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Math Help - Applications of Functions :-)

  1. #1
    Newbie
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    Question Applications of Functions :-)

    I have a couple of problems to check over for correction. I'm either over-complicating or over-simplifying them, ahahaha...

    Please consider these... They're probably really easy...

    Thank you!

    (*) A rectangle has an area of 38 square feet. Determine the perimeter as a function of the length l.

    (*) The volume of a right circular cylinder is 540 cubic centimeters. Express the height of the cylinder as a function of its radius r.

    (*) The hypotenuse of a right triangle is twice as long as the height. Determine the height as a function of the base b.
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  2. #2
    MHF Contributor
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    Hey, that is true. In Math, we either over-simplify or over-complicate things. And if we get it just right enough, we were just lucky.

    But then, who are to say what we did was just right enough?

    ---------
    (*) A rectangle has an area of 38 square feet. Determine the perimeter as a function of the length l.

    Rectangle.
    width = w
    length = L
    Perimeter = w+L+w+L = 2w +2L = 2(w+L)
    Area = w*L = wL

    wL = 38
    w = 38/L
    Substitute that into the Perimeter,
    Perimeter = 2(38/L +L) -------***
    Over-simpliying that,
    P = (76/L +2L)
    P = (76 +2L^2)/L ----------****

    --------
    (*) The volume of a right circular cylinder is 540 cubic centimeters. Express the height of the cylinder as a function of its radius r.

    Right circular cylinder.
    Radius = r
    Height = h
    Volume = pi(r^2)h

    pi(r^2)h = 540
    h = 540 / pi(r^2) ----------***

    -----------
    (*) The hypotenuse of a right triangle is twice as long as the height. Determine the height as a function of the base b.

    Right triangle.
    Base = b
    Height = h
    Hypotenuse = r

    Given:
    r = 2*h

    By Pythagorean theorem,
    r^2 = b^2 +h^2
    Substitute 2h for r,
    (2h)^2 = b^2 +h^2
    4h^2 = b^2 +h^2
    4h^2 -h^2 = b^2
    3h^2 = b^2
    h^2 = (b^2)/3
    Get the square roots of both sides,
    h = b / sqrt(3) ----------------------***
    Over-simplifying that,
    Rationalize the denominator,
    Multiply both numerator and denominator by sqrt(3),
    h = b*sqrt(3) / 3
    h = (1/3)b*sqrt(3) ----------***
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  3. #3
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    Talking AH! Cool!

    Yay, I'm happy... Thank you. I actually got the same answers... Woo-hoo!
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