The new owner of an apartment wants to install a window in the shape of a rectangle surrounded by a semicircle in order to allow more light into the apartment as shown below. The owner has 336cm of wood for a surround to the window and wants to determine the dimensions, as shown in the diagram above, that will allow as much light into the apartment as possible. a. Show that the area A, in cm2, of the window is A = 336x –(4 + n)x² . b. Hence determine, to the nearest cm, the width and the height of the window for which the area is greatest. c. Structural problems require that the width of the window should not exceed 84cm. What should the new dimensions of the window be for maximum area?

The new owner of an apartment wants to install a window in the shape of a rectangle surrounded by a semicircle in order to allow more light into the apartment as shown below. The owner has 336cm of wood for a surround to the window and wants to determine the dimensions, as shown in the diagram above, that will allow as much light into the apartment as possible. a. Show that the area A, in cm2, of the window is A = 336x –(4 + n)x² . b. Hence determine, to the nearest cm, the width and the height of the window for which the area is greatest. c. Structural problems require that the width of the window should not exceed 84cm. What should the new dimensions of the window be for maximum area?

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 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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