QA 1

course MTH 271

9/08 4pm

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assignment #001

001. Depth vs. Clock Time and Rate of Depth Change

09-03-2009

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assignment #001

001. Depth vs. Clock Time and Rate of Depth Change

09-03-2009

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Student Name:

assignment #001

09-03-2009

엝֍\S׿

assignment #001

001. Depth vs. Clock Time and Rate of Depth Change

09-03-2009

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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

&#I need to see the questions so I can be sure what your answers mean. Most of the time I can tell, but I'm dealing with information that comes in from over 1000 different files, containing a total of about 10 000 questions. While I'm familiar with the content and sequencing of the questions, having written them all, and know what I'm looking for, different students will answer these questions in different ways and I need to be able to relate your answers to the specific wording of each question. When reviewing my responses you will also need to be able to relate your answers and my comments to the specifics of the original document. So it will be important for you to insert your responses into a copy of the original document, according to instructions, without otherwise changing any of the content of the original document. This will ensure you of the best possible feedback on your work. &#