(6) (Bonus) Determine the Cartesian equation of the surface with spherical coordinate equation rho = 2 cos θ sin φ − 2 sin θ sin φ + 2 cos φ. It turns out this describes a sphere. What is the center and radius of this sphere?

Hence, the sphere has a radius of  and is centered at the point (1,-1,1)

Step-by-step explanation:

We have the equation

We have to take into account the relation between coordinates

by substituting we have:

We have to complete squares:

Hence, the sphere has a radius of  and is centered at the point (1,-1,1)

hope this helps!!

b). 4320 have a nice day

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)