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Thread: Help with Solving for Variable

  1. #1
    Junior Member
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    Help with Solving for Variable

    I'm in a hurry and I need some help with solving for the variable in these functions. I've already tried doing them all myself but I can't get the answer.

    Here are the problems:

    1. -t^(1/3) + (8/3) - 1/3(t) = 0


    2. -2sint + 2cos2t = 0


    3. e^(x^2/8)-x^(6/8)8*e^(x^2/8)
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  2. #2
    Super Member

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    Hello, dm10!

    Check the accuracy of your typing.
    And it would help if you gave us the answers you're expecting.


    1)\;\;-t^{\frac{1}{3}} + \frac{8}{3} - \frac{1}{3}t\:=\:0

    Multiply by -3: . 3t^{\frac{1}{3}} - 8 + t \:=\:0 \quad\Rightarrow\quad t + 3t^{\frac{1}{3}} - 8 \;=\;0

    Let u = t^{\frac{1}{3}} \quad\Rightarrow\quad u^3 = t

    Substitute: . u^3 + 3u - 8 \:=\:0

    But this equation has no rational roots . . .




    2)\;\;-2\sin t + 2\cos2t \:=\: 0
    Identity: . \cos2\theta \:=\:1-2\sin^2\theta

    So we have: . 2\sin t + 2(1 - 2\sin^2\!t) \:=\:0

    . . which simplifies to: . 2\sin^2\!t + \sin t - 1 \:=\:0

    . . which factors: . (\sin t + 1)(2\sin t - 1) \:=\:0

    And we have: . \begin{array}{ccccccccc}\sin t  +1\:=\:0 & \Rightarrow & \sin t \:=\:\text{-}1 & \Rightarrow & t \:=\:\frac{3\pi}{2} \\ <br />
2\sin t-1\:=\:0 & \Rightarrow & \sin t \:=\:\frac{1}{2} & \Rightarrow & t \:=\:\frac{\pi}{6},\:\frac{5\pi}{6} \end{array}




    3. e^(x^2/8)-x^(6/8)8*e^(x^2/8) . . . . What does this say ??
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