\fLet A be the area of a circle with radius r. If dr dA = 5, find dt when r = 2. dtl_J A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/ min. At what rate is the volume of the snowball decreasing when the radius is 8 cm. (Note the answer is a positive number). \"\"3 min 4 3 Hint: The volume of a sphere of radius r is V : Err? The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9.5 centimeters and the area is 95 square centimeters? cm/min Question Help. D) VideoGravel 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 12 feet high? (Give your answer as an exact value.) Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 V : gin-2h ft min A rotating light is located 20 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall. wall light Answer is a positive value. At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) knots Question Help: Video\\I A street light is at the top of a 11 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/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? E ft SCC l_J' An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 2 cm. A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per day and the sides of the square are decreasing at a rate of 1 meter per day. When the radius is 5 meters, and the sides are 19 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is S square meters per day. ' l_J A police car is located 70 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 200 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road? The actual speed (along the road) of the red car is feet per second Answer the following True or False: If an ice skater is skating directly away from a 6 meter tall lamp at 12 meters per second, and you want to calculate the rate at which the skater's shadow is increasing in length, then you need to know how far the skater has skated but you do not need to know how tall the skater is. O True 0 Palm:- Use linear approximation, i.e. the tangent line, to approximate V 16.3 as follows: Let f(:c) = M5. Find the equation of the tangent line to x) at a: = 16 ml 1 Using this, we find our approximation for V 16.3 is :l NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer. 1 as follows: Let f(:i:) = and find $ 1 0.252 Use linear approximation, i.e. the tangent line, to approximate 0 252 the equation of the tangent line to f(':) at a "nice" point near 0.252. Then use this to approximate .Question3 v I The linear approximation at a: = 0 to f(:c) : sin(7m) is y = A + Ba: where A is: Use linear approximation, i.e. the tangent line, to approximate v3 27.2 as follows: Let f(:i:) = 6/5 The equation of the tangent line to x) at m = 27 can be written in the form y=mz+b Using this, we find our approximation for V3 27.2 is [: Question Help: El Video \fLet y = 2x2. Find the change in y, Ay when x = 1 and Ax = 0.1 Find the differential dy when x = 1 and da = 0.1 Question Help: D VideoLet y = 3vx. Find the change in y, Ay when x = 1 and Ax = 0.3 Find the differential dy when x = 1 and dx = 0.3