anonymous
  • anonymous
A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@hackworthaustin123 can you help me?
anonymous
  • anonymous
yeah let me think about this.
anonymous
  • anonymous
Okay. the answer choices are.. A. 5 inches B. 4 inches C. 4.5 inches D. 5.5 inches

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More answers

anonymous
  • anonymous
@robtobey think maybe you can help?
anonymous
  • anonymous
okay so the area of this has to be length times width. So, I'm thinking the answer is 5.5. you take 18 and subtract it from 5.5. That will give you 12.5. Then you take 12.5 and divide it by 2. That'll give you 6.25. Then, you'll take 6.25 and multiply it by 2, and it'll give you 34.375, which is the largest area of all the answer choices you have.
anonymous
  • anonymous
you want the highest area of all.
anonymous
  • anonymous
Hmm okay can you explain why you chose to do those steps? And what do you think @robtobey ?
anonymous
  • anonymous
Let x be the height of one side. Cross sectional area is x(18-2x) Set the derivative of x (18 - 2 x) to zero and solve for x. x = 9/2, 18-2x = 9
anonymous
  • anonymous
Okay but 9 isn't one of my choices..
anonymous
  • anonymous
x is the depth or the height of one side. x = 9/2 or C. 4.5 inches.
anonymous
  • anonymous
Oh okay I get it now, thank you guys so much.
anonymous
  • anonymous
A plot is attached.
1 Attachment
anonymous
  • anonymous
And your welcome.
anonymous
  • anonymous
Ok thank you

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