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A ladder 23 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 л/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 x/3, find dh/dt= 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 л/3, find dw/dt= feet/sec.

A ladder 23 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 л/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 x/3, find dh/dt= 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 л/3, find dw/dt= feet/sec.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter5: Division Of Common Fractions And Mixed Numbers
Section: Chapter Questions
Problem 22A: A single-threaded (or single-start) square-thread screw is shown in Figure 5-6. The lead of a screw...
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A ladder 23 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 л/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 x/3, find dh/dt= 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 л/3, find dw/dt= feet/sec.
Transcribed Image Text:A ladder 23 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 л/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 x/3, find dh/dt= 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 л/3, find dw/dt= feet/sec.
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