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  • https://math.libretexts.org/Courses/Georgia_State_University_-_Perimeter_College/MATH_2215%3A_Calculus_III/12%3A_Vectors_and_the_Geometry_of_Space/12.7E%3A_Exercises_for_Cylindrical_and_Spherical_Coordinates
    60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and \( n\...60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and n are positive integers, may be used in applied mathematics to model tumor growth. Show that the “bumpy sphere” is contained inside a sphere of equation ρ=a+b. Find the values of θ and φ at which the two surfaces intersect.
  • https://math.libretexts.org/Courses/Misericordia_University/MTH_226%3A_Calculus_III/Chapter_12%3A_Vectors_and_the_Geometry_of_Space/12.7E%3A_Exercises_for_Cylindrical_and_Spherical_Coordinates
    60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and \( n\...60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and n are positive integers, may be used in applied mathematics to model tumor growth. Show that the “bumpy sphere” is contained inside a sphere of equation ρ=a+b. Find the values of θ and φ at which the two surfaces intersect.
  • https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/12%3A_Vectors_and_the_Geometry_of_Space/12.7%3A_Cylindrical_and_Spherical_Coordinates/Exercises_for_Cylindrical_and_Spherical_Coordinates
    60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and \( n\...60) [T] The “bumpy sphere” with an equation in spherical coordinates is ρ=a+bcos(mθ)sin(nφ), with θ[0,2π] and φ[0,π], where a and b are positive numbers and m and n are positive integers, may be used in applied mathematics to model tumor growth. Show that the “bumpy sphere” is contained inside a sphere of equation ρ=a+b. Find the values of θ and φ at which the two surfaces intersect.

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