course Mth 163 ¬ٖ_Hhɼ˝assignment #001
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10:46:39 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 --> How you can find the function or mathematical model for a graph. Just by using 3 points on a graph you can find the function that goes with the graph to make it easier to draw the graph. confidence assessment: 1
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10:48:00 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 --> The depth is changing at a slower rate. Using the change in depth compared to the change in time, we can see that between each 10 cm the depth changes it takes a few more seconds. confidence assessment: 2
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10:48:47 ** 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 --> Yes, either way you measure the change, depth by time or time by depth, you can conclude from both that the rate is slower. self critique assessment: 2
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10:56:14 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 half of a parabola, starting higher on the y-axis and sloping down till it's running along the x-axis. The graph is decreasing. I would say that the rate of the decrease slows down with respect to the change in time, there's more time in between the change in depth. When starting out the graph would start at the y axis, it does not intercept it. The graph does not intercept the x axis, once all the water is out the graph will end on the x axis. The overall shape is a stretched out parabola, like a hill on a rollercoaster, it evens out at the end of the hill but starts out up high. confidence assessment: 2
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10:58:59 ** 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 graph does start on the positive side of the y axis and is opened upward on the left. That would make a big difference if it wasn't opened on the left hand side. Depth may not be measured until the container is completely empty, but if the graph was finished out it would end on the x axis. self critique assessment: 2
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