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\fA rectangle with area A = b/ is expanding with time such that the length of the base, b (t) = 1 + 2, and the height of the rectangle is constant at h = 4. What is the formula for the rate of change of the area of the rectangle with respect to time? O dA dt = b (t) = 12 + 2 O dA dt = (th) (db ) = 0 O dA dt = di ) = 2t O dA dt = h ( db ) = 8tBob is filling up a cone, point down, with soft serve ice cream. Assume that the volume of the cone is V = arch h(t) = t. 3 : "(t) = Vt , and What is the formula for the rate of change of the volume of the cone with respect to time? d V O dt 3 d V O = 2xt2 dt 3 O d V not - d t 3 d V 2x t O dt 3Assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx di When the plane is x miles away, what is the rate of change of 0? tan (0) = O do d x d t x2+ h- dt O h2 d x dt x2+h- dt h d x O dt x2+ h- dt h d x O dt x2+ h- dt\fA cylinder is expanding at the rate of 6 cm /sec. The formula for the volume of a cylinder is: V = mr h. Let h = 2r. dr What is dt when r = 2? dr 3 O 4 1 cm/s dt O dr dt 4 X cm/s O dr 3 cm/ s dt 8 x dr O dt 2 1 cm/sThe lateral surface area of a cylinder is changing at the rate of 6 cm /sec, where S = 2rrh. Let h = 2r. What is the change in the radius when r = 2? dr 3 O cm/s dt 8 1 O dr = 3 cm/s dt 4 1 dr O = 1 2 1 cm/s dt dr 3 O cm/s dt 2V5 xA cylinder is being filled such that the height of the contents is increasing at a rate of 2 cm/sec. What is the rate of change of the volume if r =2 and V = mr h? O d V dt = 2x cm /s O d V dt = 9x cm /s O d V dt = 18x cm3/s O d V dt = 8x cm /sA ladder is 27 feet long and is leaning against the side of a house. The base is moved away at 3 ft per min. At what rate is the ladder moving down the wall when the base is 10 feet from the house? dh O dt =-1.196 ft/m O dh = -2.516ft/m dt O dh = -0.418 ft/m dt dh O dt = 0.797 ft/mAssume that an airplane is flying toward you at a constant height of 2 miles and at a speed of 100 miles per hour. When the plane is 20 miles away, what is the rate of change of 0? K cot (0) = X h O do dt = .25 degree/hr O do dt = 0.45 degree/hr O do dt = -0.5 degree/hr O do dt = 0.5 degree/hr