Define the following terms. derivative b. secant line tangent line d. tangent point Smoke is being emitted into the atmosphere from a smokestack. At any instant, the smoke filled regions form as an inverted right circular cone, the height is 2 times the diameter. If the rate of smoke emission is 200 m3fmin, how fast is the height increasing when the height is 75 m? A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 15 cmls. Find the rate at which the area within the circle is increasing after 5 s. A spherical balloon is being inflated. Find the rate of change of the volume with respect to the radius when the radius is 1.2 m. At what rate is the radius increasing when the volume is 29H m3 and the volume is increasing at a rate of 16:1 m3/sec. ? Car 1 is driving east a 60 kmfh and Dave is driving north at 70 kmf'h. Both cars are approaching the intersection of the two roads. When Car 1 is 0.4 km from the intersection, the rate of the distance between the two cars is decreasing by 90 kmfh. How far is Car 2 from the intersection when Car 1 is 0.4 km from the intersection. A water trough is 15 m long and has a cross section in the shape of an equilateral triangle that is 1.5 m across. The trough is being filled with water at a rate of 0.5 m3/minute. How fast will the water level rise when the water is 50 cm deep