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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 ​

In a free-fall experiment, an object is dropped from a height of 144 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 . Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places. ​ ​

Find if . ​

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

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

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of  with the perpendicular from the light to the wall.  ​

Use the Product Rule to differentiate. ​ ​

Use implicit differentiation to find . ​ ​

Find by implicit differentiation given that . ​

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