course Mth 163 Precalculus I07-15-2008
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11:00:42 Symbolic calculation of slope, preliminary exercise What was the function, between which two points were you to calculate the average slope and how did you get this slope?
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RESPONSE --> The function used was y = .1x^2 - 3, the x values were x = -2 and x = 7. The y values are: y = .1(-2^2) - 3 = -2.6 y = .1(7^2) - 3 = 1.9 The rise would be 1.9 - -2.6 = 4.5 The run would be 7 - -2 = 9 So we would find the slope as 4.5 / 9 = 0.5 confidence assessment: 2
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11:03:21 ** For the function y = .1 x^2 - 3 between x = -2 and x = 7 we get: slope = (y2 - y1) / (x2 - x1). For x1 = 2 and x2 = 7 we have y2 = .1 * 7^2 - 3 = 1.9 and y1 = .1 * 2^2 - 3 = -2.6, so slope = (1.9 - (-2.6) ) / ( 7 - 2) = 4.5 / 5 = .9. **
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RESPONSE --> I thought the slope should be 0.5 because the 2 was supposed to be negative. self critique assessment: 3
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14:08:41 problem 2 symbolic expression for slope, fn depth(t). What is the expression for the slope between the two specified t values?
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RESPONSE --> If we use the two values for t = 10 and t = 30 for the function y = depth(t) we can find the slope. So if y = depth(t) when t = 10, y = 10 and when t = 30, y will equal 30 because y = depth(t). The expression of the slope would be (y30 - y10) / (x10 - x 30) confidence assessment: 1
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14:10:50 ** The function is given a name: depth(t). t values are 10 and 30. So rise = depth(30) - depth(10) and run = 30 - 10 = 20. Thus slope = [ depth(30) - depth(10) ] / 20 . **
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RESPONSE --> I was making it more complicated than what it was I guess. I see that if we're given a function of depth(t) and values we can express the slope using that function. self critique assessment: 3
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14:12:36 ** The rise is the change in depth. The two depths are depth(10) and depth(30). The change in depth is final depth - initial depth, which gives us the expression depth(30)-depth(10) **
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RESPONSE --> I don't know what the program did but the answer came up before I even typed an answer in. The rise is the difference in two depths and from the previous problem the two depth measurements are depth(10) and depth(30). self critique assessment: 2
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14:13:24 What is the run between the two specified t values?
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RESPONSE --> The run is the change in time. We were given the two clock times of 10 and 30. 30 - 10 = 20 which is the run confidence assessment: 2
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14:13:31 ** run = 30 - 10 = 20 **
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RESPONSE --> ok self critique assessment: 3
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14:14:48 What therefore is the slope and what does it mean?
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RESPONSE --> The slope is the change in depth over the change in time. On a graph it describes how the line changes from one point to another. The slope give the average rate change of coordinates. confidence assessment: 1
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14:15:33 ** rise = depth(30)-(depth(10) indicates change in depth. run = 30 - 10 = 20 = change in clock time. Slope = rise / run = (depth(30) - depth(10) ) / 20, which is the average rate at which depth changes with respect to clock time between t = 10 and t = 30. **
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RESPONSE --> I didn't say depth(30) - depth(10) / 20 was the specific slope for this expression, but I did know that. self critique assessment: 3
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14:21:07 problem 5 graph points corresponding to load1 and load2 What are the coordinates of the requested graph points?
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RESPONSE --> The coordinates for the function y = springLength(load) with Load1 = 3 and Load2 = 10 would be: (3, springLength(load3) and (10, springLength(load10) confidence assessment: 1
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14:23:09 ** The horizontal axis is the 'load' asix, the vertical axis is the springLength axis. The load axis coordinates are load1 and load2. The corresponding spring lengths are springLength(load1) and springLength(load2). The springLength axis coordinates are springLength(load1) and springLength(load2). The graph points are thereofore (load1, springLength(load1) ) and (load2, springLength(load2) ). **
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RESPONSE --> I was using the information from the Exercise2-3 #3 for the springLength(load) but I understand this. self critique assessment: 3
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14:25:22 What is your expression for the average slope of the graph between load1 and load2?
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RESPONSE --> The average slope for the graph would be [(springLength(load2) - springLength(load1)] / load2 - load1 confidence assessment: 1
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14:25:31 ** rise = springLength(load2) - springLength(load1) run = load2 - load1 so slope = [ springLength(load2) - springLength(load1)] / (load2 - load1). **
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RESPONSE --> ok self critique assessment: 3
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14:28:45 ** the name of the function is depth(t). We need the slope between t = t1 and t = t2. The depths are depth(t1) and depth(t2). Thus rise is depth(t2) - depth(t1) and run is t2 - t1. Slope is [ depth(t2) - depth(t1) ] / (t2 - t1). **
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RESPONSE --> The slope of depth function is easily expressed as depth(t1) and depth(t2). Knowing this information we could find the slope using the rise and run. Rise = depth(t2) - depth(t1) and run t2 - t1. Slope (depth(t2) - depth(t1)) / t2 - t1 self critique assessment: 2
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14:50:34 problem 8 average rate from formula f(t) = 40 (2^(-.3 t) ) + 25 intervals of partition (10,20,30,40) What average rate do you get from the formula? Show your steps.
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RESPONSE --> y = f(t) = 40(2^-.3t)) + 25, so when t = 10: f(10) = 40(2^(-.3*10)) + 25 = 30 f(20) = 40(2^(-.3*20)) + 25 = 25.625 f(30) = 40(2^(-.3*30)) + 25 = 25.078 f(40) = 40(2^(-.3*40)) + 25 = 25.0098 Our average for the first two times is (25.625 - 30) / 10 = -0.4375 Then second two times we get (25.078 - 25.625) / 10 = -0.05469 The last two times have a rate of (25.0098 - 25.078) / 10 = -0.068 confidence assessment: 1
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14:51:10 ** ave rate = change in depth / change in t. For the three intervals we get (f(20)-f(10))/(20-10) = (25.625 - 30 )/(20 - 10) = -4.375 / 10 = -.4375 (f(30)-f(20))/(30-20) = (25.07813 - 25.625)/(30 - 20) = -.5469 / 10 = -.05469. (f(40)-f(30))/(40-30) = (25.00977 - 25.07813)/(40 - 30) = -.0684 / 10 = -.00684. **
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RESPONSE --> ok self critique assessment: 3
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14:51:16 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> self critique assessment: 3
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14:51:23 STUDENT RESPONSE: Ummm I know the slope formula is (y2-y1)/(x2-x1), but I always just put the number into the expression in the order I see them, but that is ok because I keep the order and get the correct answere because the y2,y1,x2,x1 or all relative. I am correct in doing this? INSTRUCTOR COMMENT: In other words you use (y1 - y2) / (x1 - x2) instead of (y2 - y1) / (x2 - x1). It's more conventional to regard, say, 10 as x1 and 20 as x2, so f(20) is y2 and f(10) is y1. If you start from the lower x number and change to the higher the difference is higher - lower, and this is the way we usually think about changes. According to this convention we calculate change in y as y2 - y1 and change in x as x2 - x1. You are doing (y1 - y2) / (x1 - x2) and you get a negative change in x, a negative denominator, and if you are thinking about change from the first quantity to the second this is backwards. However as you say both numerator and denominator follow the same order so you still get the right answer, since (y1-y2)/(x1-x2)= (y2-y1) / (x2-x1). **
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RESPONSE --> self critique assessment: 3
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assignment #009 009. Precalculus I 07-15-2008
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10:15:09 `q001. Note that this assignment has 2 questions For the function y = 1.1 x + .8, what are the coordinates of the x = x1 point, in terms of the symbol x1? What are the coordinates of the x = x2 point, in terms of the symbol x2? What therefore is the rise between these two points, and what is the run? What is the average slope of the graph between these two points? Be sure to simplify your result.
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RESPONSE --> When x = x1 we find: y = 1.1(x1) + .8 When x = x2 we find: y = 1.1(x2) + .8 Our coordinates are (x1, 1.1x1 + .8) and (x2, 1.1x2 + .8). The rise would be (1.1x2 + .8) - (1.1x1 + .8) = 1.1x2 - 1.1x1 The run would be x2 - x1. We would find the slope to be (1.1x2 - 1.1x1) - (x2 - x1) = 1.1 - 1.1 or 0 confidence assessment: 1
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10:16:24 In terms of the symbol x1 the coordinates of the x = x1 point are ( x1, 1.1 x1 + .8) and the coordinates of the x = x2 point are ( x2, 1.1 x2 + .8). The rise between the two points is therefore rise = (1.1 x2 + .8) - (1.1 x1 + .8) = 1.1 x2 + .8 - 1.1 x1 - .8 = 1.1 x2 - 1.1 x1. The run is run = x2 - x1. The slope is therefore (1.1 x2 - 1.1 x1) / (x2 - x1) = 1.1 (x2 - x1) / (x2 - x1) = 1.1.
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RESPONSE --> I see how I got the slope wrong, it does make sense that it would be 1.1. self critique assessment: 2
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10:33:46 `q002. For the function y = 3.4 x + 7, what are the coordinates of the x = x1 point, in terms of the symbol x1? What are the coordinates of the x = x2 point, in terms of the symbol x2? What therefore is the rise between these two points, and what is the run? What is the average slope of the graph between these two points? Be sure to simplify your result.
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RESPONSE --> The coordinates for the x values would be: y = 3.4x1 + 7 (x1, 3.4x1 + 7) y = 3.4x2 + 7 (x2, 3.4x2 + 7) The rise would be (3.4x2 + 7) - (3.4x1 + 7) = 3.4x2 - 3.4x1 The run would be x2 - x1 The slope would be (3.4x2 - 3.4x1) / (x2 - x1) = 3.4(x2 - x1)/(x2 - x1) = 3.4 confidence assessment: 2
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10:34:03 In terms of the symbol x1 the coordinates of the x = x1 point are ( x1, 3.4 x1 + 7) and the coordinates of the x = x2 point are ( x2, 3.4 x2 + 7). The rise between the two points is therefore rise = (3.4 x2 + 7) - (3.4 x1 + 7) = 3.4 x2 + 7 - 3.4 x1 - 7 = 3.4 x2 - 3.4 x1. The run is run = x2 - x1. The slope is therefore (3.4 x2 - 3.4 x1) / (x2 - x1) = 3.4 (x2 - x1) / (x2 - x1) = 3.4.
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RESPONSE --> ok self critique assessment: 3
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