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A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the perimeter, P, of the plate, is a minimum. (a) If the length of the plate is x cm and the breadth is y cm, draw a diagram and show that the perimeter, P, can be expressed in terms of x only as: 2х + 72х1 ст. %3D dP and dx d²P and use these derivatives to determine the (b) Find - dx2 dimensions of the component for which the perimeter is a minimum. Calculate the minimum perimeter.

A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the perimeter, P, of the plate, is a minimum. (a) If the length of the plate is x cm and the breadth is y cm, draw a diagram and show that the perimeter, P, can be expressed in terms of x only as: 2х + 72х1 ст. %3D dP and dx d²P and use these derivatives to determine the (b) Find - dx2 dimensions of the component for which the perimeter is a minimum. Calculate the minimum perimeter.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A rectangular plate with an area of 36 cm2 is to be produced on a lathe in such a way that the perimeter, P, of the plate, is a minimum. (a) If the length of the plate is x cm and the breadth is y cm, draw a diagram and show that the perimeter, P, can be expressed in terms of x only as: P = 2x + 72x-' cm. d²P dP and dx (b) Find and use these derivatives to determine the dx? dimensions of the component for which the perimeter is a minimum. Calculate the minimum perimeter.
Transcribed Image Text:A rectangular plate with an area of 36 cm2 is to be produced on a lathe in such a way that the perimeter, P, of the plate, is a minimum. (a) If the length of the plate is x cm and the breadth is y cm, draw a diagram and show that the perimeter, P, can be expressed in terms of x only as: P = 2x + 72x-' cm. d²P dP and dx (b) Find and use these derivatives to determine the dx? dimensions of the component for which the perimeter is a minimum. Calculate the minimum perimeter.
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