Rectangular Package

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 20, 2021.

  1. nycmathguy

    nycmathguy

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    Section 2.5
    Question 104

    For this problem, I seek the set up for all three parts.

    20210919_212757.jpg
     
    nycmathguy, Sep 20, 2021
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  2. nycmathguy

    MathLover1

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    a.

    volume
    V=length*width*height
    length=width=x
    height=y
    so
    V=x*x*y
    V=x^2*y

    given

    perimeter of base+height is 120
    4x+y=120
    y=120-4x


    then
    V=x^2(120-4x)
    V=120x^2-4x^3
    V=-4x^3+120x^2


    b
    upload_2021-9-19_23-20-20.png

    max at (20,16000)

    c.
    13500=-4x^3+120x^2

    x = 15
     

    Attached Files:

    MathLover1, Sep 20, 2021
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  3. nycmathguy

    nycmathguy

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    Nicely-done. I requested the set up only for each part but thank you for working it out.

    What about the two unanswered threads below?

    1. Verifying Upper & Lower Bounds

    2. Descartes' Rule of Signs

    They are two separate threads in this forum. We then move on to Section 2.6 aka Rational Functions.
     
    nycmathguy, Sep 20, 2021
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