11 questions
A company's revenue from selling a units of an item is given as R = 1200x - 3x2. If sales are increasing at the rate of 25 units per day, how rapidly is revenue increasing (in dollars per day) when 150 units have been sold? dollars per day Find - at x = 3, given the function y = 2x - 4, at the moment when dy = 1. dt A circle's radius is increasing at 0.5 feet/minute. How rapidly is its area increasing when the radius is 4 feet? Round your answer to 2 decimal places. The circle's area is increasing at min A spherical snowball is melting at a rate of 9.7 cm" . How rapidly is the radius decreasing when the min snowball's volume is 972 7 cm?? Your answer should be a signed number to reflect increasing or decreasing, and should be rounded to 3 decimal places The volume of a sphere of radius r is V - The radius is decreasing by cm/min. The altitude of a triangle is increasing at a rate of 1.5 cm/min, while the area of the triangle is increasing at a rate of 4 (cm)"/min. At what rate is the base of the triangle changing when the altitude is 11.5 cm and the area is 82 (cm)" Round your answer to 3 decimal places when necessary. cm/min A 17 feet long ladder is leaning against a vertical wall of a building. The base of the ladder is being pulled away from the wall at a rate of 8 feet per second. Determine the rate of change of the top of the ladder when the base of the ladder is 8 feet away from the wall. Building Ladder Ground feet per second A 34 feet long ladder is leaning against a vertical wall of a building. The base of the ladder is being pulled away from the wall at a rate of 3 feet per second. Determine the rate of change of the *angle* (in radians) formed by the top of the ladder and the wall when the base of the lad feet away from the wall. Building shadow A street light is at the top of a 18 ft tall pole. A woman 4.5 ft tall walks away from the pole with a Ladder speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole? Round to two decimal places. Ground radians per second At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 17 knots. How fast (in knots, to one decimal place) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) knots Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 13 feet high? Round to two decimal places. Recall that the volume of a right circular cone with height h and radius of the base r is given by V = Th min An inverted pyramid is being filled with water at a constant rate of 65 cubic b1 centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 9 cm. Find the rate at which the water level is rising when the water level is 4 cm. Use similar triangles, and the fact that the volume of a pyramid is The exact answer is cm/sec The decimal approximation (to one decimal place) is cm/sec
