For unlimited access to Homework Help, a Homework+ subscription is required.
Consider the surface of a torus with inner radius 1 and outer radius 3(imagine a donut, with donut hole of radius 1 and outer donut edge radius of 3) defined by the parameterization (*Picture*).
a) Give a normal vector to the surface of the torus.
b) Compute the surface area of the torus.
consider a rubber washer that is being compressed. the outer diameter is 4cm. the inner diameter is 1. the thickness of the washer is decreasing at 1/5 cm/minute; and the outer diameter is increasing at a rate of 1/3cm/minute. if the volume of the washer remains pi cubic cm. what rate is the inner diameter changing at the time the measurements are made
The long bones in mammals my be represented as hollow cylindrical tubes, filled with marrow, of outer radius R and inner radius r. Bones should be constructed to be lightweight yet capable of withstanding certain bending moments. In order to windstand a bending moments M, it can be shown that the mass m per unit lenght of the bone and marrow is given by. m= piÃp[M/(K(1-x^4))]^2/3 Ã [1-(1/2)Ã x^2] Wher p is the density of the bone and k is a positive constant. If x=r/R, show that m is a minimum when r=0.63R