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3. In this exercise we use the technique of completing the square to solve an optimisation problem (without needing to use differential calculus). (a) Find real numbers k and l such that the following equation holds, where x is a real number: 1800x – 10x? -10(x – k)? + l . (b) The number of pears produced by trees in a pear orchard depends on the density of the tree planting. It is known that if n trees are planted on one hectare of land then each tree will produce approximately 1800 – 10n pears. Write down a function P(n) of n that describes the total number of pears produced per hectare. (c) In the scenario of part (b), predict the number of trees per hectare that should be planted to maximise the pear yield and estimate the maximum number of pears yielded per hectare.

3. In this exercise we use the technique of completing the square to solve an optimisation problem (without needing to use differential calculus). (a) Find real numbers k and l such that the following equation holds, where x is a real number: 1800x – 10x? -10(x – k)? + l . (b) The number of pears produced by trees in a pear orchard depends on the density of the tree planting. It is known that if n trees are planted on one hectare of land then each tree will produce approximately 1800 – 10n pears. Write down a function P(n) of n that describes the total number of pears produced per hectare. (c) In the scenario of part (b), predict the number of trees per hectare that should be planted to maximise the pear yield and estimate the maximum number of pears yielded per hectare.

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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3. In this exercise we use the technique of completing the square to solve an optimisation problem (without needing to use differential calculus). (a) Find real numbers k and l such that the following equation holds, where x is a real number: 1800x – 10x² = -10(x – k)? + l. (b) The number of pears produced by trees in a pear orchard depends on the density of the tree planting. It is known that if n trees are planted on one hectare of land then each tree will produce approximately 1800 – 10n pears. Write down a function P(n) of n that describes the total number of pears produced per hectare. (c) In the scenario of part (b), predict the number of trees per hectare that should be planted to maximise the pear yield and estimate the maximum number of pears yielded per hectare.
Transcribed Image Text:3. In this exercise we use the technique of completing the square to solve an optimisation problem (without needing to use differential calculus). (a) Find real numbers k and l such that the following equation holds, where x is a real number: 1800x – 10x² = -10(x – k)? + l. (b) The number of pears produced by trees in a pear orchard depends on the density of the tree planting. It is known that if n trees are planted on one hectare of land then each tree will produce approximately 1800 – 10n pears. Write down a function P(n) of n that describes the total number of pears produced per hectare. (c) In the scenario of part (b), predict the number of trees per hectare that should be planted to maximise the pear yield and estimate the maximum number of pears yielded per hectare.
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