3/26/23, 10:53 AM HW16 Related Rates (4.1) MyOpenMath Djarudi Umukunzi Question 1 0/1 pt 100 24 The volume of a cylinder of height 8 inches and radius r inches is given by the formula V = 8r. Which is the correct expression for dV -? dt dV 0 dt dV dt dV dt dV = dr dh = 16 dt dt dr : 82. dt dr = 16 - dt dt dV 16 dt dt Suppose that the radius is expanding at a rate of 0.4 inches per second. How fast is the volume changing when the radius is 2.8 inches? Use at least 5 decimal places in your answer. answer: Question 2 cubic inches per second dr dA Let A be the area of a circle with radius r. If = 3, find when r = 3. dt dt Question Help: Video Question 3 dy Let xy = 5 and = 1. dt dx Find when x = 2. dt Question Help: Video https://www.myopenmath.com/assess2/?cid=171080&aid=12165365#/print 0/1 pt 100 24 0/1 pt 100 24 1/3 13 3/26/23, 10:53 AM Question 4 MyOpenMath 3/26/23, 10:53 AM 0/1 pt 100 24 A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the radius is 10 cm. (Note the answer is a positive number). 1 V = -rh 3 cm min Hint: The volume of a sphere of radius r is V Question Help: Video = MyOpenMath Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 13 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by ft min Question 9 A red and a blue car leave Bellevue at the same time. The red car drives north and the blue car drives east. 0/1 pt 100 24 Question 5 The area of a healing wound is given by A = r. The radius is decreasing at the rate of 5 millimeter per day at the moment when r = = 46. How fast is the area decreasing at that moment? Select an answer Question Help: Video Question 6 Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 24 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V = 1/3rh Question Help: Video Question 7 ft min The red car is going 80 kilometers per hour and the blue car is going 65 kilometers per hour. The day is clear. After 4 hours, 0/1 pt 100 24 a) how far apart are the cars? kilometers b) how fast is the distance between the cars changing? km/hr (Enter each answer as decimal rounded to 2 places.) Question 10 0/1 pt 100 24 The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7.5 centimeters and the area is 89 square centimeters? Question Help: Video Question 8 https://www.myopenmath.com/assess2/?cid=171080&aid=12165365#/print cm/min 0/1 pt 100 24 0/1 pt 100 24 0/1 pt 100 24 An 8-meter ladder is leaning against a vertical wall. If a person pulls the base of the ladder away from the wall at the rate of 0.8 m/s, what is the rate of change of the distance between the top of the ladder and the ground when the base of the ladder is A. 2 meters from the wall? B. 4 meters from the wall? C. Give the units for the answer to A and B. 2/3 https://www.myopenmath.com/assess2/?cid=171080&aid=12165365#/print 3/3 33