Can you solve this calculus area problem
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Can you solve this calculus area problem

Can you solve this calculus area problem

[From: ] [author: ] [Date: 11-09-28] [Hit: ]
-73.125 = x * (73.125/x) where 73.125 is the size of the entire page.Let x be the height of the entire page.A = (x - 1.......
A publisher decides that each page in a new book must have an area of 73.125 in^2, a 0.75 in. margin at the top and at the bottom of each page, and a 0.5 in. margin on each of the sides. What should the outside dimensions of each page be so that the printed area is a maximum?

Thanks!

-
73.125 = x * (73.125/x) where 73.125 is the size of the entire page. Let x be the height of the entire page.

The dimensions of the written area are therefore:

A = (x - 1.5) * ((73.125/x) - 1)..........Multiply that out (carefully)

A = 73.125 - x - (109.6875/x) + 1.5 = 74.625 - x - (109.6875 * x^(-1))

dA/dx = -1 + (109.6875 * x^(-2))....................... Set this equal to 0.

-1 + (109.6875 * x^(-2)) = 0

(109.6875 * x^(-2)) = 1

109.6875 = x^2

x = 10.47318 is the original height

The original width was (73.125/x) = (73.125/10.47318) = 6.98212

**************************************…
So the entire height is 10.47318

The entire width is 6.98212

**************************************…

.
1
keywords: solve,area,problem,you,Can,this,calculus,Can you solve this calculus area problem
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .