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Math Help - Urgent - Calculus

  1. #1
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    Urgent - Calculus

    1) A searchlight is kept focus on an aircraft that flies directly above the light at a constant altitude of 2 kilometers and speed of 0.2 kilometer per second. Two seconds after the plane is directly over the light, how fast (in rad/s) is the light rotating?


    2)Use a linear approximation (or differentials) to estimate

    15.97^{3/4}

    3)A curve passes through the point (0,4) and has the property that the slope of the curve at every point P is three times the y- coordinate of P. What is the equation of the curve?
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  2. #2
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    Quote Originally Posted by treetheta View Post
    ...
    3)A curve passes through the point (0,4) and has the property that the slope of the curve at every point P is three times the y- coordinate of P. What is the equation of the curve?
    1. You know: y' = 3y~\implies~\dfrac{y'}{y} = 3

    Integrate wrt x:

    \int\left(\dfrac{y'}{y}\right)dx=\int 3dx~\implies~\ln(y)=3x+k

    Solve for y:

    y = e^{3x+k}

    The graph of this function passes through P(0, 4):

    4=e^{0+k}~\implies~k=\ln(4)

    Thus: y= e^{3x+\ln(4)}  = \boxed{4\cdot e^{3x}}
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  3. #3
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    Omg, thank you so much,

    can someone help me with the remaining questions
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