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course MTH 272
May 19, 2013 at 3:28 pm
Question: `q001. If you are earning money at the rate of 8 dollars / hour and work for 4 hours, how much money do you make during this time? Answer in such a way as to explain your reasoning as fully as possible. A solution to this problem appears several lines below, but enter your own solution before you look at the given solution.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Previously Answered
Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
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Your solution:
Previously Answered
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.
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Your solution:
In order to determine the answer to this question, I divided $72 by 8 because if the person wants to work until he earns $72, then he must figure out how many hours he/she must work until he earns this amount. The answer, once you have divided $72 by 8 is 9 hours.
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
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.
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Your solution:
(8+3)*5
(8+3) = 11
11 * 5 = 55
However,
8+3*5
3*5 = 15
15+8
= 23
The reason for the difference in my answers is because of the order of operations. In the first problem, it tells you to add before you multiply; however, in the second it does not specify, so you assume, according to the order of operations that you multiply before adding.
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
(2^4)*3
2^4 = 16
16 *3 = 48
However,
2^(4*3)
4*3 = 12
2^12 = 4096
The reason for my difference in answers is because of the order of operations again. The first problem states that I must raise 2 to the fourth power before multiplying by 3; however, in the second problem, the order of operations states that I must multiply 4 by 3 before raising two to the twelfth power.
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
Your solution:
The first problem:
3^2 = 9
4*9= 36
3*5=15
15-36 = -21
OR
4*3=12
12^2 = 144
3*5=15
15-144 = -129
Again, I achieved different results because of the order of operations.
confidence rating #$&*:
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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
x y
-2 -1
-1 1
0 3
1 5
2 7
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Your solution:
I obtained these y values for plugging in the given x value into the equation ( y=2x+3). For the first given x value (-2), I plugged in -2 wherever an x was present (y= 2(-2)+3) , and obtained a y value of -1.
When the solution was graphed, I noticed that the graph was linear, crossing the y axis at 3, yielding a positive direction.
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
• Question: `q008. Let y = x^2 + 3.
x y
-2 7
-1 4
0 3
1 4
2 7
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Your solution:
In order to obtain the solutions found in the y column of this table, I plugged the given x values into the equation. For example, for the first given x value, I plugged -2 into the equation: y=(-2)^2+3, yielding an answer of 7.
The graph of this equation yields a parabola that is concave up. The vertex of this graph is located at (0,3).
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
• Question: `q009. Let y = 2 ^ x + 3
x y
1 5
2 7
3 11
4 19
Your solution:
In order to obtain the solutions illustrated in this table, I plugged the given x values into the equation. For example: When x was 1, I plugged in 1 into the equation: y=2^1+3, which gave an answer of 5.
The graph of this equation is similar to an exponential graph because depending on the number; you are raising it to different powers, which will yield an exponential graph. The graph will grow slowly at first, and then it will have exponential growth.
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
If you divide a certain positive number by 1, it will always be equal to the original number. This answer is true for all numbers.
confidence rating #$&*:
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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:
If you divide a certain positive number by a number greater than 1, if the number is positive, then the result will always be less than the original number. This is illustrated through the following example: Take a certain number: 16, and divide this number by a number greater than 1, but still positive: 2. 16 divided by 2 is eight; thus, the quotient is smaller than the original number of 16.
Let’s try another example using a certain number of 64. When you divide 64 by 8 (a number greater than 1 that is still positive), you yield 8, which is a number that is smaller than the original number.
confidence rating #$&*:
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Self-critique:
####This question was a little harder for me, not because of the mathematical process, but because of how the question was worded. It took me a little while to wrap my brain around how to actually go about proving this answer. However, once I read over the solution, I was able to fully comprehend the example and provide my own examples that are aforementioned.
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Self-critique Rating: 3
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
Your solution:
If you divide a certain positive number by a positive number that is less than 1, the answer will always be greater than the original number. Let’s use the example of taking a certain positive number of 5, and dividing it by a number that is positive, but less than 1 (0.5). 5 divided by 0.5 yields an answer of 10. Another example is dividing 10 by 0.5, which yields 20. Even with a number that is positive, less than 1, and not 0.5, the number will always be greater than the original number.
confidence rating #$&*:
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Self-critique: OK
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Self-critique Rating: OK
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Question: `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 question was a little harder for me, not because of the mathematical process, but because of how the question was worded. It took me a little while to wrap my brain around how to actually go about proving this answer. However, once I read over the solution, I was able to fully comprehend the example and provide my own examples that are aforementioned. (This is for question 11).
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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 question was a little harder for me, not because of the mathematical process, but because of how the question was worded. It took me a little while to wrap my brain around how to actually go about proving this answer. However, once I read over the solution, I was able to fully comprehend the example and provide my own examples that are aforementioned. (This is for question 11).
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Self-critique (if necessary):
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Self-critique rating:
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Good, but you omitted the given solutions.
Remember to never omit anything from the original document. Insert your solutions in the appropriate places, but don't change anything else.
Among other things, you will want the given solutions to appear on your access page.
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