Periodicity of algebraic models | Mathematics III | High School Math | Khan Academy

TL;DR

Divya takes approximately 60 seconds to complete one revolution on the Ferris Wheel, while the electrical activity of Finn's heart peaks every 0.9 seconds.

Transcript

• [Voiceover] We're told Divya is seated on a Ferris Wheel at time t equals zero. The graph below shows her height h in meters, t seconds after the ride starts. So at time equals zero, she is, looks like about two, what is this, this would be one and a half, so it looks like she's about two meters off the ground and then as time increases, she gets... Read More

Key Insights

• ❓ Divya completes one revolution on the Ferris Wheel in approximately 60 seconds.
• 🥰 Finn's heart experiences cyclical electrical activity with peaks every 0.9 seconds.
• ⌛ Graphs can be used to represent and analyze height, time, and electrical activity.
• 🥰 The best graph representation for Finn's heart activity is the one showing peaks every 0.9 seconds.

Questions & Answers

Q: How long does it take Divya to complete one revolution on the Ferris Wheel?

Divya takes approximately 60 seconds to complete one revolution on the Ferris Wheel. At the beginning, she is at the bottom, reaches the top, and continues rotating until she returns to the bottom again.

Q: What does the electrical activity of Finn's heart look like over time?

Finn's heart experiences cyclical electrical activity, peaking every 0.9 seconds. The graph that represents this situation would show peaks that occur consistently every 0.9 seconds.

Q: Which graph best represents the electrical activity of Finn's heart?

The graph that best represents the electrical activity of Finn's heart is choice C. It shows peaks that occur slightly less than every one second, close to every 0.9 seconds.

Q: How can we verify that the graph for Finn's heart activity is correct?

To verify the correctness of the graph, we can count the number of peaks within a specific time frame. In this case, if the peaks occur every 0.9 seconds, there should be four peaks within 3.6 seconds. Comparing this to the graph can help confirm the accuracy of the representation.

Summary & Key Takeaways

• Divya starts at a height of 2 meters on the Ferris Wheel, reaches a height of 34 meters, and then returns to 2 meters, completing one revolution in approximately 60 seconds.

• Finn's heart experiences cyclical electrical activity, peaking every 0.9 seconds, as observed by a doctor over time.