Assignment 1

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.

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12:41:47 Note 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 --> 4 months went up $300......went up $200 in 5 months......So it grew the most between March-July

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12:45:34 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 --> 300/5000 = 0.06.......6% 200/5300=.038.......3.8%

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12:50:44 `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 --> t=10...t=40 so 4/20= .2 t=40....t=90 so 5/20= .25 It is running out faster from t40 to t90. .05 sec faster than t10 to t40.

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12:54:15 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 --> I see what I did I put that between 80 and 40 there was a change of 20 cm .....it sould have been 40 cm but i would have still missed it because I didnt make it a negative like I should have done. I think I just tried to hurry though this problem because I missed up on all of the adding and subtracting. I also put sec/cm and it should have been cm/sec.

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12:59:13 `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 of the questions you need to find the differents either between clock times or months. So you are using the same kind of reasoning. In the first question and in the second questin you could tell by just looking that you made more money in the first four months than in the last five just as you could look at the second question and compare the differece in the clock times vs. the depth change.

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This looks good. Remember that the rate is determined by the change in both quantities--rate of change of A with respect to B is change in A divided by change in B.

Let me know if you have questions.