...This 2 questions on my review are killing me and I don't know what to do. Please any help on how to solve these two? Instructions would be helpful.
1. Water is drained out of a tank in the shape of an inverted circular cone with height 9 feet and base radius 6 feet. The water level is decreasing at 1 ft/min. At what rate is the volume decreasing when the water is 6 feet deep?
note that r/h = 6/9 ... manipulate the volume formula for a cone to get V strictly in terms of h, then take the time derivative, sub in your given values and determine dV/dt.
2. An observer stands 200 meters from the launch site of a hot-air balloon. The balloon rises vertically at a constant rate of 4 m/s. At what rate is the angle between the ground and the observers line of sight to the balloon changing 25 s after the launch pad.
right triangle trig ... balloon height is the opposite side, 200 m is the adjacent side. Assign a variable for the height and set up a trig equation in terms of and the height. Take the time derivative, sub in your given/calculated values and determine the angle's rate of change w/r to time.