Police departments estimate the speed of a car when they are given the distance that it skidded before coming to a stop. if the road surface is wet concrete, the function s(x)=√10.5x is used, where x is the skidded distance in feet and s(x) is the speed of the car in miles per hour. (a)Find the speed of the car that skidded 280 feet. Round the answer to the tenth's place and use correct units in your answer.(b)If a car is traveling at a speed of 80 miles per hour,how far will it skid on wet concrete?Round the answer to the one's place and use correct units in your answer. There are 2 parts for this answer a and b. Please help!!!!! :(
To answer part (a) of the question, we need to find the speed of the car that skidded 280 feet. The given function relates the skidded distance in feet (x) to the speed of the car in miles per hour (s(x)). The function is s(x) = √(10.5x).
(a) To find the speed of the car that skidded 280 feet, we substitute x = 280 into the function s(x) and solve for s(x).
s(x) = √(10.5x)
s(280) = √(10.5 * 280)
s(280) = √(2940)
s(280) ≈ 54.1 mph (rounded to the tenths place)
Therefore, the speed of the car that skidded 280 feet is approximately 54.1 mph.
To answer part (b) of the question, we need to find the skidded distance on wet concrete when the car is traveling at a speed of 80 miles per hour. We rearrange the given function s(x) = √(10.5x) to solve for x.
s(x) = 80
√(10.5x) = 80
10.5x = 80^2
10.5x = 6400
x = 6400 / 10.5
x ≈ 610.48 feet (rounded to the ones place)
Therefore, if a car is traveling at a speed of 80 miles per hour, it will skid approximately 610 feet on wet concrete.