Find if . ​

In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time . At what time will the object reach the ground level? ​ ​

Find an equation of the tangent line to the graph of  at the point . ​

Find the rate of change of the distance  D  between the origin and a moving point on the graph of  if   centimeters per second. ​

The radius  r  of a sphere is increasing at a rate of 2  inches per minute. Find the rate of change of the volume when  inches. ​

The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute. ​ Find the rate of change of area, A, when the radius is 3. ​

Suppose a 20-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when seconds. Round your answer to four decimal places. ​

Evaluate  for the equation at the given point. Round your answer to two decimal places, if necessary. ​

Use implicit differentiation to find . ​ ​

Find the slope-intercept form of the equation of the line tangent to the graph of  when . ​