The radius of a right circular cone is increasing at a rate of 10 inches per minute, and the height is decreasing at a rate of 8 inches per minute. What are the rates of change of the volume and surface area when the radius is 12 inches and the height is 36 inches? rate of change of the volume in/min rate of change of the surface area in?/min

3. A sector of radius 10 cm and angle Bradians is bent to form a conical cup as shown: [ignore the degree sign in the diagram, it's a mistake] sector join when edges (AB] and [CB] are joined with tape. becomes 10 cm B 10 cm Suppose that the cone has radius rand height h a. Explain why the circumference of the base of the cone is 108 b. Explain why r = 50/n c. Show that h = V100 - (50/n) d. Find the cone's volume in terms of e e. Find the maximum possible volume of the cone, and the value of e that gives this maximum.

The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the triangle is increasing at a rate of 3 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.5 centimeters and the area is 87 square centimeters? cm/min

A car's position in feet t seconds after it starts moving is given by s(t)-9t/t. The average rate of change in position with respect to time is called average velocity %3D ) Find the car's average velocity over the first 4 seconds. DO NOT INCLUDE UNITS WITH YOUR ANSWER. i) Find the car's average velocity from t = 16 to t = 25 seconds. DO NOT INCLUDE UNITS WITH YOU ANSWER. i) What units would your answers from parts i and ii be in? O A. feet O B. feet per second OC. seconds O D. seconds per foot per foot O E. feet per second per second OF. seconds per foot

The base of a triangle increases at a rate of 3 cm per minute while the height of the triangle decreases at a rate of 2 cm per minute. At what rate is the area of the triangle changing with respect to time when the height is 10 cm and the base is 15 cm? Be sure to write units for your answer.

Wilson's sand and gravel will deliver 12 yd^3 of gravel for $240, 30 yd^3 for $528, and 60 yd^3 for $948. What is the average rate of change of the cost as the number of cubic yards varies from 12 to 30? What is the average rate of change as the number of cubic yards varies from 30 to 60?