. is m highway with \"in; .Do not usea ' and b '. 150 inches. a Is decreasing by 4 inches per minute and b = 135 Inches. If the area of the eillpse remains constant at this time, how fast ~units- v , A A rescued whale is released Into the ocean 400 meters due east of a coast guard station. The whale swims directly away from the shore. coast guard point of station release e whale (a) Which of the following equations can be used to relate the angle, 0, and the distance between the whale and the point of release, x? O sec(0) = - X 400 O sin(0) = X 400 O tan(0) = 400 X O tan (0) = - X 400 O cos(0) = _x 400 (b) Which of the following would be an appropriate related rate equation for the answer to part (a)? O sec2(0) ax = 1 de dt 400 dt O sec2(0) de dx dt 400 dt O cos2(0) de dx dt dt O cos2(0) de 1 . dx dt 400 dt O sec(0) tan(0) do 1 dx 400 dt (c) If the whale swims at a constant rate of 60 meters per minute, how fast is the angle 0 changing when the whale is 300 meters from the point of release? Give an exact answer. radians per minuteA train is traveling 50 km per hour along a straight track, moving in the direction as shown in the figure below. A movie camera, 1 km away from the track, is focused on the train. x km train 1 km y km camera How fast is the distance from the camera to the train changing when the train is 3 km from the camera? Give an exact answer. ---Units---(a) Consider a circular oil slick that forms on the surface of a large lake. When the radius of the oil slick is 180 meters, the radius is expanding by 0.3 meter/minute. At that moment, how fast is the area of the slick expanding? Convert your answer to square meters per second. Give an exact answer m2/sec (b) Now let's consider the volume of another circular oil slick. For simplicity, think of the slick as a thin cylinder with uniform height. When the radius of this oil slick is 40 cm and the height is 2 cm, the radius is increasing by R cm/min and the height is decreasing by H cm/min. How fast is the volume of the oil changing in cm/min? Your answer will have R and H in it. cm$/minA hemispherical bowl of radius 11 cm contains water to a depth of h cm as shown below. (a) Find the square of the radius of the top surface of the water as a function of h. 12 = 121 - (11 - h)2 0 12 = (11 -h)2 - 121 0 12 = 121 - (11 + h)2 0 12 = 11 - (121 + h ) 2 0 12 = 121 + (11 - h) 2 (b) The water level drops at a rate of 0.1 cm per hour. At what rate is the radius of the water decreasing when the depth is 7 cm? Round your answer to four decimal places. cm/hr