course phy 201
20090828 2130
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:
8 hr times x equals 72 dollars so 72 divided by 8 is 9 hours ____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:
(8 + 3) * 5 = 11 * 5 = 55 ---- 8+3*5 = 8+15 = 23 ---- the difference is due to 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: (2^4)*3 = 48 (raised 2 to the 4th power then multiplied 3 in)---- 2^(4*3) = 4096 (multiples powers then raised 2 to the 12th power) ---- diff - order of operations ____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:3*5-4*3^2 = 15-36 = -21 ---- 3*5-(4*3)^2 = 15-144 = -129 ---- diff - 1st problem, raised 3 to the 2nd power first then multiplied but on 2nd problem, multipled 4 and 3 and then raised the solution (12) by the 2nd power. ____3____OK
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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.************
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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:
Substitute - y = 2 x + 3 --> y=2(-2)+3 --> y=-1
x = -2,-1,0,1,2 --- y = -1,1,3,5,7
--- The graph presents itself to be linear. As x increases by 1, y increases by 2
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`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
-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 = x^2 + 3 --> y = 7 ----
x = -2,-1,0,1,2 y = 7,4,3,4,7 ----
Graph is parabolic - the graph appears to be quadratic from it's ""dip"" in the middle and curving back up evenly on both sides accross the y axis (if folded over at y =3 would match) ____3____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
2
3
4
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:
2^x+3 = 5, y=5 ----
x= 1,2,3,4 - y=5,7,11,19
Graph represents an exponential shape due to the y value increasing more based upon the x value (which is y's exponential factor) ___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 - ie 1/1 = 1 which would be equal to the original number where at 102.185/1 = 102.185 which is also equal to the original 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 answer will be less than the original number because if you are dividing by a number greater than 1, the original number will become some type of fraction (or percentage, etc) less than the 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:
the resulting number will be greater than the original number due to the nature of dividing by a fraction, is in essense like multiplying. ie - 16/.5 = 16*2 .. 16/1/2 --> 32/1 = 32 ____3_____OK
&#Good responses. Let me know if you have questions. &#