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.
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
A vector with magnitude 5 points in a direction 190 degrees counterclockwise from the positive x axis.
Write the vector in component form, and show your answers accurate to 3 decimal places.
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