course Mth 271

?????m?e·K?????????????assignment #001

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

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

09-13-2007

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07:12:22

`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-July

confidence assessment: 3

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07:13:03

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 -->

self critique assessment: 3

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07:14:44

`q002. What were the precise average rates of change during these two periods?

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RESPONSE -->

First period= 300/4 = 75 $/month

Second period = 200/5 = 40 $/month

confidence assessment: 3

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07:18:46

`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 -->

it is moving quicker between t=10 and t=40

confidence assessment: 3

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07:21:39

`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 -->

they both have a change in something with respect to time

confidence assessment: 3

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From your answers it seems clear that you understand, but when you get into unfamiliar material you will need to include the details of your reasoning and your calculations.

From your answers it seems clear that you understand, but when you get into unfamiliar material you will need to include the details of your reasoning and your calculations.

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Let me know if you have questions. &#