course Phy201 ONjzճ̱assignment #001
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18:18:06 `questionNumber 10000 Physics video clip 01: A ball rolls down a straight inclined ramp. It is the velocity the ball constant? Is the velocity increasing? Is the velocity decreasing?
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RESPONSE --> I believe the velocity increases at a constant rate. The increase in velocity is constant because the incline is straight and constant. The velocity increases because of the affect of gravity pulling on the object .
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18:18:39 `questionNumber 10000 ** It appears obvious, from common experience and from direct observation, that the velocity of the ball increases. A graph of position vs. clock time would be increasing, indicating that the ball is moving forward. Since the velocity increases the position increases at an increasing rate, so the graph increases at an increasing rate. **
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RESPONSE --> ok
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18:20:18 `questionNumber 10000 If the ball had a speedometer we could tell. What could we measure to determine whether the velocity of the ball is increase or decreasing?
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RESPONSE --> We could measure the acceleration and the speed at which it is traveling.
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18:22:22 `questionNumber 10000 ** STUDENT RESPONSE: By measuring distance and time we could calculate velocity. INSTRUCTOR COMMENTS: The ball could be speeding up or slowing down--all you could get from the calculation you suggest is the average velocity. You could measure the time to travel the first half and the time to travel the second half of the ramp; if the latter is less then we would tend to confirm increasing velocity (though those are still average velocities and we wouldn't get certain proof that the velocity was always increasing). You would need at least two velocities to tell whether velocity is increasing or decreasing. So you would need two sets of distance and time measurements. **
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RESPONSE --> Ok to obtain a measurement we would need to measure the distance and time of travel in two separate locations on the incline to determine wheter the velocity is increasing or decreasing.
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18:23:48 `questionNumber 10000 What is the shape of the velocity vs. clock time graph for the motion of the ball?
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RESPONSE --> I believe that it would be a diagonal line that begins at the origin and travels upward to the top right of the graph.
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18:24:49 `questionNumber 10000 ** If the ramp has an increasing slope, the velocity would increase at an increasing rate and the graph would curve upward, increasing at an increasing rate. If the ramp has a decreasing slope, like a hill that gradually levels off, the graph would be increasing but at a decreasing rate. On a straight incline it turns out that the graph would be linear, increasing at a constant rate, though you aren't expected to know this at this point. All of these answers assume an absence of significant frictional forces such as air resistance. **
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RESPONSE --> ok
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18:26:13 `questionNumber 10000 A ball rolls down ramp which curves upward at the starting end and otherwise rests on a level table. What is the shape of the velocity vs. clock time graph for the motion of the ball?
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RESPONSE --> It would begin as a linear increase then curve to decrease as the ball slows on the level area.
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18:27:41 `questionNumber 10000 ** While on the curved end the ball will be speeding up, and the graph will therefore rise. By the time the ball gets to the level part the velocity will no longer be increasing and the graph will level off; because of friction the graph will actually decrease a bit, along a straight line. As long as the ball is on the ramp the graph will continue on this line until it reaches zero, indicating that the ball eventually stops. In the ideal frictionless situation on an infinite ramp the line just remains level forever. **
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RESPONSE --> ok,
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18:29:27 `questionNumber 10000 For the ball on the straight incline, we would certainly agree that the ball's velocity is increasing. Is the velocity increasing at a constant, an increasing, or a decreasing rate? What does the graph of velocity vs. clock time look like?
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RESPONSE --> It would increase at an increasing rate and would rise with each increase.
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18:30:32 `questionNumber 10000 ** It turns out that on a straight incline the velocity increases at a constant rate, so the graph is a straight line which increases from left to right. Note for future reference that a ball on a constant incline will tend to have a straight-line v vs. t graph; if the ball was on a curved ramp its velocity vs. clock time graph would not be straight, but would deviate from straightness depending on the nature of the curvature (e.g., slope decreasing at increasing rate implies v vs. t graph increasing at increasing rate).**
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RESPONSE --> I thought it would be linear then changed my mind. I should have went with my first instinct.
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{Lwxɓ֣֯z assignment #001 ONjzճ̱ Physics I Vid Clips 06-13-2008 [Ȍs̼ЪR°͉ assignment #000 000. `Query 0 Physics I 06-14-2008
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19:59:03 `questionNumber 0 The Query program normally asks you questions about assigned problems and class notes, in question-answer-self-critique format. Since Assignments 0 and 1 consist mostly of lab-related activities, most of the questions on these queries will be related to your labs and will be in open-ended in form, without given solutions, and will not require self-critique. The purpose of this Query is to gauge your understanding of some basic ideas about motion and timing, and some procedures to be used throughout the course in analyzing our observations. Answer these questions to the best of your ability. If you encounter difficulties, the instructor's response to this first Query will be designed to help you clarify anything you don't understand. {}{}Respond by stating the purpose of this first Query, as you currently understand it.
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RESPONSE --> The purpose of this query is to gauge my understanding of ideas about motion and timing through the labs.
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19:59:38 `questionNumber 0 If, as in the object-down-an-incline experiment, you know the distance an object rolls down an incline and the time required, explain how you will use this information to find the object 's average speed on the incline.
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RESPONSE --> You can divide the distance by the time to obtain the average speed. confidence assessment: 3
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20:01:10 `questionNumber 0 If an object travels 40 centimeters down an incline in 5 seconds then what is its average velocity on the incline? Explain how your answer is connected to your experience.
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RESPONSE --> 40cm/5sec = 8cm/sec. This is the formula that I used to calculate the average speed in my initial timing experiment. confidence assessment: 3
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20:03:19 `questionNumber 0 If the same object requires 3 second to reach the halfway point, what is its average velocity on the first half of the incline and what is its average velocity on the second half?
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RESPONSE --> 20cm/3sec = 6.7cm/sec for the first half of the incline. 8.0-6.7 = 1.3cm/sec for the second half of the incline. confidence assessment: 2
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20:09:10 `questionNumber 0 Using the same type of setup you used for the first object-down-an-incline lab, if the computer timer indicates that on five trials the times of an object down an incline are 2.42 sec, 2.56 sec, 2.38 sec, 2.47 sec and 2.31 sec, then to what extent do you think the discrepancies could be explained by each of thefollowing: {}{}a. The lack of precision of the TIMER program{}{}b. The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse){}{}c. Actual differences in the time required for the object to travel the same distance.{}{}d. Differences in positioningthe object prior to release.{}{}e. Human uncertainty in observing exactly when the object reached the end of the incline.
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RESPONSE --> a. The Timer program is only precise to the nearest tenth of a second. b. There is some uncertainty in the precision of the human trigger. Probably within 0.5 sec. c. There is probably little difference in the time for the object to travel the same distance each time. I would estimate +/- 0.001sec. d. I would say the object is positioned within +/- 0.0001cm of the same position each time. e. I would say there is probably +/- 0.05sec of uncertainty for the human observing the object reaching the end of the incline. confidence assessment: 2
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20:11:26 `questionNumber 0 What, if anything, could you do about the uncertainty due to each of the following? Address each specifically. {}{}a. The lack of precision of the TIMER program{}{}b. The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse){}{}c. Actualdifferences in the time required for the object to travel the same distance.{}{}d. Differences in positioning the object prior to release.{}{}e. Human uncertainty in observing exactly when the object reached the end of the incline.
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RESPONSE --> A. +/-.1sec B. +/- 0.05sec. c.+/- .001sec. d. +/- .001cm e. +/-.001sec confidence assessment: 2
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20:12:33 `questionNumber 0 According to the results of your introductory pendulum experiment, do you think doubling the length of the pendulum will result in half the frequency (frequency can be thought of as the number of cycles per minute), more than half or less than half?
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RESPONSE --> I think that doubling the length will result in less than half the frequency. confidence assessment: 3
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20:14:43 `questionNumber 0 Note that for a graph of y vs. x, a point on the x axis has y coordinate zero and a point on the y axis has x coordinate zero. In your own words explain why this is so.
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RESPONSE --> I am not sure if I understand why this would be unless each point would cross each axis through a linear line. confidence assessment: 0
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20:16:04 `questionNumber 0 On a graph of frequency vs. pendulum length (where frequency is on the vertical axis and length on the horizontal), what would it mean for the graph to intersect the vertical axis (i.e., what would it mean, in terms of the pendulum and its behavior, if the line or curve representing frequency vs. length goes through the vertical axis)? What would this tell you about the length and frequency of the pendulum?
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RESPONSE --> The length became very small and the frequency increased greatly. confidence assessment: 2
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20:16:55 `questionNumber 0 On a graph of frequency vs. pendulum length, what would it mean for the graph to intersect the horizontal axis (i.e., what would it mean, in terms of the pendulum and its behavior, if the line or curve representing frequency vs. length goes through the horizontal axis)? What would this tell you about the length and frequency of the pendulum?
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RESPONSE --> The length became larger and the frequency decreased greatly. confidence assessment: 2
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20:18:55 `questionNumber 0 If a ball rolls down between two points with an average velocity of 6 cm / sec, and if it takes 5 sec between the points, then how far apart are the points?
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RESPONSE --> average velocity * time = distance 6cm/s * 5sec = 30cm confidence assessment: 3
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20:19:13 `questionNumber 0 On the average the ball moves 6 centimeters every second, so in 5 seconds it will move 30 cm. {}{}The formal calculation goes like this: {}{}We know that vAve = `ds / `dt, where vAve is ave velocity, `ds is displacement and `dt is the time interval. {}It follows by algebraic rearrangement that `ds = vAve * `dt.{}We are told that vAve = 6 cm / sec and `dt = 5 sec. It therefore follows that{}{}`ds = 6 cm / sec * 5 sec = 30 (cm / sec) * sec = 30 cm.{}{}The details of the algebraic rearrangement are asfollows:{}{}vAve = `ds / `dt. We multiply both sides of the equation by `dt:{}vAve * `dt = `ds / `dt * `dt. We simplify to obtain{}vAve * `dt = `ds, which we then write as{}`ds = vAve *`dt.{}{}Be sure to address anything you do not fully understand in your self-critique.
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RESPONSE --> ok self critique assessment: 0
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20:23:19 `questionNumber 0 You were asked to read the text and some of the problems at the end of the section. Tell me about something in the text you understood up to a point but didn't understand fully. Explain what you did understand, and ask the best question you can about what you didn't understand.
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RESPONSE --> As a Chemistry major with just one more semster after this one, I am very familiar with significant figures, the SI system, conversions, and dimensions. How do you calculate % uncertainty for a measurement.
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20:26:33 `questionNumber 0 Tell me about something in the problems you understand up to a point but don't fully understand. Explain what you did understand, and ask the best question you can about what you didn't understand.
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RESPONSE --> I understand all of the problems except #'s 5, 6, 10, 11 . Those require calculation of % uncertainty and approximate uncertainty. I do not understand how to calculate uncertainty.
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{gڳ~끬剿ب~ assignment #001 001. typewriter notation qa initial problems 05-28-2008 CJݤxȐɥ| assignment #001 001. typewriter notation qa initial problems 05-28-2008 mDǥ̔ӿNTnm assignment #001 001. typewriter notation qa initial problems 05-28-2008
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20:27:09 `questionNumber 10000 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
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RESPONSE --> In x-2/x+4, the first step would be to divide 2 by x, then you would subtract that answer from x, then add four to that last answer. So for this proble if x=2, then 2 divided by 2 =1 then 2-1=1, then 1+4=5. The final answer is 5. In (x-2) / (x+4), you would perform the operations in parenthesis first, then you would divide the answer from the first parenthesis by the answer from the second. So for this problem if x=2, then 2-2=0 and 2+4=6, then 0/6=0. The final answer is 0. confidence assessment: 3
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20:29:44 `questionNumber 10000 `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation.
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RESPONSE --> I understood the order of operations and performed the calculations correctly. confidence assessment: 3
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20:32:02 `questionNumber 10000 2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64.
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RESPONSE --> I understand both how to enter exponents on a computer in written form and that they should be performed first in the order of operations. I also understand how to sbstitute a number in for x. self critique assessment: 3
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20:42:20 `questionNumber 10000 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
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RESPONSE --> The numerator of the fraction in the expression is x-3. The denominator is [(2x-5)^2*3X+1]-2+7X. When substituting x=2 for the expression, you first perform (2(2)-5)^2=(4-5)^2=-1^2=1, then you perform (1*3(2)+1)=1*6+1=6+1=7. That leaves you with 2-3 in the numerator and 7-2+7*2 in the denonminator. 2-3=-1 in the numerator. 7*2=14, so the denominator is now 7-2+14=5+14=19. confidence assessment: 3
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20:46:25 `questionNumber 10000 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7. COMMON STUDENT QUESTION: ok, I dont understand why x isnt part of the fraction? And I dont understand why only the brackets are divided by 3..why not the rest of the equation? INSTRUCTOR RESPONSE: Different situations give us different algebraic expressions; the situation dictates the form of the expression. If the above expression was was written otherwise it would be a completely different expression and most likely give you a different result when you substitute. If we intended the numerator to be x - 3 then the expression would be written (x - 3) / [(2x-5)^2 * 3x + 1 ] - 2 + 7x, with the x - 3 grouped. If we intended the numerator to be the entire expression after the / the expression would be written x - 3 / [(2x-5)^2 * 3x + 1 - 2 + 7x ].
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RESPONSE --> I did not realize the parentheses were needed to determine the numerator because the problem stated the fraction and then listed the expression. I misinterpreted the question and will now know to read questions more carefully. self critique assessment: 2
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20:56:08 `questionNumber 10000 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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RESPONSE --> Substitute 4 everywhere there is an x in the expression. Then perform 4-5 because it is in parentheses. 4-5=-1. Then perform -1^2=1. Then perform 1*4=4. Then perform 3/4=0.75. Then perform 4-1+.75-2=3+.75-2=3.75-2=1.75. confidence assessment: 3
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20:59:31 `questionNumber 10000 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first. Exponentiation precedes multiplication. Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4). Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power. -1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.
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RESPONSE --> I should probably have kept the expression as a fraction in the answer instead of converting to a decimal. self critique assessment: 2
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21:00:40 `questionNumber 10000 *&*& Standard mathematics notation is easier to see. On the other hand it's very important to understand order of operations, and students do get used to this way of doing it. You should of course write everything out in standard notation when you work it on paper. It is likely that you will at some point use a computer algebra system, and when you do you will have to enter expressions through a typewriter, so it is well worth the trouble to get used to this notation. Indicate your understanding of the necessity to understand this notation.
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RESPONSE --> It is very important to understand the computer algebra system in order to solve problems correctly. self critique assessment: 2
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21:05:33 `questionNumber 10000 `q005. At the link http://www.vhcc.edu/dsmith/genInfo/introductory problems/typewriter_notation_examples_with_links.htm (copy this path into the Address box of your Internet browser; alternatively use the path http://vhmthphy.vhcc.edu/ > General Information > Startup and Orientation (either scroll to bottom of page or click on Links to Supplemental Sites) > typewriter notation examples and you will find a page containing a number of additional exercises and/or examples of typewriter notation.Locate this site, click on a few of the links, and describe what you see there.
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RESPONSE --> I see information at the top of the page describing the information contained on the page about expressions in typewriter form, then problems in typewrite for are listed at the bottom of the page with a link to a picture of the standard form. confidence assessment: 3
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21:06:09 `questionNumber 10000 You should see a brief set of instructions and over 30 numbered examples. If you click on the word Picture you will see the standard-notation format of the expression. The link entitled Examples and Pictures, located in the initial instructions, shows all the examples and pictures without requiring you to click on the links. There is also a file which includes explanations. The instructions include a note indicating that Liberal Arts Mathematics students don't need a deep understanding of the notation, Mth 173-4 and University Physics students need a very good understanding,
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RESPONSE --> I understand. self critique assessment: 2
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21:06:32 `questionNumber 10000 while students in other courses should understand the notation and should understand the more basic simplifications. There is also a link to a page with pictures only, to provide the opportunity to translated standard notation into typewriter notation.
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RESPONSE --> ok self critique assessment: 3
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iţ댌ɬ assignment #001 001. Areas qa areas volumes misc 06-04-2008
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21:26:17 `questionNumber 10000 `q001. There are 11 questions and 7 summary questions in this assignment. What is the area of a rectangle whose dimensions are 4 m by 3 meters.
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RESPONSE --> The area of a rectangle is = to lenght * width. So 4*3 = 12 meters ^2. confidence assessment: 3
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21:26:53 `questionNumber 10000 A 4 m by 3 m rectangle can be divided into 3 rows of 4 squares, each 1 meter on a side. This makes 3 * 4 = 12 such squares. Each 1 meter square has an area of 1 square meter, or 1 m^2. The total area of the rectangle is therefore 12 square meters, or 12 m^2. The formula for the area of a rectangle is A = L * W, where L is the length and W the width of the rectangle. Applying this formula to the present problem we obtain area A = L * W = 4 m * 3 m = (4 * 3) ( m * m ) = 12 m^2. Note the use of the unit m, standing for meters, in the entire calculation. Note that m * m = m^2.
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RESPONSE --> self critique assessment: 3
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21:33:06 `questionNumber 10000 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> For a right triangle area=.5*base*height. So .5*4*3=6m^2. confidence assessment: 2
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21:34:13 `questionNumber 10000 A right triangle can be joined along its hypotenuse with another identical right triangle to form a rectangle. In this case the rectangle would have dimensions 4.0 meters by 3.0 meters, and would be divided by any diagonal into two identical right triangles with legs of 4.0 meters and 3.0 meters. The rectangle will have area A = L * W = 4.0 m * 3.0 m = 12 m^2, as explained in the preceding problem. Each of the two right triangles, since they are identical, will therefore have half this area, or 1/2 * 12 m^2 = 6.0 m^2. The formula for the area of a right triangle with base b and altitude h is A = 1/2 * b * h.
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RESPONSE --> self critique assessment: 3
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21:36:13 `questionNumber 10000 `q003. What is the area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters?
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RESPONSE --> for a parallelogram the area= the base8 altitude. So area=5.0*2.0=10.0m^2. confidence assessment: 3
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21:36:46 `questionNumber 10000 A parallelogram is easily rearranged into a rectangle by 'cutting off' the protruding end, turning that portion upside down and joining it to the other end. Hopefully you are familiar with this construction. In any case the resulting rectangle has sides equal to the base and the altitude so its area is A = b * h. The present rectangle has area A = 5.0 m * 2.0 m = 10 m^2.
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RESPONSE --> self critique assessment: 3
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21:38:33 `questionNumber 10000 `q004. What is the area of a triangle whose base is 5.0 cm and whose altitude is 2.0 cm?
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RESPONSE --> For a triangle area=.5*base*height. So area=.5*5.0*2.0=5.0cm^2. confidence assessment: 3
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21:38:59 `questionNumber 10000 It is possible to join any triangle with an identical copy of itself to construct a parallelogram whose base and altitude are equal to the base and altitude of the triangle. The area of the parallelogram is A = b * h, so the area of each of the two identical triangles formed by 'cutting' the parallelogram about the approriate diagonal is A = 1/2 * b * h. The area of the present triangle is therefore A = 1/2 * 5.0 cm * 2.0 cm = 1/2 * 10 cm^2 = 5.0 cm^2.
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RESPONSE --> self critique assessment: 3
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21:41:51 `questionNumber 10000 `q005. What is the area of a trapezoid with a width of 4.0 km and average altitude of 5.0 km?
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RESPONSE --> The areaof a trapezoid =width * altitude. So 4.0km * 5.0km = 20.0km^2. confidence assessment: 3
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21:42:08 `questionNumber 10000 Any trapezoid can be reconstructed to form a rectangle whose width is equal to that of the trapezoid and whose altitude is equal to the average of the two altitudes of the trapezoid. The area of the rectangle, and therefore the trapezoid, is therefore A = base * average altitude. In the present case this area is A = 4.0 km * 5.0 km = 20 km^2.
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RESPONSE --> self critique assessment: 3
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21:49:17 `questionNumber 10000 `q006. What is the area of a trapezoid whose width is 4 cm in whose altitudes are 3.0 cm and 8.0 cm?
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RESPONSE --> Since a trapezoid can be reconstructed to form a rectangle with the width equal to the width of the trapezoid and the average of the altitutdes equal to the altitude, the area=base * average altitude. So area = 4cm*5.5cm =22. 0cm^2. confidence assessment: 3
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21:49:27 `questionNumber 10000 The area is equal to the product of the width and the average altitude. Average altitude is (3 cm + 8 cm) / 2 = 5.5 cm so the area of the trapezoid is A = 4 cm * 5.5 cm = 22 cm^2.
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RESPONSE --> self critique assessment: 3
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21:52:50 `questionNumber 10000 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> The area of a circle = 3.14*radius^2. So area=3.14*(3.00cm)^2 = 28.26cm^2. confidence assessment: 3
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21:55:18 `questionNumber 10000 The area of a circle is A = pi * r^2, where r is the radius. Thus A = pi * (3 cm)^2 = 9 pi cm^2. Note that the units are cm^2, since the cm unit is part r, which is squared. The expression 9 pi cm^2 is exact. Any decimal equivalent is an approximation. Using the 3-significant-figure approximation pi = 3.14 we find that the approximate area is A = 9 pi cm^2 = 9 * 3.14 cm^2 = 28.26 cm^2, which we round to 28.3 cm^2 to match the number of significant figures in the given radius. Be careful not to confuse the formula A = pi r^2, which gives area in square units, with the formula C = 2 pi r for the circumference. The latter gives a result which is in units of radius, rather than square units. Area is measured in square units; if you get an answer which is not in square units this tips you off to the fact that you've made an error somewhere.
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RESPONSE --> I used the pi=3.14 to determine the approximate area. I should have left it as 9pi cm^2. self critique assessment: 2
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21:58:54 `questionNumber 10000 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> The circumference of a circle =2*pi*r. Where r is the radius. So circumference=2*pi*3cm = 6pi cm. confidence assessment: 3
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21:59:07 `questionNumber 10000 The circumference of this circle is C = 2 pi r = 2 pi * 3 cm = 6 pi cm. This is the exact area. An approximation to 3 significant figures is 6 * 3.14 cm = 18.84 cm. Note that circumference is measured in the same units as radius, in this case cm, and not in cm^2. If your calculation gives you cm^2 then you know you've done something wrong.
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RESPONSE --> self critique assessment: 3
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22:02:33 `questionNumber 10000 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> The radius of a circle is equal to one half of the diamater. The area for a circle is equal to pi* r^2. If the diameter Is 12 m, then .5*12 = 6m. The area= pi*(6m)^2 = 36 pi m^2. confidence assessment: 3
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22:02:55 `questionNumber 10000 The area of a circle is A = pi r^2, where r is the radius. The radius of this circle is half the 12 m diameter, or 6 m. So the area is A = pi ( 6 m )^2 = 36 pi m^2. This result can be approximated to any desired accuracy by using a sufficient number of significant figures in our approximation of pi. For example using the 5-significant-figure approximation pi = 3.1416 we obtain A = 36 m^2 * 3.1416 = 113.09 m^2.
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RESPONSE --> self critique assessment: 3
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22:09:38 `questionNumber 10000 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> The circumference of a circle is equal to 2*pi*r, where r is the radius. If the circumference (C) is Equal to 14 pi meters, then C = 14 pi m can be rewritten as 2* pi * r = 14 pi m. Solving algebraically, we can divide both sides by pi to get 2* r = 14m. We can then divide both sides by 2 to obtain the measurement of the radius which is r= 7m. The area of a circle = pi * r^2, where r is the radius. So area = pi*(7m)^2 = 49 pi m^2. confidence assessment: 3
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22:11:32 `questionNumber 10000 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> ok confidence assessment:
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22:18:29 `questionNumber 10000 Knowing that A = pi r^2 we solve for r. We first divide both sides by pi to obtain A / pi = r^2. We then reverse the sides and take the square root of both sides, obtaining r = sqrt( A / pi ). Note that strictly speaking the solution to r^2 = A / pi is r = +-sqrt( A / pi ), meaning + sqrt( A / pi) or - sqrt(A / pi). However knowing that r and A are both positive quantities, we can reject the negative solution. Now we substitute A = 78 m^2 to obtain r = sqrt( 78 m^2 / pi) = sqrt(78 / pi) m.{} Approximating this quantity to 2 significant figures we obtain r = 5.0 m.
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RESPONSE --> Question 11 was attached to the answer for question 10 so when I clicked on Enter response to enter my critique the screen went to the answer for question 11 and I did not get to enter my answer for question 11 which was: Since A = pi * r^2, we can rewrite the equation as 78m^2 = pi * r^2. Also since we need to solve for r, we can rewrite the equation as r = sqrt(78m^2 / pi). So r = sqrt(78 / pi) m. self critique assessment: 2
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22:23:01 `questionNumber 10000 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> We can visualize a diagonal line drawn from one corner to the opposite corner of the rectangle that divides it into two right triangles. By knowing that the area of a right triangle = .5 * base * height, we can find the area of the rectangle by multiplying the area of one triangle by 2. confidence assessment: 3
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22:25:35 `questionNumber 10000 We visualize the rectangle being covered by rows of 1-unit squares. We multiply the number of squares in a row by the number of rows. So the area is A = L * W.
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RESPONSE --> I used a different approach and was incorrect. I now know to visualize the rectangle being covered in rows of 1 inch squares and to mulitply the number of squares in a row by the number of rows to obtain the area. self critique assessment: 1
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22:30:47 `questionNumber 10000 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> We can visualize a right triangle as one half of a rectangle that is filled with rows of 1 inch squares. Since we can obtain the area of the rectangle by multiplying the number of squares in a row by the number of rows, we know that the area of the rectangle = L * W, where L = length and W = width. since the triangle is 1/2 of the rectangle, we can say that the area of the triangle = 1/2L * W. confidence assessment: 3
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22:32:14 `questionNumber 10000 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> A parallelogram can be shifted to form a rectangle so the area = L* W. confidence assessment: 3
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22:32:26 `questionNumber 10000 The area of a parallelogram is equal to the product of its base and its altitude. The altitude is measured perpendicular to the base.
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RESPONSE --> ok self critique assessment: 3
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22:33:07 `questionNumber 10000 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> Area of a trapezoid = base * average altitude. confidence assessment: 3
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22:33:17 `questionNumber 10000 We think of the trapezoid being oriented so that its two parallel sides are vertical, and we multiply the average altitude by the width.
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RESPONSE --> self critique assessment: 3
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22:33:43 `questionNumber 10000 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> The area of a circle = pi * r^2. confidence assessment: 3
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22:33:50 `questionNumber 10000 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> self critique assessment: 3
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22:35:05 `questionNumber 10000 `q017. Summary Question 6: How do we calculate the circumference of a circle? How can we easily avoid confusing this formula with that for the area of the circle?
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RESPONSE --> the circumference of a circle = 2 * pi * r. The area is in units ^2. The circumference is only in units. confidence assessment: 3
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22:35:17 `questionNumber 10000 We use the formula C = 2 pi r. The formula for the area involves r^2, which will give us squared units of the radius. Circumference is not measured in squared units.
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RESPONSE --> ok. self critique assessment: 3
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22:37:32 `questionNumber 10000 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I do not understand what this question is asking for. I had the formulas for the exercises memorized from prior education, so I guess they are organized in my brain. confidence assessment: 3
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22:37:49 `questionNumber 10000 This ends the first assignment.
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RESPONSE --> confidence assessment: 3
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iţ댌ɬ assignment #001 001. Areas qa areas volumes misc 06-04-2008
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21:26:17 `q001. There are 11 questions and 7 summary questions in this assignment. What is the area of a rectangle whose dimensions are 4 m by 3 meters.
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RESPONSE --> The area of a rectangle is = to lenght * width. So 4*3 = 12 meters ^2. confidence assessment: 3
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21:26:53 A 4 m by 3 m rectangle can be divided into 3 rows of 4 squares, each 1 meter on a side. This makes 3 * 4 = 12 such squares. Each 1 meter square has an area of 1 square meter, or 1 m^2. The total area of the rectangle is therefore 12 square meters, or 12 m^2. The formula for the area of a rectangle is A = L * W, where L is the length and W the width of the rectangle. Applying this formula to the present problem we obtain area A = L * W = 4 m * 3 m = (4 * 3) ( m * m ) = 12 m^2. Note the use of the unit m, standing for meters, in the entire calculation. Note that m * m = m^2.
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RESPONSE --> self critique assessment: 3
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21:33:06 `q002. What is the area of a right triangle whose legs are 4.0 meters and 3.0 meters?
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RESPONSE --> For a right triangle area=.5*base*height. So .5*4*3=6m^2. confidence assessment: 2
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21:34:13 A right triangle can be joined along its hypotenuse with another identical right triangle to form a rectangle. In this case the rectangle would have dimensions 4.0 meters by 3.0 meters, and would be divided by any diagonal into two identical right triangles with legs of 4.0 meters and 3.0 meters. The rectangle will have area A = L * W = 4.0 m * 3.0 m = 12 m^2, as explained in the preceding problem. Each of the two right triangles, since they are identical, will therefore have half this area, or 1/2 * 12 m^2 = 6.0 m^2. The formula for the area of a right triangle with base b and altitude h is A = 1/2 * b * h.
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RESPONSE --> self critique assessment: 3
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21:36:13 `q003. What is the area of a parallelogram whose base is 5.0 meters and whose altitude is 2.0 meters?
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RESPONSE --> for a parallelogram the area= the base8 altitude. So area=5.0*2.0=10.0m^2. confidence assessment: 3
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21:36:46 A parallelogram is easily rearranged into a rectangle by 'cutting off' the protruding end, turning that portion upside down and joining it to the other end. Hopefully you are familiar with this construction. In any case the resulting rectangle has sides equal to the base and the altitude so its area is A = b * h. The present rectangle has area A = 5.0 m * 2.0 m = 10 m^2.
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RESPONSE --> self critique assessment: 3
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21:38:33 `q004. What is the area of a triangle whose base is 5.0 cm and whose altitude is 2.0 cm?
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RESPONSE --> For a triangle area=.5*base*height. So area=.5*5.0*2.0=5.0cm^2. confidence assessment: 3
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21:38:59 It is possible to join any triangle with an identical copy of itself to construct a parallelogram whose base and altitude are equal to the base and altitude of the triangle. The area of the parallelogram is A = b * h, so the area of each of the two identical triangles formed by 'cutting' the parallelogram about the approriate diagonal is A = 1/2 * b * h. The area of the present triangle is therefore A = 1/2 * 5.0 cm * 2.0 cm = 1/2 * 10 cm^2 = 5.0 cm^2.
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RESPONSE --> self critique assessment: 3
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21:41:51 `q005. What is the area of a trapezoid with a width of 4.0 km and average altitude of 5.0 km?
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RESPONSE --> The areaof a trapezoid =width * altitude. So 4.0km * 5.0km = 20.0km^2. confidence assessment: 3
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21:42:08 Any trapezoid can be reconstructed to form a rectangle whose width is equal to that of the trapezoid and whose altitude is equal to the average of the two altitudes of the trapezoid. The area of the rectangle, and therefore the trapezoid, is therefore A = base * average altitude. In the present case this area is A = 4.0 km * 5.0 km = 20 km^2.
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RESPONSE --> self critique assessment: 3
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21:49:17 `q006. What is the area of a trapezoid whose width is 4 cm in whose altitudes are 3.0 cm and 8.0 cm?
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RESPONSE --> Since a trapezoid can be reconstructed to form a rectangle with the width equal to the width of the trapezoid and the average of the altitutdes equal to the altitude, the area=base * average altitude. So area = 4cm*5.5cm =22. 0cm^2. confidence assessment: 3
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21:49:27 The area is equal to the product of the width and the average altitude. Average altitude is (3 cm + 8 cm) / 2 = 5.5 cm so the area of the trapezoid is A = 4 cm * 5.5 cm = 22 cm^2.
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RESPONSE --> self critique assessment: 3
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21:52:50 `q007. What is the area of a circle whose radius is 3.00 cm?
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RESPONSE --> The area of a circle = 3.14*radius^2. So area=3.14*(3.00cm)^2 = 28.26cm^2. confidence assessment: 3
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21:55:18 The area of a circle is A = pi * r^2, where r is the radius. Thus A = pi * (3 cm)^2 = 9 pi cm^2. Note that the units are cm^2, since the cm unit is part r, which is squared. The expression 9 pi cm^2 is exact. Any decimal equivalent is an approximation. Using the 3-significant-figure approximation pi = 3.14 we find that the approximate area is A = 9 pi cm^2 = 9 * 3.14 cm^2 = 28.26 cm^2, which we round to 28.3 cm^2 to match the number of significant figures in the given radius. Be careful not to confuse the formula A = pi r^2, which gives area in square units, with the formula C = 2 pi r for the circumference. The latter gives a result which is in units of radius, rather than square units. Area is measured in square units; if you get an answer which is not in square units this tips you off to the fact that you've made an error somewhere.
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RESPONSE --> I used the pi=3.14 to determine the approximate area. I should have left it as 9pi cm^2. self critique assessment: 2
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21:58:54 `q008. What is the circumference of a circle whose radius is exactly 3 cm?
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RESPONSE --> The circumference of a circle =2*pi*r. Where r is the radius. So circumference=2*pi*3cm = 6pi cm. confidence assessment: 3
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21:59:07 The circumference of this circle is C = 2 pi r = 2 pi * 3 cm = 6 pi cm. This is the exact area. An approximation to 3 significant figures is 6 * 3.14 cm = 18.84 cm. Note that circumference is measured in the same units as radius, in this case cm, and not in cm^2. If your calculation gives you cm^2 then you know you've done something wrong.
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RESPONSE --> self critique assessment: 3
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22:02:33 `q009. What is the area of a circle whose diameter is exactly 12 meters?
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RESPONSE --> The radius of a circle is equal to one half of the diamater. The area for a circle is equal to pi* r^2. If the diameter Is 12 m, then .5*12 = 6m. The area= pi*(6m)^2 = 36 pi m^2. confidence assessment: 3
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22:02:55 The area of a circle is A = pi r^2, where r is the radius. The radius of this circle is half the 12 m diameter, or 6 m. So the area is A = pi ( 6 m )^2 = 36 pi m^2. This result can be approximated to any desired accuracy by using a sufficient number of significant figures in our approximation of pi. For example using the 5-significant-figure approximation pi = 3.1416 we obtain A = 36 m^2 * 3.1416 = 113.09 m^2.
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RESPONSE --> self critique assessment: 3
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22:09:38 `q010. What is the area of a circle whose circumference is 14 `pi meters?
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RESPONSE --> The circumference of a circle is equal to 2*pi*r, where r is the radius. If the circumference (C) is Equal to 14 pi meters, then C = 14 pi m can be rewritten as 2* pi * r = 14 pi m. Solving algebraically, we can divide both sides by pi to get 2* r = 14m. We can then divide both sides by 2 to obtain the measurement of the radius which is r= 7m. The area of a circle = pi * r^2, where r is the radius. So area = pi*(7m)^2 = 49 pi m^2. confidence assessment: 3
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22:11:32 `q011. What is the radius of circle whose area is 78 square meters?
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RESPONSE --> ok confidence assessment:
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22:18:29 Knowing that A = pi r^2 we solve for r. We first divide both sides by pi to obtain A / pi = r^2. We then reverse the sides and take the square root of both sides, obtaining r = sqrt( A / pi ). Note that strictly speaking the solution to r^2 = A / pi is r = +-sqrt( A / pi ), meaning + sqrt( A / pi) or - sqrt(A / pi). However knowing that r and A are both positive quantities, we can reject the negative solution. Now we substitute A = 78 m^2 to obtain r = sqrt( 78 m^2 / pi) = sqrt(78 / pi) m.{} Approximating this quantity to 2 significant figures we obtain r = 5.0 m.
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RESPONSE --> Question 11 was attached to the answer for question 10 so when I clicked on Enter response to enter my critique the screen went to the answer for question 11 and I did not get to enter my answer for question 11 which was: Since A = pi * r^2, we can rewrite the equation as 78m^2 = pi * r^2. Also since we need to solve for r, we can rewrite the equation as r = sqrt(78m^2 / pi). So r = sqrt(78 / pi) m. self critique assessment: 2
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22:23:01 `q012. Summary Question 1: How do we visualize the area of a rectangle?
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RESPONSE --> We can visualize a diagonal line drawn from one corner to the opposite corner of the rectangle that divides it into two right triangles. By knowing that the area of a right triangle = .5 * base * height, we can find the area of the rectangle by multiplying the area of one triangle by 2. confidence assessment: 3
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22:25:35 We visualize the rectangle being covered by rows of 1-unit squares. We multiply the number of squares in a row by the number of rows. So the area is A = L * W.
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RESPONSE --> I used a different approach and was incorrect. I now know to visualize the rectangle being covered in rows of 1 inch squares and to mulitply the number of squares in a row by the number of rows to obtain the area. self critique assessment: 1
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22:30:47 `q013. Summary Question 2: How do we visualize the area of a right triangle?
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RESPONSE --> We can visualize a right triangle as one half of a rectangle that is filled with rows of 1 inch squares. Since we can obtain the area of the rectangle by multiplying the number of squares in a row by the number of rows, we know that the area of the rectangle = L * W, where L = length and W = width. since the triangle is 1/2 of the rectangle, we can say that the area of the triangle = 1/2L * W. confidence assessment: 3
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22:32:14 `q014. Summary Question 3: How do we calculate the area of a parallelogram?
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RESPONSE --> A parallelogram can be shifted to form a rectangle so the area = L* W. confidence assessment: 3
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22:32:26 The area of a parallelogram is equal to the product of its base and its altitude. The altitude is measured perpendicular to the base.
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RESPONSE --> ok self critique assessment: 3
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22:33:07 `q015. Summary Question 4: How do we calculate the area of a trapezoid?
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RESPONSE --> Area of a trapezoid = base * average altitude. confidence assessment: 3
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22:33:17 We think of the trapezoid being oriented so that its two parallel sides are vertical, and we multiply the average altitude by the width.
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RESPONSE --> self critique assessment: 3
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22:33:43 `q016. Summary Question 5: How do we calculate the area of a circle?
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RESPONSE --> The area of a circle = pi * r^2. confidence assessment: 3
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22:33:50 We use the formula A = pi r^2, where r is the radius of the circle.
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RESPONSE --> self critique assessment: 3
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22:35:05 `q017. Summary Question 6: How do we calculate the circumference of a circle? How can we easily avoid confusing this formula with that for the area of the circle?
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RESPONSE --> the circumference of a circle = 2 * pi * r. The area is in units ^2. The circumference is only in units. confidence assessment: 3
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22:35:17 We use the formula C = 2 pi r. The formula for the area involves r^2, which will give us squared units of the radius. Circumference is not measured in squared units.
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RESPONSE --> ok. self critique assessment: 3
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22:37:32 `q018. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I do not understand what this question is asking for. I had the formulas for the exercises memorized from prior education, so I guess they are organized in my brain. confidence assessment: 3
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22:37:49 This ends the first assignment.
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RESPONSE --> confidence assessment: 3
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