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Math Help - Need help on study guide

  1. #1
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    Need help on study guide

    Working on a study guide for a test, not sure how to work these problems out. Anyone mind showing me how to work them out?


    Solve: 9+3/x = 2/x^2

    The function F(X) = -x^2+46x-360 models the daily profit, F(X), in hundreds of dollars, for a company that manufactures x computers daily. How many computers should be manufactured to maximize profit? What is the maximum daily profit?

    Find the domain of F(X)= x/x^2-16

    Solve: 4^x+6=16

    Solve: 3^2x+1=27

    Solve: x^1/2-2x^1/4-15=0
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  2. #2
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    Quote Originally Posted by conn337 View Post
    Working on a study guide for a test, not sure how to work these problems out. Anyone mind showing me how to work them out?


    Solve: 9+3/x = 2/x^2
    Hi conn337,

    9 + \frac{3}{x} = \frac{2}{x^2}

    \text{Assume }x \ne 0

    Multiply each term by x^2 and set equal to zero, arriving at

    9x^2+3x-2=0

    Factor and solve for x.


    Quote Originally Posted by conn337 View Post
    The function F(X) = -x^2+46x-360 models the daily profit, F(X), in hundreds of dollars, for a company that manufactures x computers daily. How many computers should be manufactured to maximize profit? What is the maximum daily profit?
    Find the x coordinate of the maximum point.

    x=\frac{-b}{2a}


    Quote Originally Posted by conn337 View Post
    Find the domain of F(X)= x/x^2-16
    f(x)=\frac{x}{x^2-16}

    Factor the denominator to get:

    f(x)=\frac{x}{(x+4)(x-4)}

    The domain of the function is all real numbers except the two that cause the denominator to be zero.

    Quote Originally Posted by conn337 View Post
    Solve: 4^x+6=16
    4^{x+6}=16

    4^{x+6}=4^2

    Use this rule: \text{If }a^x=a^y \text{ , then }x=y

    Quote Originally Posted by conn337 View Post
    Solve: 3^2x+1=27
    Solve this one like the one before it.

    Quote Originally Posted by conn337 View Post
    Solve: x^1/2-2x^1/4-15=0
    x^{\frac{1}{2}}-2x^{\frac{1}{4}}-15=0

    Use quadratic techniques to solve.

    x^{(\frac{1}{4})^2}-2x^{\frac{1}{4}}-15=0
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  3. #3
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    thanks!!
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