8 questions to be answered

A spherical snowball is melting in such a way that its radius is decreasing at a rate of 3 cm/min. Since the radius is decreasing, the rate (slope) is *negative*. At what rate is the volume of the snowball decreasing when the radius is 14 cm. Hint: The volume of a sphere of radius ris V = - mr3 (Note the answer is a negative number, since the volume is also decreasing). Give an exact value. cm3 min A 37 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 2 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 ladder is 12 feet away from the wall. Building Ladder Ground radians per second At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 25 knots. How fast (in knots, to one decimal place) is the distance between the ships changing at 3 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 10 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 = IT 3 7r h ft min An inverted pyramid is being filled with water at a constant rate of 25 cubic b2 centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 7 cm. Find the rate at which the water level is rising when the water level is 2 cm. Use similar triangles, and the fact that the volume of a pyramid is V = -bh The exact answer is cm/sec The decimal approximation (to one decimal place) is cm/sec C 1 pt shadow A street light is at the top of a 17 ft tall pole. A woman 4.25 ft tall walks away from the pole with a speed of 5 fu/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole? Round to two decimal places. ft Use linear approximation, i.e. the tangent line, to approximate v64.4 as follows: Let f(x) = VX. The equation of the tangent line to f(z) at a = 64 can be written in the form y = mx + b where m , rounded to 6 decimal places, is: and where b, rounded to 6 decimal places, is: Using this, we find our approximation for v64.4 rounded to 6 decimal places is Use linear approximation, i.e. the tangent line, to approximate 107 as follows: Let f(x) = 1 and find the equation of the tangent line to f() at a "nice" point near 1.001. Then use this to approximate 1.001