#$&*
course Mth 272
5/23 11 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)
(hrs)($8/hr)= $72
hrs= 9
It takes 9 hours to earn $72 if you earn $8 per hour.
Confidence Rating: 3
Self-critique Rating: OK
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution: (type in your solution starting in the next line)
PEMDAS
(8+3) *5
Add what is in the parenthesis first: 11
Then multiply:
(11)*5= 55
8+3*5
Multiply 3*5= 15
Then add
8+15= 23
The two equations differ because the first equation has parenthesis. According to PEMDAS, parenthesis come first before anything. In the second equation you have to follow the rule that multiplication comes before addition.
confidence rating #$&*:
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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:
PEMDAS
(2^4)*3
calculate the exponent:
(16)*3
Multiply:
48
2^(4*3)
Parenthesis always comes first:
2^(12)
calculate the exponent:
4096
In the first equation the parenthesis was around 2^4, and on the second equation, it was around 4*3, which gives two different numbers.
confidence rating #$&*:
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Self-critique rating: OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
PEMDAS
3*5-4*3^2
Exponents:
3*5 - 4 *9
Multiplication:
15 - 36
Subtraction:
-21
3*5 - (4 * 3)^2
Parenthesis:
3*5- (12)^2
Exponent:
3*5- 144
Multiplication:
15- 144
Subtraction:
-129
confidence rating #$&*:
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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.
y= 2(-2) +3
y= -1
• 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:
x y
-2 -1
-1 1
0 3
1 5
2 7
The graph makes a straight line, which means it is linear.
confidence rating #$&*:
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Self-critique Rating: OK
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x
y
-2
-1
0
1
2
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
x y
-2 7
-1 4
0 3
1 4
2 7
The graph is a quadratic graph. Point (0,3) is the lowest point, two of the points go upward on the left side, and the other two points go upward on the right side.
confidence rating #$&*:
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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.
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:
x y
1 5
2 7
3 11
4 19
Since the Y values increase by doubles, the graph is exponential.
confidence rating #$&*:
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Self-critique Rating: OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
If you divide any number by 1, it does not change.
confidence rating #$&*:
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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 because you are dividing it in half, in thirds, or fourths etc.
ex:
12/1= 12
12/2= 6
12/3 =4
confidence rating #$&*:
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Self-critique Rating: OK
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The number you attain will be greater than the original. When you divide by .5, you are really multiplying by two.
Ex:
12/1= 12
12/.75= 16
12/.5= 24
confidence rating #$&*:
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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 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.
#### 7
I did inserted the x values mentally, which could have caused an error. Next time, I should write each one down to assure no mistakes are made.
"
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.
#### 7
I did inserted the x values mentally, which could have caused an error. Next time, I should write each one down to assure no mistakes are made.
"
Self-critique (if necessary):
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Self-critique rating:
#*&!
&#Good responses. Let me know if you have questions. &#