#$&*
course Phy 241
7-29 3
Here are the remaining ten questions:*********************************************
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)
You need to divide the total amount ($72) by the hourly rate ($8) to find out that you need to work a total of 9 hours.
Confidence=3
Critique=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 problem, the parenthesis means that you work that part first. This would mean to add (8+3) which equals 11 and then multiply by 5, which gives you an anwer of 55.
In the second problem, the order of operations states that you must to multiplication or division before addition or subtraction so therefore you would multiply (3*5) and then add 8, which gives you an answer of 23.
Confidence=3
Critique=3
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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:
You must do what is in parenthesis first. 2^4= 2*2*2*2= 16 then you multiply that by 3, which equals 48.
In the other problem you must do the parenthesis first, and when multiplying these exponents you are to add the numbers together, which gives you 2^(7), which equals 2*2*2*2*2*2*2. This product is 128.
Confidence=3
Critique=3
####I was wrong in the fact that I thought when multiplying exponents you added them together, instead you do in fact multiply them. This gives the product a new meaning of 2^12=2*2*2*2*2*2*2*2*2*2*2*2=4096
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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:
In the first problem you must remember order of operations. This means you must deal with your exponents first, then multiply, then subtract. 3^2=9. This means your problem now reads 3*5-4*9=15-36= -21.
The 2nd problem you must also do the exponent first, yet in this case it pertains to what is inside of the parenthesis. So therefore you must do the multiplication in the parenthesis before then using the exponent. Then you do the rest of the multiplication before lastly subtracting. All of this is done in this order to stay within the order of operations.
(4*3)^2= 12^2=144
3*5-144=15-144= -129
Confidence=3
Critique=OK
In the next three problems, the graphs will be of one of the basic shapes listed below. You will be asked to construct graphs for three simple functions, and determine which of the depicted graphs each of your graphs most closely resembles. At this point you won't be expected to know these terms or these graph shapes; if at some point in your course you are expected to know these things, they will be presented at that point.
Linear:
Quadratic or parabolic:
Exponential:
Odd power:
Fractional positive power:
Even negative power:
partial graph of polynomial of degree 3
more extensive graph of polynomial of degree 3
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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
-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:
For this problem you need to plug “x” into the equation in order to find “y”. This graph results in an “linear equation” and will get infinitely larger.
Confidence: 3
Critique: 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: Y=x^2+3 where x could equal (-2, -1, 0,1, or 2, etc.) I have expressed above what the value of “y” is when these “x” values are plugged in. In this case, you plug “x” in and work with the exponent and then add 3 to find “y”.
This creates a U-shaped graph like that of an exponential formula. This graph will go on and on like this no matter what number is plugged into the formula.
Confidence=3
Critique= 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 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.
• 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: After the values of x are plugged into the equation to find y and the points are then plotted on the graph, it’s obvious that the points are trending in a steeper and steeper fashion toward the top right. For every 1 unit we move on the x axis, the y axis is jumping double the previous time. This results in an exponential function.
Confidence= 3
Critique= Ok
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:
Anything divided by 1 is equal to that number. The value has not changed, it stays the same.
Confidence= 3
Critique= 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 the original number is greater than 1and you divide itself by the same value, or a value equal to or less than 0, the original number becomes smaller.
Example: 1.1 / 1.1= 1
1.1/ 0= 0
Anytime a number greater than 1 is divided, it is going to become smaller. That is the whole principle of “division”.
Confidence= 3
Critique= 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:
Anytime you divide a number greater than 1 by a positive number that is less than 1, the original number is going to get larger. This is because you are dividing a number by a part of another number. For example:
36/ .5= 72
36/ .9=40
36/ .1=360
Confidence=3
Critique= 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
####I was wrong in the fact that I thought when multiplying exponents you added them together, instead you do in fact multiply them. This gives the product a new meaning of 2^12=2*2*2*2*2*2*2*2*2*2*2*2=4096
"
Self-critique (if necessary):
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Self-critique rating:
@& Your responses need to be inserted into a complete copy of the part of the document you were instructed to copy. Nothing should be deleted from that copy. Your responses should be inserted in the specified manner.
I was able to review enough of this document to tell that you're doing OK, so I won't ask you to resubmit. However if you want the posted document to be complete, and/or if you want me to give it a more thorough review, you are welcome to insert your answers into a complete copy and resubmit. In any case, in future submissions be sure to include everything.*@