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**Related Rates**By Laryssa Ferrara & Sanica Manglorkar Starring Loki, Ironman, and a Frost Giant**The Problem**Ironman is on a 13-meter ladder that is leaning against a vertical wall. Loki takes a rope and pulls the base of the ladder away from the wall at a rate of 1 meter per second. A frost giant witnesses the entire event. Find the rate at which Ironman is falling at the top of the ladder when the base of the ladder is 5 meters away from the wall.**A Diagram of the Action**y 13 M X = 5 M X ’=1 M/ sec**The Math Behind the Action**• What do we know? • c =13 m • Dr / dt= 1 m / sec • Finding rate when x = 5 m • x²+y ² =c ²**The Math Behind the Action**• X ² +y ²=13 ² • X ²+y² =169 ² • 2xx ’+2yy ’=0 • 2 (5 )(1 ) +2 (12 )y ’=0 • 2(12 )y ’ = -10 • 24y ’ = -10 • y ’ = -10/24= -5/12 When x =5 ft? 13 ² =5²+y ² y =12**The Conclusion**Ironman is falling at 5/12 ft/sec. Loki wins the battle.

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