1. Two sides of a triangle have lengths 2 m and 3 m.The angle between them is increasing at a rate of 0.2 rad/min.How fast is the area increasing when the angle between the sides of fixed length is/3?
2. The angle of elevation of the sun is decreasing at a rate of 1/4 rad/h.How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is/6?
3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station.Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station?
4. planeflyingwithaconstantspeedof300km/hpassesoveragroundradar station at an altitude of 1 km and climbs at an angle of 30.At what rate is the distance from the plane to the radar station increasing a minute later?