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1 March, 16:21

The number of mosquitoes, m (x), in millions, in a certain area depends on the june rainfall, x, in inches. the function that models that phenomenon is upper m left parenthesis x right parenthesis equals 26 x minus x squared. m (x) = 26x-x2. find the amount of rainfall that will maximize the number of mosquitoes. what is the maximum number of mosquitoes?

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  1. 1 March, 16:45
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    For this case we have the following function:

    m (x) = 26x-x2

    Deriving we have:

    m ' (x) = 26-2x

    We equal zero and clear the value of x:

    26-2x = 0

    2x = 26

    x = 26/2

    x = 13

    Substituting x in the function we have:

    m (13) = 26 * (13) - (13) ^ 2

    m (13) = 169

    Answer:

    the amount of rainfall that will maximize the number of mosquitoes is:

    x = 13 inches

    The maximum number of mosquitoes is:

    m (13) = 169
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