course phy201
6/2 1
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:
It will take 9 hours to earn $72 because 72/8= 9.
confidence rating #$&*
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Self-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:
(8+3)x5= 55 because in this case the addition in parentheses is computed first and then 5 is multiplied by that answer. In the problem 8+3x5 the answer is 23 because the multiplication is done first and the 8 is added to this result.
confidence rating #$&*
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Self-critique:ok
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
(2^4) * 3= 48 parentheses and exponents are always computed before multiplication so 2x2x2x2= 16 and 16 x3= 48.
2^(4 * 3) = 4096 because the numbers in the parentheses are always worked before the exponents so 4x3=12 and 2^12 or (2*2*2*2*2*2*2*2*2*2*2*2)= 4096
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: 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= -21 because the first step is to solve the exponent: 3 ^ 2= 9 then the equation can be written as 3*5- 4*9. multiplication is the next step so 15- 36= -21
3 * 5 - (4 * 3)^2= -129 because the order of operations is different since parentheses are now involved. 3*5- (12)^2 = 3*5-144= 15-144= -129
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique:ok
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Question: `q007. Let y = 2 x + 3.
Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 -1
-1 1
0 3
1 5
2 7
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Your solution:
If x=-2 then y= 2(-2) +3 then y= -4+3 so y= -1
If x = -1 then y= 2(-1)+3 then y=- 2+3 so y= 1
If x= 0 then y = 2(0)+3 then y= 0+3 so y=3
If x = 1 then y= 2(1)+3 then y=2+3 so y= 5
If x=2 then y= 2(2) +3 then y= 4+3 so y=7
When plotted on a graph these points form a straight line so the graph would be linear.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-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
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Your solution:
When x= -2 y= -2^2+3= 4+3= 7
When x= -1 y= -1^2+3=1+3=4
When x=0 y= 0^2 +3=0+3= 3
When x=1 y= 1^2 +3=1+3= 4
When x=2 y=2^2+3= 4+3=7
When plotted these points form a shape that rises from the point 0,3 in both directions. Both the partial graph of polynomial of degree 3 and quadratic or parabolic graph seem to share this characteristic but seeing as how the graph in this problem has a symmetry I think the closest answer would be the quadratic or parabolic graph.
confidence rating #$&*
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Self-critique: I wasn’t 100% sure as to which graph it was representing. I just made an educated guess and happened to be right
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1 5
2 7
3 11
4 19
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Your solution:
When x=1 y=2^1+3= 2+3=5
When x= 2 y= 2^2 +3= 4+3=7
When x= 3 y=2^3 +3 = 8+3=11
When x= 4 y= 2^4 +3 = 16+3=19
When plotted these points appear to increase from left to right and form a slight curve matching the characteristics of the exponential graph.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: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 solution will always be the same because dividing any number by 1 means that the number is not actually be divided at all. It is staying as one whole not being split.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: ok
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The solution will always be smaller because you are dividing the original number into more than one part.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-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:
The answer will always be greater. For example 2/ .5 = 4. The original number is less than the answer.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-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
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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 solution will always be smaller because you are dividing the original number into more than one part.
confidence rating #$&*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: ok
####I didn’t provide any examples of why my answer is correct. If I had done so my argument could have been stronger.
"
&#This looks good. Let me know if you have any questions. &#
#$&*