9 12 points previous answers a ladder 22 feet long

This preview shows page 5 - 6 out of 6 pages.

9. 1/2 points | Previous Answers A ladder 22 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of π /3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is π /3, find dh/dt=
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is π /3, find dw/dt =
6/5/2019 hw17S3.9 6/6 10. 3/3 points | Previous Answers (Old Final Exam Problem­Sp2009) An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and height 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone. (a) When the sand remaining in the upper cone has height y inches, its volume A in terms of y is $$π y 327 . (b) When the sand in the lower cone has reached a height of h inches, its volume B in terms of h is $$π−π·(3− h )327 . (Hint: B is the volume of the bottom cone minus the volume of the empty space above the sand.) (c) Assume the total volume of sand in the hourglass is 3 π /4 cubic inches. Also, assume the height of the sand in the upper cone is decreasing at a rate of 8 /100 inches per second. At the instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is increasing at a rate of $$.0232 inches per second.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture