course MTH 271 9/08 4pm ٔ妮塂oxvvvv
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15:49:57 `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 --> confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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lex}s assignment #001 001. Depth vs. Clock Time and Rate of Depth Change 09-03-2009
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15:53:44 `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 --> Your money was growing fastest from March-July than from July-December. In the July to December period, the worth of the stocks increased $200 over a 5 month period, averaging an increase of $40/month. During the March to July period, however, the worth of the stocks increased $300 over a 4 month period, thus averaging an increase of $75/month. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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15:56:20 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> Average rates of change: March to July Increase of $300 over 4 months=Avg. increase of $75/month. July to December Increase of $200 over 5 months=Avg. increase of $40/month. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:02:58 `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 depth of the water is changing more quickly between t=10s and t=40s than during t=40s and t=90s. A greater amount of water is lost over a shorter period of time during the t=10s to t=40s frame. t=10 to t=40 Loss of 40cm over 30s period=-40cm/30s=-4cm/3s=4cm decrease for every 3 seconds t=40 to t=90 Loss of 20cm over 50s period=-20cm/50s=-2cm/5s=2cm decrease for every 5 seconds confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:07:15 `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 --> Both of the preceding questions are variation of the same theme, rate of change. Both questions provide two fixed time periods over which a quantity is fluctuating. The mathematical reasoning in both cases was identical because both presented a quantity changing a greater amount over a shorter time period, both with longer time periods presenting less change. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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16:08:51