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Math Help - Multiple random questions with answers, need explaination?

  1. #1
    Newbie
    Joined
    Sep 2006
    Posts
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    Multiple random questions with answers, need explaination?

    Please explain how these questions will be solved to get these answers.

    Q: Solve for z: e^2z-1 =3
    A: (In3+1)/2

    Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
    A: 75

    Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
    A: -5

    Q: Find x: 3^2x-3x= 72
    A: 2

    Q:Simplify (a^-2 - b^-2) / (a-b)
    A: - (a+b) / (a^2b^2)

    Q:Find an equation of the circle having center (4, -3) and radius 5.
    A: x^2+y^2-8x+6y=0

    Q: What is the solutions for the equation ^3√x^2 - ^3√x - 6 = 0
    A: (-8, 27)

    Q: Find the number of consecutive odd integers beginning with 23 which are necessary to make a sum of 608.
    A: 16

    Q: Find the vertex of the parabola 4x=y^2-4y
    A: (-1,2)

    Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
    A: 150

    I really need to know this ASAP

    Thanks
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by Hi888 View Post
    Please explain how these questions will be solved to get these answers.

    Q: Solve for z: e^2z-1 =3
    A: (In3+1)/2

    Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
    A: 75

    Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
    A: -5

    Q: Find x: 3^2x-3x= 72
    A: 2

    Q:Simplify (a^-2 - b^-2) / (a-b)
    A: - (a+b) / (a^2b^2)

    Q:Find an equation of the circle having center (4, -3) and radius 5.
    A: x^2+y^2-8x+6y=0

    Q: What is the solutions for the equation ^3√x^2 - ^3√x - 6 = 0
    A: (-8, 27)

    Q: Find the number of consecutive odd integers beginning with 23 which are necessary to make a sum of 608.
    A: 16

    Q: Find the vertex of the parabola 4x=y^2-4y
    A: (-1,2)

    Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
    A: 150

    I really need to know this ASAP

    Thanks
    Hi

    e^{2z-1} =3 \implies 2z-1 = \ln(3) \implies z = \frac{\ln(3)+1}{2}

    \frac{650-200}{800-200} = \frac{x-0}{100-0} \implies \frac{450}{600} = \frac{x}{100} \implies x = 75

    g(x) = 1-x \implies g(-2) = 1-(-2) = 3 \implies f[g(-2)] = f(3) = 4-3^2 = 4-9 = -5

    3^{2x} - 3^x = 72 \implies \left(3^x\right)^2 - 3^x - 72 = 0 \implies X = 3^x \:and\: X^2 - X - 72 = 0 X = -8 \r\: X = 9) \implies X = 3^x \:and \:X = 9 \implies 3^x = 9 \implies x = 2" alt=" \implies X = 3^x \:and \X = -8 \r\: X = 9) \implies X = 3^x \:and \:X = 9 \implies 3^x = 9 \implies x = 2" />

    \frac{a^{-2} - b^{-2}}{a-b} = \frac{\frac{1}{a^2} - \frac{1}{b^2}}{a-b} = \frac{\frac{b^2-a^2}{a^2b^2}}{a-b} = \frac{(b-a)(b+a)}{a^2b^2(a-b)} = -\frac{a+b}{a^2b^2}

    (x-4)^2 + (y-(-3))^2 = 25 \implies x^2-8x+16+y^2+6y+9 = 25 \implies x^2+y^2-8x+6y=0

    23 + (23+2) + (23+4) + \cdots + (23+2n) = 608 \implies 23(n+1) + (2 + 4 + \cdots + n) = 608  \implies 23(n+1) + 2(1+2+\cdots+n)=608  \implies 23(n+1) + n(n+1) = 608 \implies n^2+24n-585=0 \implies n=15 \implies (n+1)=16

    Diagonal of the cube (length of the sides = a) is a\sqrt{3} (apply twice Pythagorean). Therefore a = 5.
    Surface area is 6 (number of faces) x 5 x 5 (surface of each face) = 150
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  3. #3
    Junior Member JoanF's Avatar
    Joined
    Apr 2009
    Posts
    39
    Q: A student's test score was 650 on a scale of 200-800. Convert this score to a scale of 0-100.
    A: 75

    Q:If f(x) = 4-x^2 and g(x)=1-x, find f[g(-2)]
    A: -5


    Q:Find an equation of the circle having center (4, -3) and radius 5.
    A: x^2+y^2-8x+6y=0


    Q: Find the vertex of the parabola 4x=y^2-4y
    A: (-1,2)


    Q: A cube has a diagonal of length 5√3. Find its surface area in sq. units.
    A: 150

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