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stevetron

  • one year ago

Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A=27x-x^2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. a.width = 13.5 ft; area = 546.8 ft2 b.width = 27 ft; area = 182.3 ft2 c.width = 13.5 ft; area = 182.3 ft2 d.width = 27 ft; area = 391.5 ft2

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  1. campbell_st
    • one year ago
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    is this a calculus or algebra question..?

  2. stevetron
    • one year ago
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    algebra

  3. campbell_st
    • one year ago
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    ok... find the line of symmetry, use \[x = \frac{-b}{2 \times a}\] so in your question b = 27 and a = -1 substitute them to find the width for the max area

  4. campbell_st
    • one year ago
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    what you have found is the line of symmetry for the parabola. The maximum area lies on the line of symmetry so given a quadratic \[ax^2 + bx + c \] the line of symmetry is \[x = \frac{-b}{2a}\] then to find the max area, substitute the value into the original equation

  5. stevetron
    • one year ago
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    so a=27*13.5-13.5^2?

  6. campbell_st
    • one year ago
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    that's correct

  7. stevetron
    • one year ago
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    thank you for explaining it

  8. campbell_st
    • one year ago
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    glad to help

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