course Mth 163 I have alot of trouble with this assignment. I'm going to go back and review. I wanted to send you what I have done so the work isn't lost. Sorry for the inconvenence. query problem 2. ave rates at midpoint timeswhat is the average rate of depth change for the 1-second time interval centered at the 50 sec midpoint?
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17:13:19 Query 4 basic function families What are the four basic functions? What are the generalized forms of the four basic functions?
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RESPONSE --> Linear, quadratic, general exponential, and power funtion Linear y=f(x)= mx+b (slope-intercept form) Quadratic y=f(x)=ax^2+bx+c Exponential y=f(x)=2^x Power function y=f(x)=x^p confidence assessment: 2
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17:13:40 ** STUDENT RESPONSE: Linear is y=mx+b Quadratic is y=ax^2 + bx +c Exponential is y= A*2^ (kx)+c Power = A (x-h)^p+c INSTRUCTOR COMMENTS: These are the generalized forms. The basic functions are y = x, y = x^2, y = 2^x and y = x^p. **
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RESPONSE --> ok self critique assessment: 3
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17:27:25 For a function f(x), what is the significance of the function A f(x-h) + k and how does its graph compare to that of f(x)?
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RESPONSE --> A f(x-h) +k is the graph of f(x) shifted to the right h units, vertically shifted up k units and either vertically shrunken (0
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17:28:24 ** STUDENT RESPONSE: A designates the x strectch factor while h affects a y shift & k affects an x shift INSTRUCTOR COMMENTS: k is the y shift for a simple enough reason -- if you add k to the y value it raises the graph by k units. h is the x shift. The reason isn't quite as simple, but not that hard to understand. It's because when x is replaced by x - h the y values on the table shift 'forward' by h units. A is a multiplier. When all y values are multiplied by A that moves them all A times as far from the x axis, which is what causes the stretch. Thus A f(x-h) + k is obtained from f(x) by vertical stretch A, horizontal shift h and vertical shift k. The two aren't the same, but of course they're closely related. **
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RESPONSE --> ok self critique assessment: 2
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17:29:48 query introduction to rates and slopes, problem 1 ave vel for function depth(t) = .02t^2 - 5t + 150 give the average rate of depth change from t = 20 to t = 40
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RESPONSE --> I don't understand what your asking. What is ""ave vel""? confidence assessment: 3
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17:32:13 ** depth(20) = .02(20^2) - 5(20) + 150 = 58 depth(40) = .02(40^2) - 5(40) + 150 = -18 change in depth = depth(40) - depth(20) = -18 - 58 = -76 change in clock time = 40 - 20 = 20. Ave rate of depth change = change in depth / change in clock time = -76 / 20 = -3.8 **
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RESPONSE --> I understand this process, but the question still doesn't make sense to me. self critique assessment: 3
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17:33:22 What is the average rate of depth change from t = 60 to t = 80?
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RESPONSE --> Obviously this pertains to the previous question that I didn't understand. Sorry. confidence assessment: 3
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17:34:45 ** depth(60) = .02(60^2) - 5(60) + 150 = -78 depth(80) = .02(80^2) - 5(80) + 150 = -122 change in depth = depth(80) - depth(60) = -122 - (-78) = -44 change in clock time = 40 - 20 = 20. Ave rate of depth change = change in depth / change in clock time = -44 / 20 = -2.2 **
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RESPONSE --> I see that you take the slope of a function from one point the next point in time. The average is a linear change. self critique assessment: 2
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17:47:51 describe your graph of y = .02t^2 - 5t + 150
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RESPONSE --> Upward facing parabola with a vertex at (125,-162 1/2) confidence assessment: 1
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17:48:56 ** The graph is a parabola. y = .02t^2 - 5t + 150 has vertex at x = -b / (2a) = -(-5) / (2 * .02) = 125, at which point y = .02 (125^2) - 5(125) + 150 = -162.5. The graph opens upward, intercepting the x axis at about t = 35 and t = 215. Up to t = 125 the graph is decreasing at a decreasing rate. That is, it's decreasing but the slopes, which are negative, are increasing toward 0.**
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RESPONSE --> sorry forgot to include where the graph intercepts at the x axis self critique assessment: 2
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17:51:50 describe the pattern to the depth change rates
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RESPONSE --> Apparently I've missed something because I'm not sure what your asking. confidence assessment: 3
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17:53:55 ** Rates are -3.8, -3 and -2.2 for the three intervals (20,40), (40,60) and (60,80). For each interval of `dt = 20 the rate changes by +.8. **
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RESPONSE --> I'm going to go back and review because I've missed something. self critique assessment: 3
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