The gas mileage for a certain vehicle can be approximated by m= -0.03x^2 +3.7x-43, where x is the speed of the vehicle in mph. Determine the

Question

The gas mileage for a certain vehicle can be approximated by m= -0.03x^2 +3.7x-43, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 25 mpg.

Round to the nearest mph.

The vehicle will get 25 mpg at speeds of approximately

mph ____and ____ mph

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Reagan 5 days 2021-09-15T19:37:05+00:00 1 Answer 0

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    2021-09-15T19:38:54+00:00

    Answer:

    The vehicle will get 25 mpg at speeds of approximately  22 mph and 101 mph.

    Step-by-step explanation:

    Given, the equation that is used to determine the gas mileage for a certain vehicle is,

    m=-0.03x^2+3.7x-43----(1)

    If the mileage is 25 mpg.

    That is, m = 25 mpg,

    From equation (1),

    -0.03x^2+3.7x-43=25

    By the quadratic formula,

    x=\frac{-3.7\pm \sqrt{3.7^2-4\times -0.03\times -43}}{2\times -0.03}

    x=\frac{-3.7\pm \sqrt{8.53}}{-0.06}

    \implies x=\frac{-3.7+ \sqrt{8.53}}{-0.06}\text{ or }x=\frac{-3.7- \sqrt{8.53}}{-0.06}

    \implies x\approx 22\text{ or }x\approx 101

    Hence, the speed of the vehicle of the vehicle are approximately 22 mph and 101 mph.

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