he length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 13 cm and the

Question

he length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

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Piper 2 hours 2021-09-11T01:21:59+00:00 1 Answer 0

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    2021-09-11T01:23:19+00:00

    Answer:

    The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm

    Step-by-step explanation:

    The area of the rectange is given by the following formula:

    A = l*w

    In which A is the area, measured in cm², l is the lenght and w is the width, both measured in cm.

    The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s.

    This means that \frac{dl}{dt} = 3, \frac{dw}{dt} = 9

    When the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

    We have to find \frac{dA}{dt} when l = 13, w = 5

    Applying implicit differentitiation:

    We have three variables(A, l, w). So

    A = l*w

    \frac{dA}{dt} = l\frac{dw}{dt} + \frac{dl}{dt}w

    \frac{dA}{dt} = 13*9 + 3*5

    \frac{dA}{dt} = 132

    The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm

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