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Problem 2 A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of T. The length of string is 54 cm. Representation, Illustration, Quantity to be Maximized or Minimized Illustration Representation: | Quantity to be Minimized Setting up of Function, Differentiation, Critical Numbers, Maximum/Minimum Value Function: Computation of Derivative Computation of Critical Numbers Computation of Minimum Value Checking using Second Derivative Test Answer in Complete Sentence

Problem 2 A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of T. The length of string is 54 cm. Representation, Illustration, Quantity to be Maximized or Minimized Illustration Representation: | Quantity to be Minimized Setting up of Function, Differentiation, Critical Numbers, Maximum/Minimum Value Function: Computation of Derivative Computation of Critical Numbers Computation of Minimum Value Checking using Second Derivative Test Answer in Complete Sentence

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2 A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of r. The length of string is 54 cm. Representation, Illustration, Quantity to be Maximized or Minimized llustration Representation: Quantity to be Minimized Setting up of Function, Differentiation, Critical Numbers, Maximum/Minimum Value Function: Computation of Derivative Computation of Critical Numbers Computation of Minimum Value Checking using Second Derivative Test Answer in Complete Sentence
Transcribed Image Text:Problem 2 A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of r. The length of string is 54 cm. Representation, Illustration, Quantity to be Maximized or Minimized llustration Representation: Quantity to be Minimized Setting up of Function, Differentiation, Critical Numbers, Maximum/Minimum Value Function: Computation of Derivative Computation of Critical Numbers Computation of Minimum Value Checking using Second Derivative Test Answer in Complete Sentence
A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of T. The length of string is 64 cm.
Transcribed Image Text:A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of T. The length of string is 64 cm.
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