An ornithologist studying the flight of birds measured the efficiency for parakeets flying at various speed in a descending flight pattern 0.18 at 12 mph, 0.23 at 22 mph and 0.15 at 30mph. the measurements suggest the efficiency e is a quadratic function of the speed s. find the quadratic function whose graph goes through the three given ordered pairs, and find the speed that gives the maximum efficiency for descending flight.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)