Simple Math Question - Can't believe I can't get this

Discussion in 'General Off-Topic Chat' started by jonthedit, Sep 15, 2014.

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  1. jonthedit
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    jonthedit GBAtemp Advanced Maniac

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    So I was doing my basic pre-cal level homework and I bumped into this question.
    [​IMG]

    Easy right?

    P = 20 [ft]

    C of Cir = 2(pi)(r), areas of cir is = pi(r^2) where r is radius

    I know this is easy... yet I can not wrap my head around the question? Maybe it is just my brain being weird and I will get it tomorrow morning.

    The problem is I am not sure what to solve for or what to do!
     
  2. geishroy

    geishroy Suspended

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    A norman window is one that consists of a rectangle with a curved top to it.
    the curved top is actually a semicircle that sits on top of the rectangle.
    if the perimeter around the norman window is 20 feet, what radius of the
    semicircle will provide the greatest window area?
    :
    Let H = the height of the rectangular portion of the window
    :
    Let x = the radius of the semi circle on top
    :
    Half the circumference = pi*x
    :
    Width of the window = 2x
    :
    The perimeter:
    2H + 2x + pix = 20
    Solve for H
    2H = 20 - 2x - pix
    H = [​IMG]
    :
    Area formula: A = (H*2x) + .5pi*x^2
    Replace H with [​IMG]
    A = 2x([​IMG])+ [​IMG]
    Cancel the 2
    A = [​IMG]+ [​IMG]

    A = [​IMG]
    Leaving us with
    A = [​IMG]
    .5*pi = 1.57
    A = [​IMG]
    A = [​IMG]
    A quadratic equation, find the vertex for max area; a=-3.57, b=20
    x = [​IMG]
    x = [​IMG]
    x = 2.8 ft radius for max area
    :
    Check solution by finding the perimeter with this radius
    Find 2H
    2H = 20 - 2(2.8) - 2.8pi
    2H = 5.6 ft
    Find perimeter:
    2H + 2x + pix = 20
    5.6 + 2(2.8) + 2.8*pi =
    5.6 + 5.6 + 8.8 = 20
    ;
    note that max area is when the rectangular portion, is a square, 5.6 by 5.6
     
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  3. jonthedit
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    jonthedit GBAtemp Advanced Maniac

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    THHANK YOU SO MUCH! This really helped me understand what I was missing!
    I can do the rest now!
     
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