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As gravel is being poured into a conical pile, its volume V changes with time. As a result, the height hand radius also change with time. Knowing that volume of the conical pile is V = ²³h the relationship with respect to time between volume and the changes in the radius and height is 0 = dV dt ○ = dV dt ○ = dV dt dr (2+2) 2rh dr dh (2²) 2r dh (2+²) dr (2².1+2rh) dh ○ = 1/27 dV dt

As gravel is being poured into a conical pile, its volume V changes with time. As a result, the height hand radius also change with time. Knowing that volume of the conical pile is V = ²³h the relationship with respect to time between volume and the changes in the radius and height is 0 = dV dt ○ = dV dt ○ = dV dt dr (2+2) 2rh dr dh (2²) 2r dh (2+²) dr (2².1+2rh) dh ○ = 1/27 dV dt

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 gravel is being poured into a conical pile, its volume V changes with time. As a result, the height ʼn and radius r also change with time. Knowing that volume of the conical pile is V = ar²h 1 the relationship with respect to time between volume and the changes in the radius and height is dr 0 = = x (2/₁² + ₁²2 ) dV dt 2rh 11 12 dh dt dt 0 0 dV dr dh # = 3x (2²²) 2r dt dt dt dV dt dV = = dt 3 dh x ( 2m +²2) (2 2rh dt dr x ( ₁2²-1 + 2 + 1 ) dh
Transcribed Image Text:As gravel is being poured into a conical pile, its volume V changes with time. As a result, the height ʼn and radius r also change with time. Knowing that volume of the conical pile is V = ar²h 1 the relationship with respect to time between volume and the changes in the radius and height is dr 0 = = x (2/₁² + ₁²2 ) dV dt 2rh 11 12 dh dt dt 0 0 dV dr dh # = 3x (2²²) 2r dt dt dt dV dt dV = = dt 3 dh x ( 2m +²2) (2 2rh dt dr x ( ₁2²-1 + 2 + 1 ) dh
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