The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to

Question

The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to stop, what distance is required for a speed of 59 mph?

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Arianna 1 week 2021-10-13T02:18:50+00:00 1 Answer 0

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    2021-10-13T02:19:50+00:00

    The distance required for a speed 59 mph is 243.67 feet

    Step-by-step explanation:

    The direct variation is a relation ship between two quantities, the

    ratio between them is constant

    • If y varies directly with x, then y = k x
    • x is the constant of variation
    • To find k substitute y and x by their initial values

    ∵ The distance it takes stop a car varies directly at the square

       of the speed of the car

    ∴ d = k v², where d is the distance in feet and v is the speed in mph

    ∵ it takes 112 feet for a car traveling at 40 mph to stop

    ∴ d = 112 feet , v = 40 mph ⇒ initial values

    – Substitute these values in the rule above to find k

    ∵ 112 = k (40)²

    ∴ 112 = 1600 k

    – Divide both sides by 1600

    ∴ k = 0.07

    ∴ d = 0.07 v² ⇒ equation of variation

    ∵ The speed v = 59 mph

    – To find the distance required for this speed substitute v in

       the equation of variation by 59

    ∵ d = 0.07 (59)²

    ∴ d = 243.67 feet

    The distance required for a speed 59 mph is 243.67 feet

    Learn more:

    You can learn more about variation in brainly.com/question/10708697

    #LearnwithBrainly

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