Read each problem carefully. Show your complete solution 1. Starting from the same point, Reden starts walking eastward at 60 cm/s while Neil starts running towards the south at 80 cm/s. How fast is the distance between Reden and Neil increasing after 2 seconds? 2. A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 25 meters above the water level and if the boat is approaching the cliff at 20 m/s, at what rate is the acute angle made by the telescope with the vertical changing when the boat is 250 meters from the shore? 3. A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the radius and height are both increasing at the rate of 3 cm/s and 8 cm/s, respectively. What is the rate of change of its total surface area when its radius and height are 60 cm and 140 cm, respectively? 4. If two resistors with resistance Ri and Ra are connected in parallel, the total resistance 1 R in ohms is given by R " R R2 . If Ri and R2 are increasing at 0.4 ohms/s and 0.25 ohms/s, respectively, how fast is R changing when R1 = 600 ohms and R2 = 400 ohms? 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second base is running towards third base at a speed of 28 ft/min. At what rate is the player's distance from the home plate changing? 6. Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he is walking at a speed of 1.5 m/s, how fast is the end of his shadow moving (with respect to the lamp post) when he is 6 meters away from the base of the lamp post? *7. Water is being poured at the rate of 2x m /min. into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of = m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep