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Homework Help: Problems involving maximum and minimum values

  1. May 30, 2005 #1
    o:)
    here comes the question

    A varianble rectangle is inscribed in a given semicircle, so that one side lies along the bounding diameter, and two vertices lie on the bounding arc.
    1 Show that wgeb tge area if tge rectangle is greatest, the sides of the rectangle are in the ratio 2:1

    2 Show further that when the perimeter of the rectangle has a turning value the sides are in the ratio 4:1,
    and determine the nature of the turning value.

    Ans:maximum

    :surprised :rofl: :confused: :yuck:
     
  2. jcsd
  3. May 30, 2005 #2
    Last edited by a moderator: Apr 21, 2017
  4. May 30, 2005 #3

    HallsofIvy

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    You have a rectangle inscribed in a semi-circle (radius not given so call it R). One side of the rectangle is along the diameter of the semi-circle. If we call the length and width of the rectangle l and w, then the area is lw and the perimeter is 2l+ 2w.
    Now: can you write w (and therefore the area and perimeter) as a function of l only?
    What is the derivative, with respect to l, of the area and perimeter functions?
     
  5. Jun 5, 2005 #4
    whozum

    excuse me whozum, :bugeye:
    if i didn't try my best to figure out this question will i simply post it here??
    i had read the that section the first day soon after i become a member here.
    if i didn't put any effort on this questions will i put any extra effort to come here and type the question to post it up here????? i would rather ignore the question.
    BTW, this is not my homework, this is the exercises i make myself do as i didn't go for math tuition or extra classes.
     
  6. Jun 5, 2005 #5
    HallsoftIvy

    okei
    if u mention it that way,,,,,,,
    can the rectangle be rectangle when inscribed in it with one side of the length is the diameter of the semicircle?
    i tried to draw it before i post this question and i found that to be a shape like trapezium..?? :uhh:
     
    Last edited: Jun 5, 2005
  7. Jun 5, 2005 #6

    HallsofIvy

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    Yes, that's what inscribed means!

    ??? What do you have to do to get a rectangle, rather than a trapezium? Is the side on the diameter of the semicircle symmetric with respect to the center of that line?
     
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