A balloon is rising vertically above a level, straight road at a constant rate of 5 11/ sec. Just when the balloon is 45 ft above the ground, a bicycle moving at a constant rate of 15 ft/ sec passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 3 seconds later? s(t) is increasing by D ft/ sec. (Simplify your answer.) 3' s(t) L _'_:-: III Iii} Coffee is draining from a conical filter into a cylindrical a. How fast is the level in the pot rising when the coffeepot at the rate of 8 in./ min. Complete parts (a) coffee in the cone is 7 in. deep? and (b). 8" (Type an exact answer, using it as needed.) 8"A light shines from the top of a pole 40 ft high. A ball is dropped from the same height from a point 20 ft away from the light. How fast is the shadow of the ball moving along the ground 1 sec later? (Assume the ball fails a distance 3 =16t2 in t sec.) The shadow is moving at a velocity of D ftlsec. (Type an integer or a decimal.) 40-ft polo . Ball at time t=0 l 1 so!) later On a morning of a day when the sun will pass directly overhead, the shadow of a 96-ft building on level ground is 40 ft long. At the moment in question. the angle 6 the sun makes with the ground is increasing at the rate of 0.24Imin. At what rate is the shadow decreasing? Remember to use radians in your calculations. Express your answer in inches per minute. The shadow is decreasing at D inches per minute. (Round to one decimal place as needed.) revolves three times each minute. As shown in the gure, P is the point on shore closest to the lighthouse and Q is a point on the shore 275 m from P. What is the A lighthouse stands 550 m off a straight shore and the focused beam of its light Lighthouse speed of the beam along the shore when it strikes the point Q? T 550 m i Q P || (I) Let x be the distance along the shore from point P to the beam and let 9 be the angle through which the light revolves. Write an equation that relates x and 8. D A spherical iron ball 10 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 13 in.3/min, how fast is the thickness of the ice decreasing when it is 3 in. thick? How fast is the outer surface area of ice decreasing? (I) Write an equation relating the volume of the sphere, V, to the thickness of the ice, x. D