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Math Help - Need some more help with these problems

  1. #1
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    Jan 2008
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    Need some more help with these problems

    Find all real solutions of the equation.
    x^2 + x - 30 = 0

    theres a smaller and larger solution


    Find all real solutions of the equation. (If there is one solution with a multiplicity of two, enter it in both answer boxes.)
    10x^2 + 60x + 90 = 0
    on this one i found the smaller solution is -3 but i dont know the larger
    dont worry about the boxes thing

    Find all real solutions of the equation.
    w^2 = 4(w + 5)

    two answers again here


    Solve the equation for x. (If there is one solution with a multiplicity of two, enter it in both answer boxes.)
    a^2x^2 + 8ax + 16 = 0


    Find all values of k that ensure that the given equation has exactly one solution.
    6x^2 + kx + 9 = 0




    A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire?






    any help would be greatly appreciated!

    thanks
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    you can solve all of these problems using the formula for the roots of a quadratic equation given in the following general form:

    p(x) = a*x^2 + b*x + c

    X1 = (-b + sqrt(b^2 - 4*a*c)) / (2*a)
    X2 = (-b - sqrt(b^2 - 4*a*c)) / (2*a)

    the discriminant is defined as
    delta = b^2 - 4*a*c

    if delta equals zero there is one root with a multiplicity of two, if it's negative then the roots are complex and if it's positive the roots are real

    A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire
    let's denote the length of the piece used for creating the square as x, and that used for creating the circle as y.

    obviously -> x+y = 370

    the area of the square is (x/4)^2
    the perimeter of the circle is 2*pi*r = y, and we know that it's area is pi*r^2
    thus we can express it's area using y as follows: pi*(y / 2*p)^2

    now we are told that both of the figures have the same area thus: (x/4)^2 = pi*(y / 2*p)^2

    which leaves us with two equations in two unknowns:

    x + y = 370
    (x/4)^2 = pi*(y / 2*p)^2

    I think that you'll be able to continue from here...
    Last edited by Peritus; January 13th 2008 at 02:21 PM.
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