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25 February, 10:21

Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square increasing when the area of the square is 16cm^ (2). Show step-by-step solution

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  1. 25 February, 11:21
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    Area of a square = length²

    A = x²

    16 = x²; x = 4

    dA/dx = 2x cm²/s

    dx/dt = 6 cm/s

    Using chain rule:

    dA/dt = dA/dx * dx/dt

    dA/dt = 2x * 6

    dA/dt = 12x

    At x = 4,

    dA/dt = 12 (4) = 48 cm²/s
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