Difeientiation Rules CHAPTER 3 250 the sape of a cone whose hae diame dhe always equl How fast is the height of dhe pile incrca when the poe is 10 t big 21 The altinke of a triangie is increasing ar a rate of 1 cm/min while the area of the triangle is increasing ar a rate of Zcmmin A what cate is the hase of the triangie changing when the altitude n 10 cm and the area is 100 cm 22 A boot is pulled into a dock by a rope aitached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat II the rope is pulied in at a ate of I m/s how fast is the boar approsching the dock when it is 8 mn from the dock? 30. A kite 10 ft above the ground moves horizontally at a speed of8 n/s Al what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? 23. At noon ship A is 100 km west of ship B. Ship A is sading sath at 35 km/h and ship B is sailing north at 25 km/h How fast is the distance berween the stups changing at 4.00 PM 31. The sides of an equilateral triangle are increasing at a rate of 10 cm/min At what rate is the area of the trangle increasing when the sides are 30 cm long? 2 sunfx/2) As the 24. A particle moves along the curve y particle passes through the point (1,ts rcoordinate increases at a nte ofy 10 cm/s How fast is the distance from the particle to the origin changing ut this instant 32. How fast is changing in Example 2 when the bottom of the ladder is 6 ft from the wall? angle between the ladder and the ground 25. Water is leaking out of an inverted.conical tank at a rale of 10.000 cm min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. Jf the water level is nising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at whoch water is being pumped into the tank 33. The top of a ladder slides down a vertical wall at a rale of 0.15 m/s At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 02 m/s How long is the ladder? 26. A tough is 10 h long and its ends have the shape of isos celes triangles that are 3 ft acrosS at the top and have a height of I ft.If the trough is being filled with water at a rate of 12 ftmn,how fast is the water level nising when the water is 6 inches deep 34. According to the model we used to solve Example 2 what happens as the top of the ladder approaches the ground? ts the model appropriate for small values of y? 35. If the minute hand of a clock has leneth c in cet