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Use implicit differentiation to solve the following related rate problems: (Include a properly labelled diagram as part of your solution.) #6. A student in Westdale's photography class is using a pinhole camera with a focal length of 20 cm to take a picture of a tree that is 6 m tall. If they start walking towards the tree at 2 m/s, how fast is the size of the image in the camera changing at the moment that they are 8 m away from the tree? (a) Sand is being dumped from a conveyor belt at a rate of 1.3 m/min. The sand forms a cone-shaped pile such that the diameter of the base is always ½ of the height of the pile. How fast is the height of the pile increasing when the pile is 3 m high? (Note: The volume of a cone is V = 7 r²h). (b)

Use implicit differentiation to solve the following related rate problems: (Include a properly labelled diagram as part of your solution.) #6. A student in Westdale's photography class is using a pinhole camera with a focal length of 20 cm to take a picture of a tree that is 6 m tall. If they start walking towards the tree at 2 m/s, how fast is the size of the image in the camera changing at the moment that they are 8 m away from the tree? (a) Sand is being dumped from a conveyor belt at a rate of 1.3 m/min. The sand forms a cone-shaped pile such that the diameter of the base is always ½ of the height of the pile. How fast is the height of the pile increasing when the pile is 3 m high? (Note: The volume of a cone is V = 7 r²h). (b)

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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#6. Use implicit differentiation to solve the following related rate problems: (Include a properly labelled diagram as part of your solution.) (а) A student in Westdale's photography class is using a pinhole camera with a focal length of 20 cm to take a picture of a tree that is 6 m tall. If they start walking towards the tree at 2 m/s, how fast is the size of the image in the camera changing at the moment that they are 8 m away from the tree? Sand is being dumped from a conveyor belt at a rate of 1.3 m³/min. The sand forms a cone-shaped pile such that the diameter of the base is always ½ of the height of the pile. How fast is the height of the pile increasing when the pile is 3 m high? (Note: The volume of a cone is V =r r²h ). (b)
Transcribed Image Text:#6. Use implicit differentiation to solve the following related rate problems: (Include a properly labelled diagram as part of your solution.) (а) A student in Westdale's photography class is using a pinhole camera with a focal length of 20 cm to take a picture of a tree that is 6 m tall. If they start walking towards the tree at 2 m/s, how fast is the size of the image in the camera changing at the moment that they are 8 m away from the tree? Sand is being dumped from a conveyor belt at a rate of 1.3 m³/min. The sand forms a cone-shaped pile such that the diameter of the base is always ½ of the height of the pile. How fast is the height of the pile increasing when the pile is 3 m high? (Note: The volume of a cone is V =r r²h ). (b)
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