1. [-/5 Points] DETAILS MY NOTES PRACTICE ANOTHER A large sphere of material is placed in a dissolving liquid. (a) When the radius is 1 m, it is observed to be changing at 4 cm/hour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time? cm$/hr (b) Suppose, instead, that the liquid is known to dissolve the material at a rate of 5 m /hour, at what rate will its radius r change with respect to time when r = 1 meter? when r = 1/2 meter? r = 1 m/hr r = 1/2 m/hr (c) What happens to the rate of change of the radius in part (b) as r - 0+? r -> co? r- ot Submit Answer 2. [-/1 Points] DETAILS MY NOTES PRACTICE ANOTHER Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 4 feet? ft2/min Submit Answer 3. [-/1 Points] DETAILS MY NOTES PRACTICE ANOTHER A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and car B is driving east along the second road. At a particular time car A is 10 kilometers to the north of P and traveling at 80 km/hr, while car B is 15 kilometers to the east of P and traveling at 110 km/hr. How fast is the distance between the two cars changing? km/hr Submit Answer4. [-/2 Points] DETAILS MY NOTES PRACTICE ANOTHER A volcanic cone spews fine particles of rock which land in the surrounding area and cause the size of the cone to increase. (a) Suppose that a volcanologist takes measurements that show that when the cone is 80 meters wide and 40 meters tall, its height is increasing at 0.5 meters/day. If the assumption is made that the cone will retain its height-width proportion, what is the rate at which the volume of rock is being released by the volcano? m3/day (b) Suppose that the volcanologist takes more measurements and realizes the original assumption was poorly made, because the width is increasing at 0.6 meters/day. What would be the new finding for the rate at which the volume of rock is being released by the volcano? m3/day Submit Answer 5. [-/2 Points] DETAILS MY NOTES PRACTICE ANOTHER Write the first derivative of the given function. f ( x ) = x5/3In(x) f ' ( x ) = For which x-values does f(x) have horizontal tangents? (Enter your answers as a comma-separated list. ) X = Submit Answer 6. [-/1 Points] DETAILS MY NOTES PRACTICE ANOTHER Find the derivative of f(x) = 3 Inx when x = e. X f'(e) = Submit