Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Solve for t? confused?

(3/4)t^(1/4) - (1/2)t^(3/4) = 0

what is t?

Update:

0, 9/4 is wrong or not all answers

Update 2:

Actually it looks like you people are right and the answer key may be wrong, thanks for the help on doing this question everyone

Sorry to have doubted your response! :)

4 Answers

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    t = {0,9/4}

    (3/4)t^(1/4) = (1/2)t^(3/4)

    (3/4)^4 * t = (1/2)^4 * t³

    t² = (6/4)^4

    t = (3/2)²

    But note that t = 0 solves the original equation too.

    Since you doubt, plug and check.

    (3/4) * 0^(1/4) = (1/2) * 0^(3/4) ... Yep.

    (3/4) * (9/4)^(1/4) = (1/2) * (9/4)^(3/4)

    (81/256) * (9/4) = (1/16) * (729/64)

    79/1060 = 729/1060 ... Yep

    If you still doubt, plot

    y(t) = (3/4)t^(1/4) - (1/2)t^(3/4)

    and see how many times it crosses the t axis.

  • 1 decade ago

    (3/4)t^(1/4) = (1/2) t^ (3/4)

    Take both sides to the 4th power.

    81/256 t = 1/16 t^3

    Multiple by 16: t^3 - 81/16 t = 0 Factor

    t (t + 9/4) ( t - 9/4) = 0 t = 0, 9/4, - 9/4

    But -9/4 must be rejected . In the original problem you would be taking the 4th root of a negative number.

  • 1 decade ago

    t = 9/4

  • 1 decade ago

    One solution, by inspection is t = 0.

    Let's look for another:

    (3/4)t^(1/4) - (1/2)t^(3/4) = 0

    Add (1/2)t^(3/4) to both sides:

    (3/4)t^(1/4) = (1/2)t^(3/4)

    Multiply both sides by 2:

    (3/2)t^(1/4) = t^(3/4)

    Divide both sides by t^(1/4)* ... note, if t = 0, you can't do this step.

    3/2 = t^(3/4) / t^(1/4)

    Remember this rule x^a / x^b = x^(a-b):

    3/2 = t^(1/2)

    3/2 = √t

    Square both sides:

    9/4 = t

    Answer:

    t = 0

    t = 9/4

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