Put the expression 250 within means

Put the expression < 250; within means <,

solve by factoring; this sets up two regions, one true and one false - which region states the speed within which the car can stop in 250ft

Solution

On a certain stretch of road, the distance d (in feet) required to stop a car that is traveling at a speed v (in mph) before the brakes are applied can be approximated by d(v) = 0.5v² +2.5v. Thus, the speeds (v) for which the car can be stopped within 250 feet are given by 0.5v² +2.5v < 250 or, on multiplying both the 2, we get v² + 5v -500 < 0 or, v² +25v-20v-500 < 0 or, v(v+25) – 20(v+25) < 0 or, (v+25)(v-20) < 0 . Since v cannot be negative, this means that v < 20 or, v (0, 20). Thus, the car can be stopped within 250 feet if it is travelling at a speed less than 20 mph.