a) An open-top box is to be constructed with 1500 cm^2 of material. The length of the base is to be twice the width. Find the largest possible volume of the box. b) A rancher wants to fence in an area of 2,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of the fence that the rancher can use? c) A cylindrical can without a top must be constructed to contain V = 2000 cm3 of liquid. Find the base radius r and height h that will minimize the amount of material needed to construct the can.
a) An open-top box is to be constructed with 1500 cm^2 of material. The length of the base is to be twice the width. Find the largest possible volume of the box. b) A rancher wants to fence in an area of 2,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of the fence that the rancher can use? c) A cylindrical can without a top must be constructed to contain V = 2000 cm3 of liquid. Find the base radius r and height h that will minimize the amount of material needed to construct the can.
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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5. a) An open-top box is to be constructed with 1500 cm^2 of material. The length of the base is to be twice the width. Find the largest possible volume of the box.
b) A rancher wants to fence in an area of 2,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of the fence that the rancher can use?
c) A cylindrical can without a top must be constructed to contain V = 2000 cm3 of liquid. Find the base radius r and height h that will minimize the amount of material needed
to construct the can.
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