Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 32R
There is a point (p,q) on the graph of f(x)=x2 and a point (r,s) on the graph of g(x)=x−8,wherep>0andr>0. If the line through (p,q)and(r,s) is also tangent to both the curves at these points, respectively, then the value of P+r is_________.
A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/m∈ . When the thickness of ice is 5cm, then find the rate at which the thickness of ice decreases.