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If the original 24 m edge length x of a cube decreases at the rate 5m/min, when x=3 at what rate does the cube's surface area change

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  1. 6 May, 06:59
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    Let s be the surface area and t = time in minutes

    s=6x²

    d/dt (s) = d/dt (6x²)

    ds/dt=12x (dx/dt)

    given that x=3, then

    ds/dt=12 (3) (-5)

    ds/dt=-180m²/min

    b] Let the volume be v

    v=x³

    d/dt (v) = d/dt (x³)

    dv/dt=3x² (dx/dt)

    when x=3, then

    dv/dt=3 (3²) (-5)

    dv/dt=-135m³/min
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