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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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    @hackworthaustin123 can you help me?

  2. anonymous
    • one year ago
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    yeah let me think about this.

  3. anonymous
    • one year ago
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    Okay. the answer choices are.. A. 5 inches B. 4 inches C. 4.5 inches D. 5.5 inches

  4. anonymous
    • one year ago
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    @robtobey think maybe you can help?

  5. anonymous
    • one year ago
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    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.

  6. anonymous
    • one year ago
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    you want the highest area of all.

  7. anonymous
    • one year ago
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    Hmm okay can you explain why you chose to do those steps? And what do you think @robtobey ?

  8. anonymous
    • one year ago
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    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

  9. anonymous
    • one year ago
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    Okay but 9 isn't one of my choices..

  10. anonymous
    • one year ago
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    x is the depth or the height of one side. x = 9/2 or C. 4.5 inches.

  11. anonymous
    • one year ago
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    Oh okay I get it now, thank you guys so much.

  12. anonymous
    • one year ago
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    A plot is attached.

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  13. anonymous
    • one year ago
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    And your welcome.

  14. anonymous
    • one year ago
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    Ok thank you

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