A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when its base is 13 feet from the wall? Round your answer to two decimal places. ​ ​

An airplane flies at an altitude of 6  miles towards a point directly over an observer. Consider  and  as shown in the following figure. The speed of the plane is400 miles per hour. Find  when  miles. Round your answer to three decimal places. ​ ​

Find the derivative of the function. ​ . ​

All edges of a cube are expanding at a rate of 7  centimeters per second. How fast is the volume changing when each edge is 2  centimeters? ​

An airplane is flying in still air with an airspeed of 283  miles per hour. If it is climbing at an angle of 21 °, find the rate at which it is gaining altitude. Round your answer to four decimal places. ​

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch). A model that approximates the data is . Find the rate of change of T with respect to p when . Round your answer to two decimal places. p 5 10 14.696 (1 atm) 20 30 40 60 80 100 T 327.43 404.29 448.84 485.71 536.18 573.59 629.02 670.61 704.38 ​

A point is moving along the graph of the function  such that  centimeters per second. Find  when . ​

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 . ​