Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x = 0 corresponds to 6 A.M. Time, x Temperature, y 0 34 2 50 4 60 6 64 8 63 10 59 12 53 14 46 16 40 18 36 20 34 22 37 24 45 These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24 (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperature during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x = 0 corresponds to 6 A.M. Time, x Temperature, y 0 34 2 50 4 60 6 64 8 63 10 59 12 53 14 46 16 40 18 36 20 34 22 37 24 45 These data can be approximated by the model y = 0.026 x 3 − 1.03 x 2 + 10.2 x + 34 , 0 ≤ x ≤ 24 (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperature during this 24-hour period. (e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where
x
=
0
corresponds to 6 A.M.
Time, x
Temperature, y
0
34
2
50
4
60
6
64
8
63
10
59
12
53
14
46
16
40
18
36
20
34
22
37
24
45
These data can be approximated by the model
y
=
0.026
x
3
−
1.03
x
2
+
10.2
x
+
34
,
0
≤
x
≤
24
(a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window.
(b) How well does the model fit the data?
(c) Use the graph to approximate the times when the temperature was increasing and decreasing.
(d) Use the graph to approximate the maximum and minimum temperature during this 24-hour period.
(e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.
Explain the conditions under which the Radius of Convergence of the Power Series is a "finite positive real number" r>0
This means that when the Radius of Convergence of the Power Series is a "finite positive real number" r>0, then every point x of the Power Series on (-r, r) will absolutely converge (x ∈ (-r, r)). Moreover, every point x on the Power Series (-∞, -r)U(r, +∞) will diverge (|x| >r). Please explain it.
Explain the conditions under which Radious of Convergence of Power Series is infinite. Explain what will happen?
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