Gravel is being dumped from a conveyor belt at a rate of 30 ft/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.) ft/min

Find the intensities of earthquakes whose magnitudes are aR=6.0andbR=7.9.

The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?

A 10.00-inch diameter pulley rotates at 160.0 rpm. A belt connects this 10.00-inch diameter pulley with a 6.5-inch diameter pulley. An 8.00-inch diameter pulley is fixed to the same shaft as the 6.50-inch pulley. A belt connects the 8.00-inch pulley with a 3.50-inch diameter pulley. Determine the revolutions per minute of the 3.50-inch diameter pulley. Round the answer to 1 decimal place.

A carbide milling cutter is used for machining a 27.25-inch length of stainless steel. The cutting time is 12.35 minutes, the cutting speed is 240 feet per minute, and the feed is 0.01 inches per revolution. What is the diameter of the carbide milling cutter? Round the answer to 2 decimal places.

Estimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.

Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A right circular cone 12.7 centimeters high contains 198.7 cubic centimeters of material. Find the area of the base of the cone. Round the answer to the nearest square centimeter.

A shaft is being cut in a lathe. The tool feeds (advances) 0.015 inch each time the shaft turns once (1 revolution). How many revolutions will the shaft turn when the tool advances 3.120 inches? Round the answer to 2 decimal places.

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid brass casting in the shape of a right circular cone has a base diameter of 4.36 inches and a height of 3.94 inches. Find the weight of the casting. Brass weighs 0.302 pound per cubic inch.

The half-life of magnesium-27 is 9.45 minutes. How much of a 10-mg sample will be left in 6 minutes?