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Math Help - Application in the derivative ..?

  1. #1
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    Application in the derivative ..?

    I hope that someone help me in solving these application. (plz, I want to solution step by step)..


    Q1:

    A Cassna plane takes off from an airport at sea level and it's altitude (in feet) at time t (in minutes) is
    given by h= 2000 ln (t+1) .
    find the rate of climb at time t = 3min .


    Q2:

    If the variable sound power W is given by W = T^2 + t + 1 , Find the rate of change of the sound
    pressure P , at time t= 3 s .


    Q3:

    A computer is programmed to inscribe a series of rectangle in the first quadrant under the curve of y=e^-x
    What is the greatest area of the largest rectangle that can be inscribed ? .


    Q4:

    A point moves along the x axis so that it's position x at time t is specificed by the function x(t)= t^3-8t+8 .
    determine the following :
    a- the acceleration at times when the velocity is zero .
    b- the average velocity over the time interval (0,6) .


    I'm sorry for all this quastion ..
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  2. #2
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    Hello, explore!

    Q3: A computer is programmed to inscribe a series of rectangles
    in the first quadrant under the curve of y\,=\,e^{-x}

    What is the greatest area of the largest rectangle that can be inscribed?
    Code:
                |
           *    |
             *  |
                *
                |   *
                + - - - - *
                |:::::::::|y      * 
                |:::::::::|                 *
          - - - + - - - - * - - - - - - - - - - 
                |    x

    The area of the rectangle is: . xy

    So we have the area function: . A \:=\:x\cdot e^{-x}

    Maximize it . . .

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  3. #3
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    if you know that you need to use the derivative, then where are you having trouble with these?
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, explore!

    Code:
                |
           *    |
             *  |
                *
                |   *
                + - - - - *
                |:::::::::|y      * 
                |:::::::::|                 *
          - - - + - - - - * - - - - - - - - - - 
                |    x
    The area of the rectangle is: . xy

    So we have the area function: . A \:=\:x\cdot e^{-x}

    Maximize it . . .
    NICE ^_^ .. But what is the next step after we found the area function ??


    Quote Originally Posted by artvandalay11 View Post
    if you know that you need to use the derivative, then where are you having trouble with these?
    I know that my friend ^_^ .. I can't solve these problem ^_^ because I don't know when, why and where I will use the derivative ??
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  5. #5
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    for the second one, you need to find the rate of change (a.k.a. the value of the derivative) at t=3,... so take a derivative and plug in 3 for t

    using the same idea you should be able to do 1
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