A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius '1' decreases. Assume that n0 clay is lost in the process. Suppase the height of the cylinder is increasing by 0.1 centimeters per second. What is the rate at which the radius is changing when the radius is 6 centimeters and the height is 8 centimeters? y; (Include help (units) with your answer.) Helium is pumped into a spherical balloon at a rate of 4 cubic feet per second. How fast is the radius increasing after 3 minutes? Note: The volume of a sphere is given by V = (4/3) mr3. Rate of change of radius (in feet per second) =A price p (in dollars) and demand a: for a product are related by 222 + 23p + 501:2 : 6200. If the price is increasing at a rate on dollars per month when the price is 10 dollars, nd the rate of change of the demand. Rate of change of demand = f, The altitude ofa triangle is increasing at a rate of 3.000 centimeters/minute while the area of the triangle is increasing at a rate of 3.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 12.000 centimeters and the area is 91.000 square centimeters? f. (Enter a positive number if the base is increasing, negative if it is decreasing.) If f is the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance q from the lens, where f, p, and q are related by the lens equation What is the rate of change of p with respect to q if q = 7 and f = 2? (Make sure you have the correct sign for the rate.)