course MTH 173 s_V㝭assignment #001
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22:44:44 `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 --> Well in four months between mid-march and mid-july the stocks made 300 dollars and in the following 5 month period the stocks only made 200 dollars so the money was growing faster when it made 300 dollars in four months. confidence assessment: 3
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22:45:31 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 --> understood self critique assessment: 3
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22:48:09 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> The first period of four months and 300 dollars the money averaged 75 dollars/month and in the second period of five months and 200 dollars the money averaged 40 dollars/month. confidence assessment: 2
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22:48:30 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 --> understood self critique assessment: 3
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22:51:56 `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 --> Between t=10 and t=40 (30 seconds) the water depth changes by 40cm and between t=40 and t=90 (50 seconds) the water depth only changes by 20 cm therefore we can conclude that the water is changing more quickly between the clock times of t=10 and t=40. confidence assessment: 2
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22:52:15 `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 --> understood confidence assessment:
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22:53:48 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 --> understood self critique assessment: 3
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