......!!!!!!!!...................................
22:25:51 Query Introduction to General Themes; Examples (no summary needed) What were some of the things in this introduction that you found interesting or surprising?
......!!!!!!!!...................................
RESPONSE --> Math has always been fascinating to me. You can always apply some sort of mathematical equation to most anything that you do in daily life from walking to driving to working and so on. Most everything invloves math and to understand it helps you to understand why some things are the way they are.
.................................................
......!!!!!!!!...................................
22:25:58 ** Continue to the next question **
......!!!!!!!!...................................
RESPONSE --> Ok.
.................................................
......!!!!!!!!...................................
22:29:33 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.
......!!!!!!!!...................................
RESPONSE --> The depth is changing at a slower and slower rate. This can be supported by simply looking at the data. The depth in relation to the time decreased at a rate that though it slowed as the depth was lowered it nevertheless continued to drop. The first reading I had was at time 5.3 seconds and depth of 63.7 cm. The next reading was at 10.6 seconds and a depth of 54.8. The next data was at 15.9 seconds at 46.0 cm. Each reading has the depth decreasing and with each reading it decreases at a rate that is decreasing as well.
.................................................
......!!!!!!!!...................................
22:30:11 ** 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. **......!!!!!!!!...................................
RESPONSE --> I understand this concept.
.................................................
......!!!!!!!!...................................
22:31:43 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?
......!!!!!!!!...................................
RESPONSE --> The graph of depth vs. clock time initially takes a pretty steep drop in the first couple of readings but then there is a significant drop as to the depth as time goes on. So the line initially drops at a fairly rapid rate but then takes on a much gentler slope as the water decreases in the bottle.
.................................................
......!!!!!!!!...................................
22:32:19 ** 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. **......!!!!!!!!...................................
RESPONSE --> Ok.
.................................................
暫߁ġoh assignment # hQrQԐzՇ Precalculus I 09-11-2005