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.
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.
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.