Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the s

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Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2

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Mộc Miên 3 months 2021-07-28T14:36:20+00:00 1 Answers 3 views 0

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    2021-07-28T14:38:19+00:00

    Answer:

    The area of the square is increasing at a rate of 40 square centimeters per second.

    Step-by-step explanation:

    The area of the square (A), in square centimeters, is represented by the following function:

    A = l^{2} (1)

    Where l is the side length, in centimeters.

    Then, we derive (1) in time to calculate the rate of change of the area of the square (\frac{dA}{dt}), in square centimeters per second:

    \frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}

    \frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt} (2)

    Where \frac{dl}{dt} is the rate of change of the side length, in centimeters per second.

    If we know that A = 25\,cm^{2} and \frac{dl}{dt} = 4\,\frac{cm}{s}, then the rate of change of the area of the square is:

    \frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)

    \frac{dA}{dt} = 40\,\frac{cm^{2}}{s}

    The area of the square is increasing at a rate of 40 square centimeters per second.

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