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22:01:16 Query Introduction to General Themes; Examples (no summary needed) What were some of the things in this introduction that you found interesting or surprising?
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RESPONSE --> that the rate of flow decreased as the water level got lower
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22:01:22 ** Continue to the next question **
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RESPONSE --> k
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22:02:25 Query Introductory Flow Experiment (no summary needed) Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? Support your conclusion.
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RESPONSE --> slower and slower rate. the time intervals increased per centimeter of decrease in water level
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22:02:43 ** If you time the water at equal time intervals you should find that the depth changes by less and less with each new interval. If you timed the depth at equal intervals of depth you should find that each interval takes longer than the one before it. } Either way you would conclude that water flows from the hole at a decreasing rate. The reason is that as the water depth decreases the pressure forcing the water out of the hole decreases. **
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RESPONSE --> ok
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22:08:06 ** The graph will start on the positive y axis and will decrease at a decreasing rate. The shape of the graph is the left-hand side of a parabola that opens upward. The right-hand half of the parabola does not correspond to the flow. The lef-hand half of the parabola, which corresponds to the flow, gets less and less steep with increasing clock time, matching the fact that that the rate of decrease is slowing. At the instant the containers empties, the water will be at the level of the hole. If depth is measured relative to the hole, then at the instant depth will reach zero. The corresponding graph point will lie on the t axis and will correspond to the vertex of the parabola. **
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RESPONSE --> time is measure on X (t) axis and depth is measured on the Y axis. Time is increasing - water level is decreasing. The rate of water flow decreases as time increases. no the graph does not intercept the Y or the X axis. It's shaped like a banana.
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fx֞}Ĕhwɵ\ assignment #001 Ή禈ϏHKޔ Precalculus I 02-04-2006
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22:17:20 Query Introduction to General Themes; Examples (no summary needed) What were some of the things in this introduction that you found interesting or surprising?
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RESPONSE --> previously answered
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22:17:27 ** Continue to the next question **
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RESPONSE --> previously answered
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22:17:34 Query Introductory Flow Experiment (no summary needed) Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? Support your conclusion.
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RESPONSE --> previously answered
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22:17:39 ** If you time the water at equal time intervals you should find that the depth changes by less and less with each new interval. If you timed the depth at equal intervals of depth you should find that each interval takes longer than the one before it. } Either way you would conclude that water flows from the hole at a decreasing rate. The reason is that as the water depth decreases the pressure forcing the water out of the hole decreases. **
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RESPONSE --> previously answered
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22:18:02 What does the graph of depth vs. clock time look like? Is it increasing or decreasing? Does the rate of increase or decrease speed up or slow down? Does your graph intercept the y axis? Does it intercept the x axis? How would you describe its overall shape?
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RESPONSE --> previously answered
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22:19:10 ** The graph will start on the positive y axis and will decrease at a decreasing rate. The shape of the graph is the left-hand side of a parabola that opens upward. The right-hand half of the parabola does not correspond to the flow. The lef-hand half of the parabola, which corresponds to the flow, gets less and less steep with increasing clock time, matching the fact that that the rate of decrease is slowing. At the instant the containers empties, the water will be at the level of the hole. If depth is measured relative to the hole, then at the instant depth will reach zero. The corresponding graph point will lie on the t axis and will correspond to the vertex of the parabola. **
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RESPONSE --> * the answer was previously listed under the original question and then when I hit Next Question/Answer the entire form closed. It let me back in...so I'm hoping I'm still in the right place...I will submit all of the work at one time.
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WܡȒũ؏x assignment #001 Ή禈ϏHKޔ Precalculus I 02-04-2006
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22:20:19 Query Introduction to General Themes; Examples (no summary needed) What were some of the things in this introduction that you found interesting or surprising?
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RESPONSE --> previously answered
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22:20:23 ** Continue to the next question **
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RESPONSE --> previously answered
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22:20:25 Query Introductory Flow Experiment (no summary needed) Is the depth changing at a regular rate, at a faster and faster rate, or at a slower and slower rate? Support your conclusion.
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RESPONSE --> previously answered
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22:20:30 ** If you time the water at equal time intervals you should find that the depth changes by less and less with each new interval. If you timed the depth at equal intervals of depth you should find that each interval takes longer than the one before it. } Either way you would conclude that water flows from the hole at a decreasing rate. The reason is that as the water depth decreases the pressure forcing the water out of the hole decreases. **
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RESPONSE --> previously answered
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22:20:36 What does the graph of depth vs. clock time look like? Is it increasing or decreasing? Does the rate of increase or decrease speed up or slow down? Does your graph intercept the y axis? Does it intercept the x axis? How would you describe its overall shape?
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RESPONSE --> previously answered
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22:20:43 ** The graph will start on the positive y axis and will decrease at a decreasing rate. The shape of the graph is the left-hand side of a parabola that opens upward. The right-hand half of the parabola does not correspond to the flow. The lef-hand half of the parabola, which corresponds to the flow, gets less and less steep with increasing clock time, matching the fact that that the rate of decrease is slowing. At the instant the containers empties, the water will be at the level of the hole. If depth is measured relative to the hole, then at the instant depth will reach zero. The corresponding graph point will lie on the t axis and will correspond to the vertex of the parabola. **
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RESPONSE --> k
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"
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12:54:09 `q001. It will be very important in this course for your instructor to see and understand the process of visualization and reasoning you use when you solve problems. This exercise is designed to give you a first experience with these ideas, and your instructor a first look at your work. Answer the following questions and explain in commonsense terms why your answer makes sense.
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RESPONSE --> It is extremely important for Mr. Smith to see where our answers come from and that we understand the process of where we got the answer. We have to be able to write down what we did in a way that helps him to visualize our understanding.
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12:58:46 For each question draw a picture to make sense out of the situation, and include a description of the picture. Samples Sample question and response Question: If a bundle of shingles covers 30 square feet, how many bundles are required to cover a 600 square foot roof? Response: We might draw a picture of a rectangle representing the area, dividing the rectangle into a number of smaller rectangles each representing the area covered by a single bundle. This makes it clear that we are dividing the roof area into 1-bundle areas, and makes it clear why we are going to have to divide. Reasoning this problem out in words, we can say that a single bundle would cover 30 square feet. Two bundles would cover 60 square feet. Three bundles would cover 90 square feet. We could continue in this manner until we reach 600 square feet. However, this would be cumbersome. It is more efficient to use the ideas of multiplication and division. We imagine grouping the 600 square feet into 30 square foot patches. There will be 600 / 30 patches and each will require exactly one bundle. We therefore require 600 / 30 bundles = 20 bundles. {}Your responses might not be as clear as the above, though they might be even more clear. I won't be looking for perfection, though I wouldn't object to it, but for a first effort at visualizing a situation and communicating a reasoning process. This is not something you are used to doing and it might take a few attempts before you can achieve good results, but you will get better every time you try. {}You might be unsure of what to do on a specific question. In such a case specific questions and expressions of confusion are also acceptable responses. Such a response must include your attempts to come up with a picture and reason out an explanation. For example your response might be Sample expression of confusion: I've drawn a picture of a pile of bundles and a roof but I'm not sure how to connect the two. I tried multiplying the number of bundles by the square feet of the roof but I got 18,000, and I know it won't take 18,000 bundles to cover the roof. How do you put the area covered by a bundle together with the roof area to get the number of bundles required? A poor response would be something like 'I don't know how to do #17'. This response reveals nothing of your attempt to understand the question and the situation. Nor does it ask a specific question. Incidentally, you might be tempted to quote rules or formulas about rates and velocities in answering these questions. Don't. This exercise isn't about being able to memorize rules and quote them. It is about expanding your ability to visualize, reason and communicate.
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RESPONSE --> k
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12:59:33 In your own words briefly summarize the instructions and the intent of this exercise.
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RESPONSE --> We are to take each question and try to put into our own words the process that we start and come to the anwer so that Mr. Smith will know that we are understanding our material.
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13:01:23 `q001. If you earn 50 dollars in 5 hours, at what average rate are you earning money, in dollars per hour?
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RESPONSE --> $50/5 gives a rate of $10 per hour that you are earning money.
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13:02:20 If you travel 300 miles in 6 hours, at what average rate are you traveling, in miles per hour?
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RESPONSE --> Traveled 300 miles in a total of 6 hours. 300/6 = 50 miles per hour that you are traveling. Should I say approximately 50 mph because of differentiating circumstances in a 6 hour period.
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13:03:33 `q002. If a ball rolling down a grooved track travels 40 centimeters in 5 seconds, at what average rate is the ball moving, in centimeters per second?
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RESPONSE --> the ball travels 40 cm in 5 sec, then 40/5= 8 ; the average rate is 8 cm per sec that the ball is moving
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13:04:38 02-04-2006 13:04:38 The preceding three questions illustrate the concept of a rate. In each case, to find the rate we divided the change in some quantity (the number of dollars or the distance, in these examples) by the time required for the change (the number of hours or seconds, in these examples). Explain in your own words what is meant by the idea of a rate.
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NOTES -------> rate is found by dividing the change is qnty, dollars, or distance by the # of hours or secs that was required for the change.
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13:24:53 `q003. If you are earning money at the average rate of 15 dollars per hour, how much do you earn in 6 hours?
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RESPONSE --> in 6 hours at an average rate of $15 per hour, you will earn: 6 * 15 = 90.00 in six hours
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13:25:57 If you are traveling at an average rate of 60 miles per hour, how far do you travel in 9 hours?
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RESPONSE --> traveling an avg rate of 60 miles per hour in 9 hours you will travel: 9*60=540 miles
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13:26:47 `q004. If a ball travels at and average rate of 13 centimeters per second, how far does it travel in 3 seconds?
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RESPONSE --> ball travels at an avg rate of 13 cm per sec, in 3 sec the ball travels: 13*3=39 cm
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13:28:18 In the preceding three exercises you turned the concept of a rate around. You were given the rate and the change in the clock time, and you calculated the change in the quantity. Explain in your own words how this increases your understanding of the concept of a rate.
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RESPONSE --> I copied the notes concerning rates and wrote some notes and I still figured the exercises the way that made sense to me...I was confused in the fact that we were calculating the CHANGE in quantity.
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13:29:35 `q005. How long does it take to earn 100 dollars at an average rate of 4 dollars per hour?
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RESPONSE --> to earn $100 at an avg rate of $4 per hour: $4/$100 shows that it will take 25 hours to earn $100.
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13:39:43 How long does it take to travel 500 miles at an average rate of 25 miles per hour?
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RESPONSE --> If you are traveling 25 mph it will take you: 500/25 = 20 hours to travel 500 miles
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13:41:01 `q006. How long does it take a rolling ball to travel 80 centimeters at an average rate of 16 centimeters per second?
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RESPONSE --> if a rolling ball is traveling an avg rate of 16 cm per sec it will take the ball: 80/16 = 5 sec to travel 80 cm
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13:41:40 In the preceding three exercises you again expanded your concept of the idea of a rate. Explain how these problems illustrate the concept of a rate.
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RESPONSE --> we used the rate divided into the change of hours to reach the answer to each problem
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Oh{v Student Name: assignment #001 001. Rates "