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12. A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the angle of the rope to the ground remains 75° and the rope is pulled in at 8 ft/s, how quickly is the elevation of the balloon changing?

12. A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the angle of the rope to the ground remains 75° and the rope is pulled in at 8 ft/s, how quickly is the elevation of the balloon changing?

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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12. A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the angle of the rope to the ground remains 75° and the rope is pulled in at 8 ft/s, how quickly is the elevation of the balloon changing? Let z be length of the rope and y be the elevation of the balloon. Write an equation relating z and y. Choose the correct answer below. A. sin (75°) = OC. sin (75°) = ○ E. tan (75%) = A. C. E. dy dt dy dt Differentiate both sides of the equation with respect to t. Choose the correct answer below. dy dt y Z (1) ○ ft. y = cos (75°) y Oft/s. =tan (75°). ft²/s. O ft³/s. dz tan (75%) dt dz dt dz dt The elevation of the balloon is decreasing at a rate of about (1) (Do not round until the final answer. Then round to two decimal places as needed.) B. cos (75%) = O D. tan (75°) OF. cos (75°) = B. D. F. dy dt dy dt dy dt = = y Z y Z sin (75°). dz dt dz cos (75%) dt 1 dz sin (75) dt
Transcribed Image Text:12. A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the angle of the rope to the ground remains 75° and the rope is pulled in at 8 ft/s, how quickly is the elevation of the balloon changing? Let z be length of the rope and y be the elevation of the balloon. Write an equation relating z and y. Choose the correct answer below. A. sin (75°) = OC. sin (75°) = ○ E. tan (75%) = A. C. E. dy dt dy dt Differentiate both sides of the equation with respect to t. Choose the correct answer below. dy dt y Z (1) ○ ft. y = cos (75°) y Oft/s. =tan (75°). ft²/s. O ft³/s. dz tan (75%) dt dz dt dz dt The elevation of the balloon is decreasing at a rate of about (1) (Do not round until the final answer. Then round to two decimal places as needed.) B. cos (75%) = O D. tan (75°) OF. cos (75°) = B. D. F. dy dt dy dt dy dt = = y Z y Z sin (75°). dz dt dz cos (75%) dt 1 dz sin (75) dt
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