Math Problem Statement
The accompanying table shows eleven altitudes (in thousands of feet) and the speeds of sound (in feet per second) at these altitudes. Complete parts (a) through (d) below.
Altitude, x
Speed of sound, y
00
1116.61116.6
55
1095.61095.6
1010
1077.41077.4
1515
1057.21057.2
2020
1037.11037.1
2525
1014.91014.9
3030
994.3994.3
3535
968.3968.3
4040
968.5968.5
4545
968.5968.5
5050
968.5968.5
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(a) Display the data in a scatter plot. Choose the correct graph below.
Solution
matplotlib.pyplot as plt
Data for the scatter plot
altitude = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50] speed_of_sound = [1116.6, 1095.6, 1077.4, 1057.2, 1037.1, 1014.9, 994.3, 968.3, 968.5, 968.5, 968.5]
Creating the scatter plot
plt.figure(figsize=(8, 6)) plt.scatter(altitude, speed_of_sound, c='blue', label="Speed of Sound") plt.title("Scatter Plot of Altitude vs Speed of Sound") plt.xlabel("Altitude (thousands of feet)") plt.ylabel("Speed of Sound (feet per second)") plt.grid(True) plt.legend() plt.show()The scatter plot displays the relationship between altitude (in thousands of feet) and the speed of sound (in feet per second). The data points show a general decrease in speed with increasing altitude, leveling off around 968.5 feet/second for altitudes above 35,000 feet.
Would you like details on interpreting the plot or have further questions? Here are five related questions:
- How does the speed of sound generally vary with altitude?
- Can we fit a trendline or regression model to this data?
- At what altitude does the speed of sound stabilize?
- Is there a theoretical explanation for the leveling off of the speed of sound?
- How does temperature or pressure affect the speed of sound at these altitudes?
Tip: In physics, the speed of sound decreases with altitude primarily due to lower temperatures, which affect air density.
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Math Problem Analysis
Mathematical Concepts
Data Visualization
Scatter Plots
Relationship Analysis
Formulas
None (focus on data representation)
Theorems
None (conceptual understanding of data trends)
Suitable Grade Level
Grades 9-12