A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90 degrees. What depth will provide maximum cross-sectional area and hence allow the most water to flow?

18 in^2

Step-by-step explanation:

1  )The three sides of the gutter add up to 12

            2x+ y = 12  

2)  Subtract 2x from both sides.

           y = 12 — 2x  

3 )Find the area of the rectangle in terms of x and simplify.

    Area = xy = x(12 — 2x) = -2x^2+12x = f(x)  

4 )  x=-b/2a

     x co-ordinate of the vertex= -12/2(-2)=3

5 )Plug in 3 for x into they equation.

    y co-ordinate of the vertex= 12 — 2(3) = 6  

6  )  Plug in 3 for x and 6 for y.  

      Area= xy = 3(6) = 18  

RESULT  

            18 in^2

step-by-step explanation:

yes it represnts a functio, their are not 2 of the same numbers on the both sides