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Math Help - NEED HELP! AP Exam tomorrow! Variety of topics

  1. #1
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    NEED HELP! AP Exam tomorrow! Variety of topics

    Since I don't feel like forcing you guys to analyze my unique typing methods, I photoshopped my questions to make them easier to analyze. Thanks a million!

    Problem: Let the velocity at a time t of a point moving on a line be defined by V(t). How many centimeters did the point travel from t = 0s to t = 2.5s.



    Answer: 9.882, but how? I tried integrating and got this



    Problem 2:



    Find the value of b such that:



    Answer: Don't have it with me, but all of the answers are written in terms of a, for example, here is a (possibly) incorrect answer of "a squared over quantity a squared minus one". Oh, and I have NO idea how to do this one. What does D sub x even mean?

    More problems to come, Thanks all! And no, I don't expect everyone to photoshop me an answer
    Last edited by Thikr; May 4th 2010 at 04:22 PM.
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  2. #2
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    your solution is correct for the given velocity function.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    your solution is correct for the given velocity function.
    So could my answer key be wrong or am I misinterpreting the problem?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Thikr View Post
    So could my answer key be wrong or am I misinterpreting the problem?
    As far as what your question is asking, I'd say the answer key is screwed up.
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  5. #5
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    Quote Originally Posted by Thikr View Post
    So could my answer key be wrong or am I misinterpreting the problem?
    have you posted the complete problem ?
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    Quote Originally Posted by skeeter View Post
    have you posted the complete problem ?
    Word for word.
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  7. #7
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    D_x means the derivative w/r to x.

    \frac{d}{dx} \left(\frac{e^{bx}}{e^{ax}}\right) =

    \frac{e^{ax} \cdot be^{bx} - e^{bx} \cdot ae^{ax}}{e^{2ax}}=

    \frac{e^{ax+bx}(b - a)}{e^{2ax}} = e^{bx-ax}(b-a)


    \frac{f'(x)}{g'(x)} = \frac{be^{bx}}{ae^{ax}} = \frac{b}{a}e^{bx-ax}


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

    ab-a^2 = b<br />

    ab-b = a^2

    b(a-1) = a^2

    b = \frac{a^2}{a-1}

    btw, you will not see a question like this on the AP exam ... too much time-consuming algebraic manipulation.
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    Quote Originally Posted by skeeter View Post
    D_x means the derivative w/r to x.

    \frac{d}{dx} \left(\frac{e^{bx}}{e^{ax}}\right) =

    \frac{e^{ax} \cdot be^{bx} - e^{bx} \cdot ae^{ax}}{e^{2ax}}=

    \frac{e^{ax+bx}(b - a)}{e^{2ax}} = e^{bx-ax}(b-a)


    \frac{f'(x)}{g'(x)} = \frac{be^{bx}}{ae^{ax}} = \frac{b}{a}e^{bx-ax}


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

    ab-a^2 = b<br />

    ab-b = a^2

    b(a-1) = a^2

    b = \frac{a^2}{a-1}

    btw, you will not see a question like this on the AP exam ... too much time-consuming algebraic manipulation.
    Damn you properties of exponentials... that makes total sense, thanks so much man, more coming later if you are up for a late night tutoring session. What program/site do you use to post your work?
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