Rie Man vs. The Limit: A Calculus Chronicle
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- It was a quiet morning in the city until Rie Man witnessed The Limit wreaking havoc on the public from its historic bridge.
- Rie Man approaches a 90° intersection travelling northbound while chasing The Limit who has turned and is moving eastbound. Using his enhanced calculus power, Rie Man figures out the distance between him and the villain is increasing at 35 mph when he is travelling 1.0 mi north of the intersection and The Limit is 0.75 mi to the east. Rie Man wants to figure out what The Limit's speed is if he is moving at 45 mph at the instant movement.
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- x
- z
- Using the equation x^2 + y^2 = x^2 and Pythagorean's Theorem, Rie Man figures out the distance (z) between the villain and him is 1.25 mi. Rie Man then takes the derivative of the equation to get the new equation of 2x dx/dt + 2y dy/dt = 2z dz/dt. Plugging in all the known variables in the equation, Rie Man uses algebra to figure out The Limit's speed is 118.3 mi/hr when he is moving at 45 mph at the instant of measurement.
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- After catching The Limit and turning him into the authorities. Rie Man wants to know what his average speed was to make improvements to his suit. If Rie Man travels 25 miles in 15 minutes and 60 miles in 30 minutes. What is Rie Man's average velocity over the entire distance travelled?
- To figure out his average speed, Rie Man adds up the miles he travelled to get the total distance of 85 miles. Next, Rie Man adds up the time taken to travel each distance to calculate the total time of 45 minutes. Using the equation for average speed (total distance/total time -- 85/45), Rie Man figures out his average speed is 1.88 mi/min or 113.3 mi/hr (multiply 1.88 by 60 for conversion of minutes to hours).
- THE ENDRIE MAN VS. THE LIMIT: A CALCULUS CHRONICLE
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