#$&*
course Phy 232
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: (type in your solution starting in the next line)
When my hourly income is $8/hr, for each hour of work I do, I earn $8. Thus, if I work for 4 hours, I will earn $8/hr * 4hrs = $32. After 4 hours of work at a rate of $8/hr, I will have earned $32.
confidence rating #$&*: 3
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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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: (type in your solution starting in the next line)
On an hourly income, I earn $168 in 12 hours. Thus, in order to calculate my hourly wage, I simply divide $168/12hours, to give me a ratio of dollars/hours. $168/12hours = $14/hour. Thus, my hourly wage is $14/hr.
confidence rating #$&*: 3
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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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: (type in your solution starting in the next line)
If my hourly wage is $8/hr, then in one hour I make $8. So, in order to make $72, I must work for $72/$8/hr = 9 hours.
confidence rating #$&*: 3
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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)
The steps for simple arithmetic, as learned in elementary school, are Please Excuse My Dear Aunt Sally. P - parentheses, E - exponent, M - multiplication, D - division, A - addition, S - subtraction. Thus, start out with the parentheses, going left to right. (8 + 3) = 11. Then multiplication, 11*5 = 55, and 3*5 = 15. And finally addition, for the second problem, 15 + 8 = 23. Thus, the first problem (8+3)*5 equals 55, and the second one 8+3*5 equals 23. The reason there is a difference in the results, is simply because the order of operations, parenthesis “trump” everything else.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
Once again, we use the order of operations. For (2^4)*3, start out by calculating 2^4, since it is in parentheses, which is 16. Then, multiply by 3 to get 48. For, 2^(4*3), you begin by calculating 4*3, since this is in parentheses and is the exponent. 4*3 = 12, and thus, 2^12 = 4096. The reason these results are different is simple, because the 2^4 was in parentheses in the first one, you calculate the power of 2 before multiplying by 3, unlike in the second problem, where the exponent was multiplied by 3.
confidence rating #$&*:
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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.
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Your solution:
Using the order of operations, for 3*5-4*3^2, start out with the exponent. Thus, 3^2 = 9. Now, proceed with multiplication, 3*5 = 15 and 4*9 = 36. Finally, finish with subtraction, 15 - 36 = -21.
For, 3*5 - (4*3)^2, start out with the parentheses; thus, (4*3) = 12. Now for the exponent, 12^2 = 144. Next is multiplication, 3*5 = 15. Finally, finish with subtraction, 15 - 144 = -129
The reason these results are different is because the first problem contained no parentheses, so it was not forced to complete an operation before another like in the second problem.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
When evaluating for y with a value of x, simply plug the value of x into the equation given and follow the order of operations to solve for y. Thus, in y = 2x + 3, where x = -2, y = 2(-2) + 3. So, y = -4 + 3 = -1. Therefore, when x = -2, y = -1.
When x = -2, y = 2(-2) + 3. Thus, y = -1.
When x = -1, y = 2(-1) + 3. Thus, y = 1.
When x = 0, y = 2(0) + 3. Thus, y = 3.
When x = 1, y = 2(1) + 3. Thus, y = 5.
When x = 2, y = 2(2) + 3. Thus, y = 7.
x y
-2 -1
-1 1
0 3
1 5
2 7
The graph of the function y = 2x +3 is a linear function. This is because the highest power in the equation is 1. Thus, each increment of x is the same and each increment of y is the same.
confidence rating #$&*:
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Self-critique (if necessary): OK. #### The more proper way of saying this would be, this is because the degree of the polynomial is 1.
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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 evaluating for y in a function, you simply plug in the value for x and follow the order of operations to solve for y. Thus in y = x^2 + 3, when x = -2, y = (-2)^2 + 3 = 7.
When x = -2, y = (-2)^2 + 3. Thus, y = 7.
When x = -1, y = (-1)^2 + 3. Thus, y = 4.
When x = 0, y = (0)^2 + 3. Thus, y = 3.
When x = 1, y = (1)^2 + 3. Thus, y = 4.
When x = 2, y = (2)^2 + 3. Thus, y = 7.
x y
-2 7
-1 4
0 3
1 4
2 7
The graph of the function is a parabola because the degree of the polynomial function is 2. The graph is shifted up 3 units from (0,0).
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1
2
3
4
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
When evaluating for y in the function, you simply plug in your value of x and solve. In this case, when x = 1, y = 2^(1) + 3 = 5. Thus when x = 1, y = 5.
When x = 1, y = 2^(1) + 3 = 5. Thus, y = 5.
When x = 2, y = 2^(2) + 3 = 7. Thus, y = 7.
When x = 3, y = 2^(3) + 3 = 11. Thus, y = 11.
When x = 4, y = 2^(4) + 3 = 19. Thus, y = 19.
x y
1 5
2 7
3 11
4 19
The graph of the function is a curve that is increasing and always positive. The function most resembles the function in question 8, x^2 +3. This is because function 8 is a parabola and this function in question 9 is a curve that looks similar to a sideways parabola.
confidence rating #$&*:
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Self-critique (if necessary): 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:
When you divide a certain positive number by 1, you are essentially breaking up the positive number into 1 part(s). Since the positive number itself is only one number, dividing the number by 1 is equal to the original number.
confidence rating #$&*:
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Self-critique (if necessary): OK
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Self-critique Rating: OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution: If you take a positive number and divide it by a number greater than 1the result is less than the original number. This is because when you take a positive number and divide it into more than 1 part you automatically get a smaller number by common sense.
confidence rating #$&*:
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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:
If you divide a certain positive number by a positive number less than 1, the result is greater than the original number. When dividing by 1, you get the original number. However, when dividing by an amount less than the amount you have, you end up with a larger number, because you are “breaking up” the original number into less than 1 part(s).
confidence rating #$&*:
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Self-critique (if necessary): 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 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
#### The more proper way of saying this would be, this is because the degree of the polynomial is 1.
"
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
#### The more proper way of saying this would be, this is because the degree of the polynomial is 1.
"
Self-critique (if necessary):
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Self-critique rating:
#*&!
@& Good, but you appear to be omitting the given solutions.
Insert your responses into a copy of each document, but in future submissions don't delete anything from that document.*@