Final answer:
To calculate the car's speed for a stopping distance of 200 feet, plug the distance into the equation y = 0.005x² + 0.10x + 5 and solve for x using the quadratic formula. Only the positive solution is relevant for the speed.
Step-by-step explanation:
To find the speed of a car that takes 200 feet to stop, we can use the given equation y = 0.005x² + 0.10x + 5, where y represents the distance needed to stop in feet, and x is the speed of the car in miles per hour. We need to solve the equation for x when y is given as 200 feet.
Plugging in the distance, we have:
200 = 0.005x² + 0.10x + 5
We then rearrange the equation and solve for x which will give us a quadratic equation:
0.005x² + 0.10x - 195 = 0
The quadratic formula, x = (-b ± √(b² - 4ac))/(2a), is used to solve for x, where a = 0.005, b = 0.10, and c = -195. After calculating, we obtain two possible solutions for x, but only the positive solution is meaningful for the speed of a car.