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Math Help - Answer Checks!!

  1. #1
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    Answer Checks!!

    ok so i did these problems and i would like someone to check my answers and telll me how i did...thanks alot

    find an exact solution for each problem.

    4x+19=e^(2ln(x))

    so i rearanged this equation to

    x^2-4x-19=0

    then from there i used the quadratic eq. and came up with

    x= 2+sqrt(23) and x=2-sqrt(23)


    next one

    1-2sin(t)/ln(t)=0

    rearranged this to get

    1-2sin(t)=0

    then

    sin(t)=1/2

    i did inverse sin of 1/2 and came up with pi/6
    the problem wanted the exact solution for

    2pi<t<5pi/2

    and with that i came up with 13pi/6

    and for the last one

    f(x)=4^x, and the slope of the tangent line of f(x) at x=0 is
    f`(x)=ln4. use the tangent line to estimate f(0.11) and f(0.2)

    i used ln4 for m is the equation

    y=mx+b

    then plugged one of the given points in 4^x to get a y value, then used the x and y to find b in the tangent line equation, once i found b i plugged in the given values to find y

    i came up with

    f(0.11) = 1.14

    f(0.2) = 1.28

    if someone could check my answers and let me know how i did that would be great thanks alot

    mathlete
    Last edited by mathlete; February 12th 2008 at 09:13 AM.
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  2. #2
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    mathlete, mathlete, mathlete... I expect more from you.

    Rule #1 -- It's not an equation if you don't see one of these "=".

    Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

    The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

    My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

    After requiring x > 0, how do you feel about your answers?
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  3. #3
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    yes i know its not an equation without an = sign...

    i meant to put

    x^2-4x-19=0

    sorry


    Quote Originally Posted by TKHunny View Post
    mathlete, mathlete, mathlete... I expect more from you.

    Rule #1 -- It's not an equation if you don't see one of these "=".

    Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

    The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

    My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

    After requiring x > 0, how do you feel about your answers?
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  4. #4
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    You didn't address the Domain Issues.
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  5. #5
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    Ok, well tell me what was wrong with the equation that i rearranged


    Quote Originally Posted by TKHunny View Post
    You didn't address the Domain Issues.
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  6. #6
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    Already did. See Rule #2, Above.

    e^{2ln(x)} is not quite x^{2}. What's the difference?

    Note: If we allow x to be complex, and the logarithm to provide complex values, then maybe they are EXACTLY the same. I still don't like it, but I guess I can deal with my emotional issues. :-)
    Last edited by TKHunny; February 13th 2008 at 06:14 AM.
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