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SOVA2 [1]
3 years ago
15

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 provid

e maximum​ cross-sectional area and hence allow the most water to​ flow?
Mathematics
1 answer:
fredd [130]3 years ago
7 0

Answer:

18 in^2

Step-by-step explanation:

<em>1  )The three sides of the gutter add up to 12</em>

            2x+ y = 12  

<em>2)  Subtract 2x from both sides. </em>

           y = 12 — 2x  

<em>3 )Find the area of the rectangle in terms of x and simplify.</em>

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

<em>4 )  x=-b/2a</em>

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

<em>5 )Plug in 3 for x into they equation.</em>

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

<em>6  )  Plug in 3 for x and 6 for y.  </em>

      Area= xy = 3(6) = 18  

RESULT  

            18 in^2

 

 

 

 

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