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course Mth 163
8/22 6
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
9 hours. 72$/ 8$= 9 hours to earn 72 dollars
3
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)
55 and 23. In the first question you do the work in parenthesis first because it comes before multiplication in the order of operations. In the second one, you do the multiplication first because it comes before addition in the order of operations.
3
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:
48 and 4096. Where the parentheses are placed makes the difference in the answers. In the first one you raise the power and then multiply. In the second one you multiply then raise the power.
3
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:
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-21 and -129. 3^2=9, then 3*5=15 and 4*9=36, finally 15-36=-21. So you do the exponent first, the mult. Second and then the subtraction. For the second problem, you mult. 4*3 first because of parentheses which gives you 12. Then you do the exponent which would be 12^2=144. You go back and mult. 3*5=15 and finally you subtract 15-144=-129.
3
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:
Y=2x+3. To figure out what y for x=-2 you just substitute -2 in for x. y=2(-2)+3=-1. Same for the following: y=2(-1)+3=1; 2(0)+3=3; 2(1)+3=5; 2(2)+3=7
X Y
-2 -1
-1 1
0 3
1 2
2 7
The graph was linear. It started in the lower left quadrant and steadily went up in a slant to end in the upper right quad.
3
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.
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Your solution:
When x= -2 we get (-2)^2+3=4+3=7
When x= -1 we get (-1)^2+3=1+3=4
When x-0 we get (0)^2+3=0+3=3
When x=1 we get (1)^2+3=1+3=4
When x=2 we get (2)^2+3=4+3=7
X Y
-2 7
-1 4
0 3
1 4
2 7
When these points are graphed we see that the y values have symmetry. The graph is degree three polynomial.
3
####I knew this graph had symmetry. However, I didn’t realize that the degree three polynomial graph did not have right-left symmetry. I can now see why I chose the wrong graph and how the quadratic graph differs from the polynomial graph and how their symmetry is different as well.
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.
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Your solution:
When x = 1 we get y = 2^1 + 3 = 2 + 3 = 5.
When x = 2 we get y = 2^2 + 3 = 4 + 3 = 7.
When x = 3 we get y = 2^3 + 3 = 8 + 3 = 11.
When x = 4 we get y = 2^4 + 3 = 16 + 3 = 19.
x y
1 5
2 7
3 11
4 19
The graph starts in bottom left and increases steeper as it goes up. The graph is exponential.
3
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 anytime you divide a number by one it equals the number.
3
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 result is less than original number. 18/2=9; 18/3=6; 18/6=3; 18/9=2; 18/18=1. Each time the answer is always less than original number.
3
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:
Greater.
3
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.
Solution: ####I knew this graph had symmetry. However, I didn’t realize that the degree three polynomial graph did not have right-left symmetry. I can now see why I chose the wrong graph and how the quadratic graph differs from the polynomial graph and how their symmetry is different as well.
"
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