Alter lled with liquid is in the shape of a 1trertex-down cone with a height of 12 inches and a diameter of 8 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 1 cubic inches per second, how fast is the level oftne liquid dropping when the liquid is 3 inches deep? Answer: titSpi E infsec Hint: Recall the similar triangle property. At noon: person A is 1 miles east of person B. Person A is wallting east at 4 miles per hour and person E is wallting north at 6 miles per hour. {You can olielr on the graphic to enlarge the image.) How fast is the distance between the people changing at 3 PM? Answer: 2 miles i' hr. Atrough is.! = 3 it long and has a cross section of an isosceles trapezoid with base of It = 1 ft, height of h = 2 it, and top of t = 2 it [see picture below]. (You can clicir oh the graph to enlarge the image. ,l If the trough is being lled with water at a rate of 2 15th how fast is the water level rising when the water is 8 inches cleep? Answer: I ft-fmJ'Jl. You are blowing air into a spherical balloon at a rate of 11 cubic inches per second. lGiven that the radius of the balloon is 3 inches when t = 4 seconds answerthe following questions: {a}: How fast is the radius of the balloon growing att = 4 seconds Answer: 2 inches per second. {bj What is the rate of change of the surface area at t = 4 seconds"?r Answer: 2 square inches per second. A street light is at the tsp of a pale that is 1|] feet tall. A wernah E ft tall walits away from the pole with a speed of 5 ft-'see along a straight path. How fast is the tip of her shadow moving when she is El] ft from the base of the pale"? Answer: I ftfsee. Gratrel is being dumped from a conveyor belt at a rate of T cubic feet per minute. It terms a pile in the shape eta right eireular eene whose height and base diameter are always equal to each ether. How fast is the height or the pile increasing when the pile is 4 feet high? Answer: | I ftfrner Let HI] = 3/432 +1tr+ 18 m = z {b} Find the equation of the tangent line to the curve 3; 2 at} at the point [2, Er]. y2 Let at] = 51115 :33. {at First = z {b} Find the equation eftne tangent line to the curve y 2 at] at the point (5", 1}. y: 2