A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formula, a is the

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A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 4 apparel items will be manufactured, how many units of fabric should be ordered?

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niczorrrr 5 years 2021-09-03T10:19:36+00:00 1 Answers 114 views 0

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  1. giabao
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    2021-09-03T10:20:50+00:00
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    Questions:

    A clothing manufacturer uses the model a = √(f + 4) – √(36 – f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?


    Answer:

    32 units of fabrics

    Step-by-step explanation:

    Given

    a = \sqrt{f + 4} - \sqrt{36 - f}

    Required

    Find f when a  = 4

    Substitute 4 for a

    4 = \sqrt{f + 4} - \sqrt{36 - f}

    Rewrite as:

    \sqrt{36 - f} + 4 = \sqrt{f + 4}

    Square both sides

    (\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2

    (\sqrt{36 - f} + 4)^2 = f + 4

    36 - f + 8\sqrt{36 - f} + 16 = f + 4

    Collect Like Terms

    8\sqrt{36 - f}= f +f+ 4 - 36 -16

    8\sqrt{36 - f}= 2f -48

    Divide through by 2

    4\sqrt{36 - f}= f -24

    Square both sides

    16(36-f) = (f - 24)^2

    16(36-f) = f^2 - 48f + 576

    576-16f = f^2 - 48f + 576

    -16f = f^2 - 48f

    Collect like terms

    f^2 - 48f + 16f = 0

    f^2 -32f = 0

    Factorize

    f(f - 32) = 0

    f = 0 or f = 32

    f can not be 0 because some units must be ordered.

    So, f = 32

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