course Mth 173 dÛžð©óã½Çc§E£Xô±ë¤…ø|å½Ñassignment #001
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15:02:47 `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 --> sm = 5000 sj = 5300 sd = 5500 From March-July, my money grew $300 dollars in 4 months. An average of $75/month. From March-December, my money grew $200 in 5 months. An average of $40/month. My money grew faster from March-July. confidence assessment: 3
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15:03:36 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> March-July = $75/month July-December = $40/month confidence assessment: 3
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15:03:44 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 --> ok self critique assessment: 3
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15:08:57 `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 water is changing more quickly between t = 10 and t = 40. 4cm/3s (aprox. 1.333cm/sec) The water is changing less quickly between t = 40 and t = 90. 2cm/5s (.4cm/sec) confidence assessment: 3
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15:10:22 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 --> My mistake was, instead, of subtracting 80 from 40, I subtracted 40 from 80. And the same for the other set of numbers. self critique assessment: 2
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15:12:11 `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 cases, I had to find the difference in averages of two situations. The first was the average of money versus time, the second was depth versus time. confidence assessment: 2
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15:12:22 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 --> ok self critique assessment:
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