10. You have a load of tiles that can cover an area of 400 t. You want to cover a rectangular shape of dimensions x and y, using all 400 ft'of tiles availabie. At the same time you have limited material to build a border around the rectangle, so you want to keep the perimeter of the rectangle at a minimum. Find the dimensions x and y of the rectangle, which has area equal to 400 ft'and minimum perimeter. 400 Hint. The area is xy = 400 y= The perimeter is P-2x+2y. Substitute y in terms of x in this equation to get the perimeter as a function of x. Plot the function P(x) with respect to x for x in the range (1, 80]. The minimum of the function Pfx) will occur at a critical point x. To make a precise identification of this point x. plot the first derivative of P(x) and find out where P'(x) = 0. After you calculate the dimension x, you can calculate the dimension y. A- 400 ft y

10. You have a load of tiles that can cover an area of 400 t. You want to cover a rectangular shape of dimensions x and y, using all 400 ft'of tiles availabie. At the same time you have limited material to build a border around the rectangle, so you want to keep the perimeter of the rectangle at a minimum. Find the dimensions x and y of the rectangle, which has area equal to 400 ft'and minimum perimeter. 400 Hint. The area is xy = 400 y= The perimeter is P-2x+2y. Substitute y in terms of x in this equation to get the perimeter as a function of x. Plot the function P(x) with respect to x for x in the range (1, 80]. The minimum of the function Pfx) will occur at a critical point x. To make a precise identification of this point x. plot the first derivative of P(x) and find out where P'(x) = 0. After you calculate the dimension x, you can calculate the dimension y. A- 400 ft y

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

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