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a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. dr Use the chain rule for differentiation to find an expression for in terms of r, where t is dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.

a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. dr Use the chain rule for differentiation to find an expression for in terms of r, where t is dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 9CR
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Part b and d onl

a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. Use the chain rule for differentiation to find an expression for in terms of r, where t is dr dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.
Transcribed Image Text:a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. Use the chain rule for differentiation to find an expression for in terms of r, where t is dr dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.
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