Hello. Could you help me solve these applications of derivatives (Optimization) questions. Please provide explanation so that it's understandable. The answer for the first one is incorrect (9.6 m/s). Thanks!

A floodlight is positioned on the ground shining on a white wall 10 m away. A woman 1.6 m tall starts at the wall and walks towards the light at a rate of 1.2 m/s. How fast is the height of her shadow on the wall increasing when she is 2 m from the light? . '6 m/s (I 9.6 m/s . '43 m/s I:I12mls Water is flowing at 4.7 cm3/s into a conical vase with a top radius of 38 cm and a height of 53 cm. How fast is the depth increasing when the water is 40 cm above the vertex? Enter your answer rounded to 4 decimal places (for example in the form 0.1234}. Do not include units. Two cars leave an intersection, one 25 minutes after the other. The first car, A, travels north at the speed of 55 km/h and the second car. B. travels west at a speed of 65 km/h. How fast are the cars separating from each other 45 minutes after the first car leaves the intersection? A water trough has an isosceles triangular cross section that is 40 m across the top and 15 m deep. The trough is 2 m long. It is being filled at a rate of 0.4 m3/minute. How fast does the water level rise when the deepest point is 1 m deep? Enter your answer rounded to 3 decimal places. Do not enter units in your answer. An open rectangular box has an area of 441 cm2. If its length must be 3 times its width, find its dimensions so that its volume is a maximum.There is a 4 km long straight beach. At one end. there is a boat anchored at A, 3 km off the beach. At the other end, there is another boat anchored at B, 5 km off the beach. A sailor from the first boat is to bring a passenger to the beach and proceed to the second boat to pick up another passenger. At what point. C, along the beach should the first passenger be dropped in order to minimize the distance? Fill in the blank to answer this question. The boat would land _______ krn down the beach from a point across from A. [Write your answer to 1 decimal place. Do not include units in your answer.) The curve y= sin[x} + cosix} has two points where the tangent line is horizontal on the interval 05x5 2a. The y co-ordinates of these points is the positive and negative square root of a positive integer. What is this integer? An airplane is directly overhead and flying east at 175 m/s at an altitude of 1200 m. A searchlight on the ground in the same vertical plane must be kept on the airplane. What is the rate of revolution of the searchlight when the airplane has flown 600 m east