# Has climbed up 6 feet of the ladder the ladder makes

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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= \$\$ 3 · (1 622) feet/sec. (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 \$\$2 1822 =
10. 3/3 points | Previous Answers (Old Final Exam Problem-Sp2009) An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and
12/14/16, 3)59 PM hw17S3.9 Page 7 of 7 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 27 y 3 . (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 27(3 h )3 . (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 7 /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 \$\$7100((54)(23)4) inches per second.