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We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. SO

We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. SO

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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I. We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum. (Apply the 2d derivative of the formulated equation to check if the point x is minimized) 3. We want to construct a box with a square base and we only have 10 m² of material to use in construction of the box. If all the material is used in the construction process determine the maximum volume that the box can have. 4. We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners as shown below and fold up the sides to form a box, also shown below. Determine the height of the box that will give a maximum volume.
Transcribed Image Text:I. We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum. (Apply the 2d derivative of the formulated equation to check if the point x is minimized) 3. We want to construct a box with a square base and we only have 10 m² of material to use in construction of the box. If all the material is used in the construction process determine the maximum volume that the box can have. 4. We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners as shown below and fold up the sides to form a box, also shown below. Determine the height of the box that will give a maximum volume.
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