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course Mth 163
6/1 around 6:00 pm.
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
If I am earning 8 dollars per hour I will have to work for 9 hours to earn 72 dollars. The reason why is because 72 divided by 8 equals to 9. And, 8 times 9 is 72.
confidence rating #$&*:
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Self-critique (if necessary): 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.
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Your solution: (type in your solution starting in the next line)
In the first expression (8 + 3) * 5, I decided to add what was inside of the parentheses first and then multiply by 5 the result from the addition operation. So from the addition inside the parentheses I got 11 and then multiplied 11 by 5 which is equal to 55. The reason why I did the operation inside the parentheses first is because according to the rules of operations what is inside of parentheses has to be evaluated before a multiplication as in this case. The answer is 55.
In the second expression 8 + 3 * 5, I calculated the multiplication operation before I did the addition. So 3 times 5 is 15, and 15 plus 8 is 23. According to the rules of operations multiplication is prior to addition. The answer is 23.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
When I calculated the first expression (2^4) * 3, I evaluated what was inside of the parentheses first and then multiplied it by three. So the number 2 raised to the fourth power equals 16, and 16 multiplied by 3 is 48. The answer is 48.
On the next expression 2^(4 * 3), I calculated what was inside the parentheses first, and then evaluated the rest. I multiplied 4 times 3 which is 12, and then I evaluated 2 to the twelfth power which is 4096. The answer is 4096.
confidence rating #$&*:
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Self-critique (if necessary): 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.
Your solution:
When I calculated the expression 3 * 5 - 4 * 3 ^ 2, first I evaluated the 3 to the second power which is 9, then I calculated 3 times 5 which is 15, and then 4 times 9 which is 36. Finally, I added 15 to -36 which is -21. The answer is -21.
On the next expression 3 * 5 - (4 * 3)^2, first I calculated what was inside of the parentheses which is 12, then I evaluated 12 to the second power which is 144, and then I multiplied 3 times 5 which is 15. Finally, I added 15 to -144 which is -129. The answer is -129.
confidence rating #$&*:
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Self-critique (if necessary): 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.
x y
-2
-1
0
1
2
• 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:
To evaluate y = 2 x + 3 for x = -2, I replaced the x in the equation for a -2. Then I solved the equation for y by multiplying 2 times -2 which is -4, and then adding -4 and 3 which is -1. The result is y = -1.
To evaluate y = 2 x + 3 for x = -1, x = 0, x = 1, and x = 2 I proceeded similarly as the previous exercise. First, I replaced the x values -1, 0, 1, and 2 each at a time in the equation for the variable x. Then I solved the equation for y, and the y values are:
x y
-2 -1
-1 1
0 3
1 5
2 7
The graph I drew has a horizontal x-axis from -4 to 4, and a vertical y-axis from -4 to 8. I started plotting the point (-2, -1) in the third quadrant, then the point (-1, 1) in the second quadrant, then the point (0, 3) in the y-axis, then the point (1, 5) in the first quadrant, and the last point (2, 7) in the first quadrant. Finally, I drew a straight line connecting all the points. I decided to choose the Linear shape graph as the one that most resembles my graph because it too shows a straight line.
confidence rating #$&*:
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Self-critique (if necessary): 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.
x y
-2
-1
0
1
2
• 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:
When I evaluated y = x^2 + 3 for x = -2, I the x value of -2 for the x variable in the equation. Then I solved the equation for the variable y by raising the -2 to the second power which is 4, and then adding 4 and 3 which is 7. The result is y = 7.
Then to evaluate y = x^2 + 3 for x = -1, x = 0, x = 1, and x = 2 I replaced each of the x values into the x variable in the equation, and solved for y as I did in the previous exercise. The y values are:
x y
-2 7
-1 4
0 3
1 4
2 7
I decided to draw a horizontal x-axis from the number -4 to 4, and a vertical y-axis from the number -2 to 9. Then I plotted the first point (-2, 7) in the second quadrant, then the point (-1, 4) in the second quadrant, then the point (0, 3) in the y-axis, then the point (1, 4) in the first quadrant, and the last point (2, 7) in the first quadrant. Finally, I connected all the points and realized they made a curve line. I chose the Quadratic or Parabolic graph as the one that most resembles my graph because it also shows a curve line pointing upward and both sides are equal.
Confidence Rating: 3
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Self-critique (if necessary): I did not include in my solution the fact that if we move the graph right one unit from the lowest point of the graph, the graph goes up one unit. I also, did not mention the aspect of symmetry between the points of the graph. In addition, I am not sure if I fully understand the fact that if we move the graph to the write one unit and to the left one unit it rises one unit, shouldn´t it just stay the same height and only move right and left? Well, actually after writing this I think I am starting to understand the meaning in the given solution. I think it was trying to show how both sides of the graph are symmetric because in both sides they rise the same units.
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Self-critique Rating: 3
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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.
x y
1
2
3
4
• 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:
To evaluate y = 2 ^ x + 3 for x = 1, first I evaluated two to the first power which is 2 by replacing the x variable in the equation by the x value 1, and then added 2 plus 3 which is 5. The result is y = 5.
Next to evaluate y = 2 ^ x + 3 for x = 2, x = 3, and x = 4 I replaced the x values into the x variable in the equation each at a time. The y values are:
x y
1 5
2 7
3 11
4 19
When sketching my graph I decided to draw a horizontal x-axis from -2 to 6, and a vertical y-axis from -2 to 20. Then I started to plot the several points starting with the first (1, 5), then the point (2, 7), then the point (3, 7), and the last point (4, 19). All the points are in the first quadrant so I connected all the points with a non-straight line. I decided to select the Exponential graph due to the fact that the line also looked slightly curved like mine did, as well as going in the same direction.
confidence rating #$&*:
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Self-critique (if necessary): Before I read the given solution I did not realize the fact that the increase in the y value is the double of the previous one. In addition, I did not write on my solution that the graph was increasing very fast, the y values double each time we move to the right. Also, I did not mention that one of the characteristics of the Exponential graph is that it gets steeper and steeper as it increases from left to right.
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Self-critique Rating: 3
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result is equal to the original number because if I divide something in one it stays the same, it doesn´t change.
confidence rating #$&*:
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Self-critique (if necessary): 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?
Your solution:
The result is less than the original number because if you divide something in two for example, you are going to have less than what you had to start with. And the same happens if you divide by bigger numbers; you will end up with less than the original and more parts.
confidence rating #$&*:
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Self-critique (if necessary): After I read the given solution I was able to understand better the concept of dividing a positive number by a number greater than one. The example in the given solution was really helpful to understand that dividing by bigger and bigger numbers will result in more and lesser parts.
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Self-critique Rating: 3
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result is greater than the original number because if you divide by a number less than one you get a bigger number.
confidence rating #$&*:
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Self-critique (if necessary): After I read the explanation in the given solution I understood a lot better the reason why you get a bigger number if you divide by a number less than one. If you divide a number by 1 you get the original number, and if you divide by a positive number you get a smaller number than the original. So if you divide by a number less than one you get a bigger number than the original.
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Self-critique Rating: 3
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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
In my opinion I wrote self-critiques every time I felt I wasn´t sure about something written in the given solutions that I could not fully understand throughout the time I was working on these exercises. Also, sometimes I used self-critiques to try to see if I could understand something better if I would write down what I wasn’t sure, and most of the times it helped me to make sense of a concept that wasn´t clear to me before. In addition, I tried to give as much detail in my solutions as I thought to be necessary in order to understand the reason why I got my results and how I got them. For that reason, when I went back to read my work and check to see if there was something missing in my solutions that was addressed in the given solutions, or that I hadn´t already written a self-critique for I could not find nothing in specific.
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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 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
In my opinion I wrote self-critiques every time I felt I wasn´t sure about something written in the given solutions that I could not fully understand throughout the time I was working on these exercises. Also, sometimes I used self-critiques to try to see if I could understand something better if I would write down what I wasn’t sure, and most of the times it helped me to make sense of a concept that wasn´t clear to me before. In addition, I tried to give as much detail in my solutions as I thought to be necessary in order to understand the reason why I got my results and how I got them. For that reason, when I went back to read my work and check to see if there was something missing in my solutions that was addressed in the given solutions, or that I hadn´t already written a self-critique for I could not find nothing in specific.
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Self-critique (if necessary):
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Self-critique rating:
#*&!
@& You are making good use of the self-critique process, which should be helpful to you as you work through this course.*@