Q\\ A 13-foot ladder is leaning against a vertical wall (see gure) when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.7 It;l 5. How fast is the top of the ladder sliding down the wall when the foot of the ladder is 12 ft from the wall? Let x be the distance from the foot of the ladder to the wall and let y be the distance from the top of the ladder to the ground. Write an equation relating it and y. x2+zyz=169 Differentiate both sides of the equation with respect to t. _.:dx ..dy (Mylar- To. When the foot of the ladder is 12 ft from the wall, the top of the ladder is sliding down the wall at a rate of ft I s. \\ (Round to two decimal places as needed.) _ P Leg!\" (331* A port and a radar station are 5 mi apart on a straight shore running east and west. A ship leaves the port at noon traveling at a rate of 20 mifhr. If the ship maintains its speed and course, what is the rate of change of the tracking angle 6 between the shore and the line between the radar station and the ship at 12:30 PM? (Hint: Use the law of sines.) Use the Law of Sines to nd an equation relating the angle, 9, the angle that the ship left the port at, the distance between the radar system and the ship, a, and the distance between the port and the ship, s. Evaluate any known trigonometric functions of 45 as needed. .. a: "9-: ._ . sun _ Riff (Type an exact answer.) Find the related rates equation, evaluating any trigonometric functions of (45) as needed. ' ds da .2 a tit '5 dt The rate of change of the tracking angle 9 between the shore and the line between the radar station and the ship at 12:30 PM is V (Round to four decimal places as needed.) 2 x Use the Quotient Rule to find g'(1) given that g(x) = X+1 . g'(1) = (Simplify your answer.)