A spherical balloon currently has a radius of 18 mm. If the radius is still growing at a rate of 5 mm per second, at what rate is air being pumped into the balloon? Round your answer to the nearest hundredth. A balloon is rising at a rate of 2 meters per second from a point on the ground 60 meters from an observer: Find the rate of change of the angle of elevation from the observer to the balloon when the balloon is 31 meters above the ground. An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 9 cm. Find the rate at which the water level is rising when the water level is 3 cm. b1 b2 r At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PVl'4 = C where C is a constant. Suppose that at a certain instant the volume is 600 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 12 kPa/ minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? 3 :J \"m min (Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. ) Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 16 centimeters per minute when the height of the water is 1.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. 3 :3 mm \fFind the slope of the tangent line to the curve 9:2 arctan(a:) = e\" at the point (2, 1.488)