Q1:

The circulation time of a mammal (the average time it takes for all the blood in the body to circulate once and return to the heart) is proportional to the fourth root of the body mass of the mammal. Circulation time, T, is measured in seconds and body mass, m, is measured in kilograms. (a) If the proportionality constant is 17.6, write a formula for the circulation time of a mammal. Use a lower case In. T(m) = X (b) The body mass of a growing child is 39 kg and is increasing at a rate of 0.3 kg/month. What is the rate of change of the circulation time of the child? Round your answer to 3 decimal places. sec/month Sand falls from a hopper at a rate of 0.2 cubic meters per hour and forms a conical pile beneath. Suppose the radius of the cone is always half the height of the cone. (a) Find the rate at which the radius of the cone increases when the radius is 3 meters. x meters per hour (b) Find the rate at which the height of the cone increases when the radius is 3 meters. x meters per hour A pyramid has height h and a square base with side x. The volume of a pyramid is V = xzh. If the height remains xed and the side of the base is decreasing by 0.002 meter/yr, what rate is the volume decreasing when the height is 120 meters and the width is 150 meters? meters3/year