Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 8x − x2 x = 0 y = 16

Completing the square gives

and

tells us the parabola intersect the line at one point, (4, 16).

Then the volume of the solid obtained by revolving shells about is

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

m∠a is 90°

m∠b is 40°