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As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point at the end of the rod as shown. (a) Use the Pythagorean Theorem to show that L² = (x - r cos 0)² + ² sin²0. (b) Differentiate the equation in part (a) with respect to t to show that 0= = 2(x - r co - r cos 0) (+r sind) + 2r² sin (c) Calculate the speed of the piston when and the wheel rotates at 4 revolutions per minute. L de cos 0 dt. = , assuming that r = 10 cm, L = 30 cm, Piston moves back and forth

As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point at the end of the rod as shown. (a) Use the Pythagorean Theorem to show that L² = (x - r cos 0)² + ² sin²0. (b) Differentiate the equation in part (a) with respect to t to show that 0= = 2(x - r co - r cos 0) (+r sind) + 2r² sin (c) Calculate the speed of the piston when and the wheel rotates at 4 revolutions per minute. L de cos 0 dt. = , assuming that r = 10 cm, L = 30 cm, Piston moves back and forth

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point at the end of the rod as shown. (a) Use the Pythagorean Theorem to show that L² = (x − r cos 0)² + ² sin² 0. (b) Differentiate the equation in part (a) with respect to t to show that 0=2(x-r cos 0) (d+rsin 0df)+2r² sin cos de. dt (c) Calculate the speed of the piston when , assuming that r = 10 cm, L = 30 cm, and the wheel rotates at 4 revolutions per minute. L X = Piston moves back and forth e
Transcribed Image Text:As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a piston back and forth in a straight line. Let x be the distance from the origin to point at the end of the rod as shown. (a) Use the Pythagorean Theorem to show that L² = (x − r cos 0)² + ² sin² 0. (b) Differentiate the equation in part (a) with respect to t to show that 0=2(x-r cos 0) (d+rsin 0df)+2r² sin cos de. dt (c) Calculate the speed of the piston when , assuming that r = 10 cm, L = 30 cm, and the wheel rotates at 4 revolutions per minute. L X = Piston moves back and forth e
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