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(*sfrsi'z) At noon, ship A is 1001011 west of ship B. Ship A is sailing south at 20km/h and ship B is sailing north at 30km/h. How fast is the distance between the ships changing at 4200pm? The distance between the ships is changing at a rate of a - kilometers per hour. (*Vkrir) Consider the growth of a cell, assumed to be spherical in shape. Suppose that the radius of the cell, 1-, increases at a constant rate per unit time. (Call the constant Re.) Express your answers in terms of the radius of the cell 1' and its growth rate k. (a) At what rate does the volume, V, increase ? w dt _ (b) At what rate does the surface area, 5', increase ? dt _ (c) At what rate does the ratio of surface area to volume S/V change? av]: $7 0 Does the ratio S/V decrease or increase as the cell grows? '? (*'ki'fn' In 1905 a Bohemian farmer accidentally allowed several muskrats to escape an enclosure. Their population grew and spread, occupying increasingly larger areas throughout Europe. In a classical paper in ecology, it was shown by the scientist Skellam (1951) that the square root of the occupied area increased at a constant rate, 1:. Determine the rate of change of the distance (from the site of release) that the muskrats had spread. For simplicity, you may assume that the expanding area of occupation is circular, with radius r(t). Simplify your answer so that it only depends on k. 1" (t) = (*i'rsr) Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is GmM F: 7'2 2 where G is the gravitational constant and 1- is the distance between the bodies. 8 (a) Find dF/dq' : I. [What does the minus sign mean?] (b) Suppose it is known that Earth attracts an object with a force that decreases at a rate of 2 N/km when r = 20000 km. How fast does this force change when 7' = 10000 km? E The force changes at a rate of I N/km