mathematics

posted by .

Please help me answer this question;

1.A metal gutter open at the tops and ends, is bent up from material 30 cm wide to form a rectangular cross section.
a) If the base of the gutter is x cm wide, find the height of the gutter.
b)Show that the area of the gutter cross section is given by A = 15x - x^2/2.

Thanks.

  • mathematics -

    Make a sketch of the cross-section
    I would assume the you are bending the 30 cm wide piece so that the two sides of the gutter are of equal height.
    then if the base is x cm, then the height must be (30-x)/2 or 15 - x/2 or 15 - (1/2)x

    Area = base x height
    = x(15 - x/2) = 15x - x^2/2

  • mathematics -

    thank you very much for your help.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math Wrod Problem

    1. A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimentions of the cross-section if the carrying capacity of the trough is …
  2. calculus

    A long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?
  3. geometry

    a piece of rectangular sheet metal is 20 in. wide. It is made into a rain gutter by turning up the edges to form parallel sides. Let x represent the length of each of the parallel side. (a)give the restrictions on x (b)determine a …
  4. pre-calc

    construction of a rain gutter: a piece of rectangular sheet metal is 20 inches wide. it is to be made into a rain gutter by turning the edges to form parallel sides. let x represent the length of each of the parallel. a) give the restrictions …
  5. math problem

    A simple rain gutter is constructed using a sheet of aluminum that is 40cm wide. The edges are turned up to form right angles. Determine the depth of the gutter that will maximize the cross-sectional area (allowing the greatest amount …
  6. spc

    a long strip of sheet metal 12 inches wide is to be formed into an open gutter with a rectangular cross-section as shown. what is the maximum possible area of the cross-section?
  7. Pre-Calc)

    a piece of rectangular sheet metal is 20 in wide. It's to be made into rain gutter by turning the edges to form parallel sides. Let x represent the length of each of parallel sides. a. give restrictions on x. b. determine a function …
  8. Calculus

    A 10-foot section of gutter is made from a 12-inch-wide strip of sheet metal by folding up 4-inch strips on each side so that they make the same angle with the bottom of the gutter. Determine the depth of the gutter that has the greatest …
  9. Calculus

    A 10-foot section of gutter is made from a 12-inch-wide strip of sheet metal by folding up 4-inch strips on each side so that they make the same angle with the bottom of the gutter. Determine the depth of the gutter that has the greatest …
  10. Algebra

    A rain gutter is made from sheets of aluminum that are 11 inches wide. As shown in the figure the edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 10 in.². Show …

More Similar Questions