Maximize the function f(x,y,z)=x²+y²+z² subject to the constraint curve x+y+z−18=0.
Find dw⁄dt given that w=x²+y², x=3t and y=5t+2.
Find the volume of the solid bounded by the surface z=16−x²−y² and the plane z=1.
A man throws a ball horizontally out of a window with an initial velocity of 12 meters per second. Find the velocity of the ball in the vertical direction just before it hits the ground and the final horizontal distance it travels if the window is 11 meters above the ground.