Math

posted by .

The area of a rectangular photograph is 59 square inches.It is to be mounted on a rectangular card with a boarder of 1 inch at each side and 2 inches at the top and bottom.Express the total area of the photograph and the boarder,A, as a function of the width of the photograph,x.what width produces the maximum area

  • Math -

    let p = area of photo = 59
    let x be the width. So, the height is 59/x

    m = (x+2)(59/x + 4)
    m = 59 + 118/x + 4x + 8

    to find max mounted area, set m' = 0

    m' = -118/x² + 4 = (4x² - 118)/x^2

    So, m' = 0 when 4x²-118 = 0
    x² - 29.5 = 0
    x = 5.43"

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math Measurements

    If the length (L) of the prism is 10 inches, and each rectangular face has a width (W) 2ã3 of inches, determine the total surface area of the prism in square inches. Round your answer to the nearest inch.
  2. Math

    A printed page is to have a total area of 100 square inches. The top and bottom margins are to be 1 inch and the side margins to be 1.5 inches. Let l represent the total length of the page and w represent the total width of the page. …
  3. Math

    A printed page is to have a total area of 100 square inches. The top and bottom margins are to be 1 inch and the side margins to be 1.5 inches. Let l represent the total length of the page and w represent the total width of the page. …
  4. Math

    A printed page is to have a total area of 100 square inches. The top and bottom margins are to be 1 inch and the side margins to be 1.5 inches. Let l represent the total length of the page and w represent the total width of the page. …
  5. Calculus

    4. A printed page is to have a total area of 100 square inches. The top and bottom margins are to be 1 inch and the side margins to be 1.5 inches. Let l represent the total length of the page and w represent the total width of the …
  6. math

    In an 8 inch by 12 inch rectangular photograph, the image of a building is 5 inches high. If the photograph is magnified until its perimeter is 720 inches, what is the height, in inches, of the image of the building in the larger photograph?
  7. Pre-Calc

    A page that is x inches wide and y inches high contains 30 square inches of print. The margins at the top and bottom are 2 inches and the margins on the side are 2 inch wide. A. show that the total area A on the page is A=2x(2x+7)/(x-4) …
  8. Calculus

    1) A rectangular page is to contain 16 square inches of print. The page has to have a 2-inch margin on top and at the bottom and a 2-inch margin on each side. Find the dimensions of the page that minimize the amount of paper used. …
  9. Calculus

    A rectangular page is to have a print area of 96 square inches. The top and bottom margins are to be 1.5 inches each and the left and right margins are to be 1 inch each. What dimensions will minimize the total area of the page. I …
  10. Algebra

    I would like some help on this problem.... A rectangular photograph has an area of 40 square inches. If the width of the photograph is 3 inches more than its height, find the dimensions of the photograph.

More Similar Questions