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course MTH 271
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)
$8/hr * ? hr = $72
72/8 = 9 hours
confidence rating #$&*:
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q004. Calculate (8 + 3) * 5 and, 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)
(8 + 3) * 5= 8 + 3 * 5=
11*5= 8+15=
55 23
confidence rating #$&*:
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
Your solution:
(2^4) * 3= 2^(4 * 3)=
16*3= 2^12=
48 4096
Because of the setup of these problems, the final answer is, and must be, very different in each. The number of times 2 is multiplied in the second problem is much higher, making the answer a larger number.
Confidence Rating: 3
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
Your solution:
3 * 5 - 4 * 3 ^ 2= 3 * 5 - (4 * 3)^2=
(3*5)-(4*(3^2))= (3*5)-(12^2)=
15-(4*9)= 15-144=
15-36= -129
-21
confidence rating #$&*:
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Self-critique (if necessary): OK
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 x + 3
y= (2*-2) +3
y= -4+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
-1 1
0 3
1 5
2 7
• 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 find y=2x+3 with an x-value of -2, I substituted -2 for x in the equation, and found y. In the table, I did the same with different x values, ending with (-2,-1), (-1,1),(0,3),(1,5), and (2,7). The graph is linear, because it is an unending straight line, increasing at regular intervals. This graph fits exactly the values in the table.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 7
-1 4
0 3
1 4
2 7
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
The graph of y=x^2+3 is a parabola. It increases above (0,3) and decreases towards (0,3) and is symmetrical about that point. The x^2 makes it a parabola. The +3 raises that parabola by 3 units.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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 5
2 7
3 11
4 19
• 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.
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Your solution:
This graph increases exponentially because the x value is an exponent. When the values cross 0 on the x-axis, it begins to grow a lot. It has been raised 3 units because of the +3. These features make this is an exponential graph.
confidence rating #$&*:
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Self-critique (if necessary):OK
Self-critique Rating:OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The answer is equal to the original.
confidence rating #$&*:
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Self-critique (if necessary): OK
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: Less than original
confidence rating #$&*:
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Self-critique (if necessary): Ok
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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 solution will be greater.
Confidence Rating: 2
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Self-critique (if necessary):
####
On this question, I was originally very unsure of the answer, and had to check with my calculator to make sure that I understood correctly. This is a rule that is often taken for granted, but I obviously had to think hard about when I consciously thought about it.
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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.
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
####12
On this question, I was originally very unsure of the answer, and had to check with my calculator to make sure that I understood correctly. This is a rule that is often taken for granted, but I obviously had to think hard about when I consciously thought about it.
"
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.
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
####12
On this question, I was originally very unsure of the answer, and had to check with my calculator to make sure that I understood correctly. This is a rule that is often taken for granted, but I obviously had to think hard about when I consciously thought about it.
"
Self-critique (if necessary):
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Self-critique rating:
#*&!
&#This looks good. Let me know if you have any questions. &#