course mth 163 ????????z??assignment #001001. `query1
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17:19:59 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 --> I found all the math needed for the fish pond surprising; I don't think I would have thought about all those different factors on my own. I also liked the explanation for why math is important (because being able to do math keeps us from being helpless and relying solely on computers to do everything for us). I guess it's like exercise for your logic...if you never do things for yourself, you're going to atrophy.
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17:24:43 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 --> It's changing at a slower and slower rate. The change in the depth decreased more and more as time went on, meaning it was taking longer for the same amount of water to flow out.
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17:25:18 ** 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 --> okay
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17:27:07 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 --> The graph is decreasing. The rate of decrease is slowing down. My graph doesn't cross the x or y axist, and is a slight curve downward.
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17:31:15 ** 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 --> Oh, yeah, I forgot that since it begins at time = 0, it is on the y axis, and that it has to end with depth = 0, making it on the x-axis. My graph looks more like it's curving down, but looking at it now, I think that's because i didn't connect the points very well.
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???????????assignment #001 ????????z??Precalculus I 09-10-2006 "