Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank.
(1 point) Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A, B,C,D, or E) in each blank. A. tan(arcsin(x/9)) B. cos(arcsin(x/9)) C. (1/2) sin(2 arcsin(x/9)) D. sin(arctan(x/9)) E. cos(arctan(x/9)) X 1. 81 81 - x2 2. /81 + x2 9 3. /81 + x2 4. 81 - x2 V81 - x2 5. 9\f\f\f(1 point) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 11 cm. Your answer (cubic centimeters per minute) should be a positive number. Hint: The volume of a sphere of radius r is 41513 V: 3 The diameter is twice the radius. (1 point) Water is leaking out of an inverted conical tank at a rate of 10200 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 17 centimeters per minute when the height of the water is 2.5 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 3.3 ft/s. (a) How rapidly is the area enclosed by the ripple increasing when the radius is 2 feet? The area is increasing at ft 2 / s . (b) How rapidly is the area enclosed by the ripple increasing at the end of 8 seconds? The area is increasing at ft 2 / s .(1 point) At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 5 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
