(1 point) A street light is at the top of a 12.0 ft. tall pole. A man 6.5 ft tall walks away from the pole with a speed of 5.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 49 feet from the pole? Your answer: ft/sec Hint: Draw a picture and use similar triangles.(1 pomt) You are blowing air into a spherical balloon at a rate of % cubic inches per second. (The reason tor this strange looking rate is that it WIII simplify your algebra a little )Assume the radius of your balloon is zero at time zero. Let Ht), A{t). and V(t) denote the radius. the surface area, and the volume of your balloon attime t. respectively. (Assume the thickness of the skin is zero )All of your answers below are expreSSions in t r'(t) 2 inches per second A'(t) 2 square inches per second, and V'[t) 2 cubic inches per second. Hint: The surface area A arid the volume V ofa sphere of radius 't' are given by 4W3 4424711"? and V: (1 point) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 13 cm. Your answer (cubic centimeters per minute) should be a positive number. Hint: The volume of a sphere of radius r is V = 4mp3 3 The diameter is twice the radius.(1 point) Water is leaking out of an inverted conical tank at a rate of 14300 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 11 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 22 centimeters per minute when the height of the water is 4.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Your answer: cubic centimeters per minute.(1 point) A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s. (a) How rapidly is the area enclosed by the ripple increasing when the radius is 3 feet? The area is increasing at ft2 / s. (b) How rapidly is the area enclosed by the ripple increasing at the end of 9.8 seconds? The area is increasing at ft2 / s.(1 point) At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t