The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval

Question

The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).

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Hưng Khoa 4 years 2021-07-27T02:27:46+00:00 1 Answers 71 views 0

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  1. phucdien
    0
    2021-07-27T02:29:07+00:00
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    Answer:

    The average value of the cost function over the interval  is of $23,500.

    Step-by-step explanation:

    Average value of a function:

    The average value of a function, over an inteval [a,b], is given by:

    A = \frac{1}{b-a} \int_{a}^{b} f(x) dx

    In this case:

    Function C(x) = 20000 - 10x, interval with a = 0,b = 700

    So

    A = \frac{1}{700} \int_{0}^{700} 20000+10x dx

    A = \frac{1}{700} (20000x+5x^2)|_{0}^{700}

    So

    A = \frac{20000(700)+5(700)^2}{700} = 23500

    The average value of the cost function over the interval  is of $23,500.

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