course Mth 173 E‘êÀˆëa»Ã÷¶èÿŽœ“À–ÈÓ¶ÖÁäassignment #001
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07:47:27 `qNote that there are four questions in this assignment. `q001. If your stocks are worth $5000 in mid-March, $5300 in mid-July and $5500 in mid-December, during which period, March-July or July-December was your money growing faster?
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RESPONSE --> March to July because there were 4 months of interest of $300 versus 5 months during the July to December span and only grew $200. confidence assessment: 3
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07:47:51 The first period (4 months) was shorter than the second (5 months), and the value changed by more during the shorter first period (increase of $300) than during the longer second perios (increase of $200). A greater increase in a shorter period implies a greater rate of change. So the rate was greater during the first period.
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RESPONSE --> I got the answer correct self critique assessment: 3
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08:00:48 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> The average rate of change during March-July is 300/4 = $75 The average rate of change during July-December is 200/5 = $40 The average rate of change during both period is 500/9 = $55.56 confidence assessment: 3
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08:01:03 From mid-March thru mid-July is 4 months. A change of $300 in four months gives an average rate of change of $300 / (4 months) = $75/month. From mid-July through mid-December is 5 months, during which the value changes by $200, giving an average rate of $200 / (5 months) = $40 / month. Thus the rate was greater during the first period than during the second.
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RESPONSE --> I got the answer correct. self critique assessment: 3
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08:12:33 `q003. If the water in a uniform cylinder is leaking from a hole in the bottom, and if the water depths at clock times t = 10, 40 and 90 seconds are respectively 80 cm, 40 cm and 20 cm, is the depth of the water changing more quickly or less quickly, on the average, between t = 10 sec and t = 40 sec, or between t = 40 sec and t = 90 sec?
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RESPONSE --> The average loss of depth between 10 & 40 second is -1.33 (10-40=30; 80-40=-40; -40/30 = -1.33). The depth is decreasing more quickly between these two times. The average loss of depth between 40& 90 second is -.40 (40-90 = 50; 40-20 = -20; -20/50 = -.40). confidence assessment: 3
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08:12:46 Between clock times t = 10 sec and t = 40 sec the depth changes by -40 cm, from 80 cm to 40 cm, in 30 seconds. The average rate is therefore -40 cm / (30 sec) = -1.33 cm/s. Between t = 40 sec and t = 90 sec the change is -20 cm and the time interval is 50 sec so the average rate of change is -20 cm/ 50 sec = -.4 cm/s, approx. The depth is changing more quickly during the first time interval.
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RESPONSE --> I got the answer correct. self critique assessment: 3
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08:14:15 `q004. How are the two preceding questions actually different versions of the same question? How it is the mathematical reasoning the same in both cases?
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RESPONSE --> In both the previous questions, you are taking the average of two points using the depth vs. clock time average calculation. However, they are different in the case that one is discussing monetary interest and the other depth change. confidence assessment: 3
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08:14:35 In each case we were given a quantity that changed with time. We were given the quantities at three different clock times and we were asked to compare the rates of change over the corresponding intervals. We did this by determining the changes in the quantities and the changes in the clock times, and for each interval dividing change in quantity by change in clock time. We could symbolize this process by representing the change in clock time by `dt and the change in the quantity by `dQ. The rate is thus rate = `dQ /`dt.
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RESPONSE --> I got the answer correct. self critique assessment: 3
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