A rocket follows a path given by y=x1 over 75 x³ (distances inmiles). If the horizontal velocity is given by vx=x, find the magnitude and direction of the velocity when the rocket hits the ground(assume levelterrain) if time is in minutes.

The magnitude is approximately _____ miles per minute.

Assume that x=x(t) and y=y(t). Let y=x³+1 and dx/dt=3 when x=2.

Find dy/dt when x=2

Assume that all variables are implicit functions of time t. Find the indicated rate.

x²+3y²+2y=24; dx/dt=5 when x=4 and y=2; find dy/dt

When a circular plate of metal is heated in anoven, its radius increases at a rate of 0.04cm/min. At what rate is theplate's area increasing when the radius is 56 cm?

The rate of change of the area is ________ cm²/min.