An metal cube with each edge of length s millimeters is expanding uniformly as a consequence of being heated. (a) Find the average rate of change of the volume of the cube with respect to an edge as s increases from 5.0 to 5.1 mm. Do not round your answer. average rate: 76.51 mm³/mm (b) Find the instantaneous rate of change of the volume of the cube with respect to an edge at the instant when s= 5 mm. Do not round your answer.

A particle moves in a straight line with velocity 10 – 4t ft/s. Find the total displacement and total distance traveled over the time interval [0, 9]. Displacement: Distance: → -> ft. ft.

Water is being poured into an inverted cone at the rate of 4 cubic centimeters per second. The cone has a maximum radius of 6cm and a height of 30 cm. At what rate is the height increasing when the height is 3cm? 1 The volume of a cone is v 3 71 1 30

A parked car dripping transmission fluid is creating a circular puddle whose area (in square inches) is A = ² where r is the radius of the circle in inches. Find the rate at which the area of the puddle is increasing at the instant when the radius is 18 inches and increasing at a rate of 4 inches per minute. When the radius is 18 inches, the area is changing at approximately (Round to the nearest thousandth as needed.) square inches per minute.