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?

The distance required for a speed 59 mph is 243.67 feetStep-by-step explanation:The direct variation is a relation ship between two quantities, the ratio between them is constantIf y varies directly with x, then y = k xx is the constant of variationTo 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 feetThe distance required for a speed 59 mph is 243.67 feetLearn more:You can learn more about variation in brainly.com/question/10708697#LearnwithBrainly