5. [013.5 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER (a) Consider a circular oil slick that forms on the surface of a large lake. When the radius of the oil slick is 160 meters, the radius is expanding by 0.9 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 mZ/sec X (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 50 cm and the height is 2 cm, the radius is increasing by R cm/min and the height is decreasing by H cm/rnin. How fast is the volume of the oil changing in cm3/min? Your answer will have R and H in it. 6. [1.5I3 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER A hemispherical bowl of radius 18 cm contains water to a depth of h crn as shown below. m w w (a) Find the square of the radius of the top surface of the water as a function of h. Or2=(187h)27324 Or2=187(324+h)2 OR=324(18+h)2 Or2=324+(187h)2 r2=324(18h)2 V (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 5 cm? Round your answer to four decimal places. Sam/hr . [213.5 Points] PREVIOUS ANSWERS A rescued whale is released into the ocean 300 meters clue east of a coast guard station The whale swims directly away from the shore ASK YOUR TEACHER coast guard pointof statim release )9 I whale (a) Which of the following equations can be used to relate the angle, 8, and the distance between the whale and the point of release, x? _ x O cusljd) 300 . 9 : x O sln( ) 300 300 t a : _ 0 an( ) x a = i 0 sec( } 300 t 5 = L (i) an( } 300 a? (b) which of the following would be an appropriate related rate equation for the answer to part (a)? 1 0'9 300 dt 2 11:. Osectahjt 7 O cusz(6} = df dt 2 as 1 dz 6 _ : 55\" lo? 300 df d9 7 1 O sec(5}tan(9) 300 a dt 2 7 1 dx 0 cm (5)0? ' 300 0': (c) If the whale swims at a constant rate of 60 meters per minute, how fast is the angle 6 changing when the whale is 400 meters from the point of release?J Give an exact answer. radians per minute