable, but will then expect a very good and complete response). However it will probably be less work for you if you find something yourself.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
####Self critique: Although I understand this problem, I find it hard to actually explain myself. When I read the given solution, it was very understandable but I couldn’t come to that explanation on my own. This helped me realize I need to better understand my answer before giving it and moving on.
"
Self-critique (if necessary):
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Self-critique rating:
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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.
However, in order to better understand the process, you are asked here to go back and find something in one of the given solutions that you did not address in your solution, and insert a self-critique. You should choose something that isn't trivial to you--something you're not 100% sure you understand.
If you can't find anything, you can indicate this below, and the instructor will point out something and request a response (the instructor will select something reasonable, but will then expect a very good and complete response). However it will probably be less work for you if you find something yourself.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
####Self critique: Although I understand this problem, I find it hard to actually explain myself. When I read the given solution, it was very understandable but I couldn’t come to that explanation on my own. This helped me realize I need to better understand my answer before giving it and moving on.
"
Self-critique (if necessary):
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Self-critique rating:
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