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5 October, 06:48

The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the square changing when the sides are 14 m long? b. At what rate is the area of the square changing when the sides are 25 m long?

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  1. 5 October, 07:03
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    The area of a square is given by:

    A = s²

    A is the square's area

    s is the length of one of the square's sides

    Let us take the derivative of both sides of the equation with respect to time t in order to determine a formula for finding the rate of change of the square's area over time:

    d[A]/dt = d[s²]/dt

    The chain rule says to take the derivative of s² with respect to s then multiply the result by ds/dt

    dA/dt = 2s (ds/dt)

    A) Given values:

    s = 14m

    ds/dt = 3m/s

    Plug in these values and solve for dA/dt:

    dA/dt = 2 (14) (3)

    dA/dt = 84m²/s

    B) Given values:

    s = 25m

    ds/dt = 3m/s

    Plug in these values and solve for dA/dt:

    dA/dt = 2 (25) (3)

    dA/dt = 150m²/s
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