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course Mth 272
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)
If you earn 8 dollars/hour it will take 9 hours to earn $72 because 72/8=9
confidence rating #$&*:
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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)
(8+3)x5= 55. You first must solve what is in parenthesis then multiply. 8+3x5=23. You must first multiply then add 8.
confidence rating #$&*:
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Self-critique (if necessary):OK
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Self-critique Rating:OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution:
(2^4)*3=48. First you must do what is in parenthesis then multiply by 3. 2^(4*3)=4096. First you must do what is in parenthesis then solve the exponent.
confidence rating #$&*:
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Self-critique (if necessary):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:
3*5-4*3^2=-21. First you must solve exponents then perform multiplucation and then subtract. 3*5-(4*3)^2=-129. First solve for what is in parenthesis then perform multiplucation and then subtract.
confidence rating #$&*:
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Self-critique (if necessary):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
-1 1
0 3
1 5
2 7
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.
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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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
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.
We note that there is a symmetry to the y values. The lowest y value is 3, and whether we move up or down the y column from the value 3, we find the same numbers (i.e., if we move 1 space up from the value 3 the y value is 4, and if we move one space down we again encounter 4; if we move two spaces in either direction from the value 3, we find the value 7).
A graph of y vs. x has its lowest point at (0, 3).
If we move from this point, 1 unit to the right our graph rises 1 unit, to (1, 4), and if we move 1 unit to the left of our 'low point' the graph rises 1 unit, to (-1, 4).
If we move 2 units to the right or the left from our 'low point', the graph rises 4 units, to (2, 7) on the right, and to (-2, 7) on the left.
Thus as we move from our 'low point' the graph rises up, becoming increasingly steep, and the behavior is the same whether we move to the left or right of our 'low point'. This reflects the symmetry we observed in the table. So our graph will have a right-left symmetry.
Two of the depicted graphs curve upward away from the 'low point'. One is the graph labeled 'quadratic or parabolic'. The other is the graph labeled 'partial graph of degree 3 polynomial'.
If we look closely at these graphs, we find that only the first has the right-left symmetry, so the appropriate graph is the 'quadratic or parabolic' graph
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Self-critique (if necessary):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 5
2 7
3 11
4 19
Looking at the numbers in the y column we see that they increase as we go down the column, and that the increases get progressively larger. In fact if we look carefully we see that each increase is double the one before it, with increases of 2, then 4, then 8.
When we graph these points we find that the graph rises as we go from left to right, and that it rises faster and faster. From our observations on the table we know that the graph in fact that the rise of the graph doubles with each step we take to the right.
The only graph that increases from left to right, getting steeper and steeper with each step, is the graph labeled 'exponential'.
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Self-critique (if necessary):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: equal to the original number because any number divided by one is that number.
confidence rating #$&*:
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Self-critique (if necessary):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: less than the original number because the greater the number divided by the less of the original number you have.
confidence rating #$&*:
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Self-Critique (if necessary):OK
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution: The result if greater than the original number because divided by a number such as .5 would be equal to multiplying the original number by 2 therfore you would have a larger number.
confidence rating #$&*:
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Self-Critique (If necessary):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.
Self Critque: #### In my solution to question 4 I could have explained the order of operations more closely and I could have explained my thought process in solving the problem in greater detail.
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