1. A ladder 5m long is leaning against a wall. If the lower end of ...

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1. A ladder 5m long is leaning against a wall. If the lower end of the ladder slides away from the wall at a rate of 0.5 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 4 m from the base of the wall? 2. Water is flowing into a vertical cylindrical tank of diameter 6 m at the rate of 5 m3/min. Find the rate at which the depth of the water is rising. 3. A girl flies a kite at a height 30 m above her hand. If the kite flies horizontally away from the girl at the rate of 2 m/sec, at what rate is the string of the kite being let out when the length of the string is 70 m. 4. A spherical balloon filled with gas has a leak that causes the gas to escape at a rate of 1.5 m3/min. At what rate is the surface area of the balloon shrinking when the radius is 4 m? 5. A revolving light, located 5 km from a straight shoreline, turns at a constant speed of 3 rad/min. With what speed is the spot of light moving along the shore when the beam makes an angle of 60o with the shoreline? (Hint: Make sure you are working in radians.)

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