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The way of understanding why radians have no dimension is to look at their definition in terms of arc-length (length) divided by radius (length).verty said:
Differentiation with units- Related Rates problem
- Thread starter opus
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Homework Help Overview
The problem involves a spherical balloon being filled with air at a constant rate of 2 cm³/sec, and the inquiry focuses on determining how fast the radius of the balloon is increasing when the radius is 3 cm. The subject area pertains to related rates in calculus, specifically involving differentiation and unit analysis.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants discuss the differentiation of the volume function and the treatment of units during this process. Questions arise regarding the omission of units in the differentiation step and the subsequent introduction of units in the final expressions. There is also exploration of why units are separated in the resulting equations.
Discussion Status
The discussion is ongoing, with participants providing insights into the differentiation process and unit handling. Some participants express confusion about the treatment of units, while others offer clarifications regarding the dimensional consistency of the equations presented. There is no explicit consensus yet, as participants continue to explore the nuances of the problem.
Contextual Notes
Participants note that the problem is derived from a textbook and express concerns about the clarity of the unit treatment in the provided equations. There is an acknowledgment of potential oversights in the text regarding unit representation.
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