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(*rihf?) Let A be the area of a circle with radius T cm. If 7- is increasing at a constant rate of 4 cm/s then when 7' = 4 cm, the area A IS Increasing at a rate of cm ls (*ri'r) The length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of 5cm/s. When the length is 30cm and the width is 20cm, how fast is the area of the rectangle increasing? a The area of the rectangle is increasing at a rate of I 7 O (*i'r) The radius r of a sphere is expanding at a rate of 14 metres per minute. Determine the rate at which the volume is changing with respect to time when 7' = 6m. E . The volume is changing at a rate of I Ins/mm. (*i'fnfti'r) An inverted cylindrical cone, 32 m deep and 16 m in diameter across the top, is being filled with water at a constant rate of 13 m3/min. At what rate is the water rising in the tank when the depth of the water is: 1 meter? Answer: 10 meters? Answer: 31 meters? Answer: (*i'dt) The pressure P and volume V of an expanding gas are related by the formula PVb = C, where b and C are constants (this model assumes adiabatic expansion, withou heat gain or loss). Find % n b : 1.4, P : 7kPa, V = 130cm2, and % = 40cm3/min. % kPa/min (*if'ri'r) If f is the focal length of a convex lens and an object is placed at a distancep from the lens, then its image will be at a distance qfrom the lens, where f, p, and qare related by the lens equation 1 1 1 qu What is the rate of change ofp with respect to q if q = 2 m and f = 4 m? (Make sure you have the correct sign for the rate.) 77:: .m/s