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course phy 121
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? Solution: If you work for 4 hours, then if you earn 8 dollars for every one of those hours you earn 4 * 8 dollars = 32 dollars
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Self-critique (if necessary): ok
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Self-critique Rating: 3
Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
Solution: If you earn $168 and work 12 hours, for every hour you are earning $14 an hour. 168/12=14 dollars
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Self-critique Rating: 3
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Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72?
If you earn $72 and are earning 8 dollars an hour, you will be working 9 hours. 72/8=9 hours
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Self-critique Rating: 3
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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.
First calculate 8+3 first which equals 11 then multiply 11*5 which equals 55.
First you have to know the order of operations rule. You calculate 3*5 first which is 15 then add 8 which equals 23.
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Self-critique (if necessary): ok
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Self-critique Rating: 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.
To evaluate (2^4) * 3 we first evaluate the grouped expression 2^4, which is the fourth power of 2, equal to 2 * 2 * 2 * 2 = 16. So we have (2^4) * 3 = 16 * 3 = 48.
To evaluate 2^(4 * 3) we first do the operation inside the parentheses, obtaining 4 * 3 = 12. We therefore get 2^(4 * 3) = 2^12 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 4096.
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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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.
To calculate 3 * 5 - 4 * 3 ^ 2, the first operation is the exponentiation operation ^.
The two numbers involved in the exponentiation are 3 and 2; the 4 is 'attached' to the 3 by multiplication, and this multiplication can't be done until the exponentiation has been performed.
The exponentiation operation is therefore 3^2 = 9, and the expression becomes 3 * 5 - 4 * 9.
Evaluating this expression, the multiplications 3 * 5 and 4 * 9 must be performed before the subtraction. 3 * 5 = 15 and 4 * 9 = 36 so we now have 3 * 5 - 4 * 3 ^ 2 = 3 * 5 - 4 * 9 = 15 - 36 = -21.
To calculate 3 * 5 - (4 * 3)^2 we first do the operation in parentheses, obtaining 4 * 3 = 12. Then we apply the exponentiation to get 12 ^2 = 144. Finally we multiply 3 * 5 to get 15. Putting this all together we get 3 * 5 - (4 * 3)^2 =
3 * 5 - 12^2 =
3 * 5 - 144 =
15 - 144 = -129.
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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Question: `q007. Let y = 2 x + 3
We easily evaluate the expression:
•When x = -2, we get y = 2 x + 3 = 2 * (-2) + 3 = -4 + 3 = -1.
•When x = -1, we get y = 2 x + 3 = 2 * (-1) + 3 = -2 + 3 = 1.
•When x = 0, we get y = 2 x + 3 = 2 * (0) + 3 = 0 + 3 = 3.
•When x = 1, we get y = 2 x + 3 = 2 * (1) + 3 = 2 + 3 = 5.
•When x = 2, we get y = 2 x + 3 = 2 * (2) + 3 = 4 + 3 = 7.
Filling in the table we have
x y
-2 -1
-1 1
0 3
1 5
2 7
When we graph these points we find that they lie along a straight line.
Only one of the depicted graphs consists of a straight line, and we conclude that the appropriate graph is the one labeled 'linear'
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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Question: `q008. Let y = x^2 + 3.
Evaluating y = x^2 + 3 at the five points:
•If x = -2 then we obtain y = x^2 + 3 = (-2)^2 + 3 = 4 + 3 = 7.
•If x = -1 then we obtain y = x^2 + 3 = (-1)^2 + 3 = ` + 3 = 4.
•If x = 0 then we obtain y = x^2 + 3 = (0)^2 + 3 = 0 + 3 = 3.
•If x = 1 then we obtain y = x^2 + 3 = (1)^2 + 3 = 1 + 3 = 4.
•If x = 2 then we obtain y = x^2 + 3 = (2)^2 + 3 = 4 + 3 = 7.
The table becomes
x y
-2 7
-1 4
0 3
1 4
2 7
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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Question: `q009. Let y = 2 ^ x + 3.
Recall that the exponentiation in the expression 2^x + 1 must be done before, not after the addition.
When x = 1 we obtain y = 2^1 + 3 = 2 + 3 = 5.
When x = 2 we obtain y = 2^2 + 3 = 4 + 3 = 7.
When x = 3 we obtain y = 2^3 + 3 = 8 + 3 = 11.
When x = 4 we obtain y = 2^4 + 3 = 16 + 3 = 19.
x y
1 5
2 7
3 11
4 19
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Self-critique (if necessary): ok
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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?
If you divide any number by 1, the result is the same as the original number. Doesn't matter what the original number is, if you divide it by 1, you don't change it.
confidence rating #$&*:
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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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?
If you split something up into equal parts, the more parts you have, the less will be in each one. Dividing a positive number by another number is similar. The bigger the number you divide by, the less you get.
Now if you divide a positive number by 1, the result is the same as your original number. So if you divide the positive number by a number greater than 1, what you get has to be smaller than the original number. Again it doesn't matter what the original number is, as long as it's positive.
Students will often reason from examples. For instance, the following reasoning might be offered:
OK, let's say the original number is 36. Let's divide 36 be a few numbers and see what happens:
36/2 = 18. Now 3 is bigger than 2, and
36 / 3 = 12. The quotient got smaller. Now 4 is bigger than 3, and
36 / 4 = 9. The quotient got smaller again. Let's skip 5 because it doesn't divide evenly into 36.
36 / 6 = 4. Again we divided by a larger number and the quotient was smaller.
That is a pretty convincing argument, mainly because it is so consistent with our previous experience. In that sense it's a good argument. It's also useful, giving us a concrete example of how dividing by bigger and bigger numbers gives us smaller and smaller results.
However specific examples, however convincing and however useful, don't actually prove anything. The argument given at the beginning of this solution is general, and applies to all positive numbers, not just the specific positive number chosen here.
confidence rating #$&*:
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
If you split something up into equal parts, the more parts you have, the less will be in each one. Dividing a positive number by some other number is similar. The bigger the number you divide by, the less you get. The smaller the number you divide by, the more you get.
Now if you divide a positive number by 1, the result is the same as your original number. So if you divide the positive number by a positive number less than 1, what you get has to be larger than the original number. Again it doesn't matter what the original number is, as long as it's positive.
confidence rating #$&*:
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Self-critique (if necessary): ok
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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.
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Self-critique (if necessary): ok
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Self-critique Rating: 3
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#*&!
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Your work looks good.
However you have deleted large parts of the original document.
In future assignments be sure you insert your answers into a complete copy of the document, without removing anything.
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