Display Title

Closed Captioned Video: Algebra Applications: Rational Functions

Closed Captioned Video: Algebra Applications: Rational Functions

Topic

Rational Functions

Description

This video explores the application of rational functions across three diverse domains. It begins by examining the relationship between pressure and volume in submarines, showcasing how water pressure impacts vessel integrity and the importance of rational functions in predicting safe depths. The analysis extends to scuba diving safety, highlighting how pressure-volume relationships inform practices to avoid conditions like the bends. Next, the video delves into surface area-to-volume ratios in animals, linking these ratios to evolutionary adaptations. Using rational functions, it demonstrates why larger animals like polar bears retain heat better in cold climates, while smaller animals or those with larger surface areas, such as snakes, efficiently lose heat in warmer regions. Finally, the video focuses on the optics of the Hubble Space Telescope, illustrating how lens properties and the concept of asymptotes in rational functions enhance image clarity for distant objects. The discussion includes focal length, object distance, and image distance, emphasizing the mathematical constraints and resolutions that make the Hubble an invaluable tool for deep-space observation. This comprehensive exploration of rational functions ties mathematical concepts to real-world applications in engineering, biology, and astronomy.

The relevance of this video to the topic of Rational Functions lies in its ability to contextualize mathematical concepts with real-world applications, making it easier for students to grasp abstract ideas.

Teacher's Script: Today, we’ll watch a video on Rational Functions. This video explores the application of rational functions across three diverse domains. It begins by examining the relationship between pressure and volume in submarines, showcasing how water pressure impacts vessel integrity and the importance of rational functions in predicting safe depths. The analysis extends to scuba diving safety, highlighting how pressure-volume relationships inform practices to avoid conditions like the bends. Next, the video delves into surface area-to-volume ratios in animals, linking these ratios to evolutionary adaptations. Using rational functions, it demonstrates why larger animals like polar bears retain heat better in cold climates, while smaller animals or those with larger surface areas, such as snakes, efficiently lose heat in warmer regions. Finally, the video focuses on the optics of the hubble space telescope, illustrating how lens properties and the concept of asymptotes in rational functions enhance image clarity for distant objects. The discussion includes focal length, object distance, and image distance, emphasizing the mathematical constraints and resolutions that make the Hubble an invaluable tool for deep-space observation. This comprehensive exploration of rational functions ties mathematical concepts to real-world applications in engineering, biology, and astronomy, connecting these concepts to real-world scenarios. As you watch, consider how this applies to what we’ve been learning about rational functions.

For a complete collection of videos related to Rational Functions click on this link: Algebra Applications: Rational Functions Collection.

Common Core Standards CCSS.MATH.CONTENT.HSF.IF.C.7.D, CCSS.MATH.CONTENT.7.NS.A.3
Duration 21.42 minutes
Grade Range 6 - 9
Curriculum Nodes Algebra
    • Rational Expressions and Functions
        • Rational Expressions
        • Rational Functions and Equations
Copyright Year 2020
Keywords algebra, rational functions, applications of rational functions, Closed Captioned Video