Assignment 1

course Mth 173

šìÖïè¢óZ~áÛëL¢w†é´Ö‹›Qè°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

01-30-2008

......!!!!!!!!...................................

12:12:46

`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?

......!!!!!!!!...................................

RESPONSE -->

March-July

5300-5000= 300

5500-5300= 200

confidence assessment: 3

.................................................

......!!!!!!!!...................................

12:13:18

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.

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

You didn't really answer the question.

&#

Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions (to which I will respond).

.................................................

......!!!!!!!!...................................

12:13:58

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

......!!!!!!!!...................................

RESPONSE -->

250$

confidence assessment: 1

.................................................

......!!!!!!!!...................................

12:14:17

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.

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

&#

This also requires a self-critique.

.................................................

......!!!!!!!!...................................

12:17:12

`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?

......!!!!!!!!...................................

RESPONSE -->

the depth is changing more quickly between t = 10 sec and t = 40 sec, and less quickly between t = 40 sec and t = 90 sec

confidence assessment: 3

.................................................

......!!!!!!!!...................................

12:17:38

01-30-2008 12:17:38

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.

......!!!!!!!!...................................

NOTES ------->

The given solution provides much more detail than your solution. Self-critique is needed here.

.......................................................!!!!!!!!...................................

12:18:39

`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?

......!!!!!!!!...................................

RESPONSE -->

I use the same method to figure out the answer. They are both difference questions.

confidence assessment: 3

good answer

.................................................

......!!!!!!!!...................................

12:19:00

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.

......!!!!!!!!...................................

RESPONSE -->

self critique assessment: 3

.................................................

See my notes on self-critique. I still can't tell what you do and do not understand about these questions, though it's clear that you understand a good bit. Your answer on the last question is encouraging.