course MTH 173 I couldn't find the query to run for Assignment 0. When I ran the query and typed assignment number 0 in the field the program wouldn't run. So, I viewed all of the video clips and started on Assignment 1. My first few assignments are going slowly. I just got my new calculator and found the cds I misplaced after completing the orientation assignments. I should be back on track in the next couple of weeks. ??w??v?????????assignment #001001. Depth vs. Clock Time and Rate of Depth Change
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23:48:13 `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 --> The money is growing faster from March to July, there is a shorter time span with more money gain. dy = change in amount dt = change in time in months dy/dt for March-July = (5300-5000)/(7-3) = $300/4months = $75/month dy/dt for July-Dec = (5500-5300)/(12-7)= $200/3months = $66.7/month confidence assessment: 2
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23:50:00 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 --> I actually feel kind of dumb. I was headed to the right response and actually had $200 in 5 months but got sidetracked and wrote in 3. I do understand the increase with a shorter period and greater increase self critique assessment: 2
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23:51:22 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> I gave the rate for March to July corrected for July-Dec: dy/dt = (5500-5300)/(12-7) = $200/5months = $40/month confidence assessment: 2
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23:52:13 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 --> Completely understand this concept. The numbers I used for my months should be fairly obvious. self critique assessment: 2
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23:56:30 `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 would change more quikly on the average between t=10 and t=40 because there is a shorter amount of time with a greater change in depth. confidence assessment: 2
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23:57:46 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 actually held my self back from entering these results because I thought you would follow the same format as before, asking the reasoning, and then asking for the actual work. I obtained the same answers in my notebook before entering my response in the reasoning. self critique assessment: 2
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23:59:57 `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 questions are asking rates of change. The reasoning would be the same because we were asking ourselves which rate is faster. We reasoned both out by finding the difference of quantity divided by the difference in time. confidence assessment: 2
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