(a) HA is the area of a circle with radius r and the circle expands as time passes, find % in terms of %. d_A : 1 dt (it (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how f the radius is 27 m? rnzls Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cmzls) is the area of the square increasing when the area of the square is 81 cm2? x was The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm? (Round your answer to two decimal places.) mm3/s H++=s\":mmm:mmEMmumd=01AL dt dt d: The weight w or an astronaut (in pounds) is related to her height h above the surface of the earth (in miles) by 3960 2 W = W0 3960 + h where \"'0 is the weight of the astronaut on the surface of the earth. If the astronaut weighs 135 pounds on earth and is in a rocket, being propelled upward at a speed of 11 mils, find the rate at which her weight is changing (in lb/s) when she is 30 miles above the earth's surface. (Round your answer to four decimal places.) :llb/s A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base with a speed of 30 ft/s. $90 ft (a) At what rate (in ft/s) is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) ft/s (b) At what rate (in ft/s) is his distance from third base increasing at the same moment? (Round your answer to one decimal place.) ft /s A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.5 ft/s, how fast (in rad/s) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.) Wall 10 X Ground @ rad/s