Q:

The gas mileage for a certain vehicle can be approximated by m= -0.03x^2 +3.7x-43, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 25 mpg.Round to the nearest mph.The vehicle will get 25 mpg at speeds of approximatelymph ____and ____ mph

Accepted Solution

A:
Answer:The vehicle will get 25 mpg at speeds of approximately Β 22 mph and 101 mph.Step-by-step explanation:Given, the equation that is used to determine the gas mileage for a certain vehicle is,[tex]m=-0.03x^2+3.7x-43----(1)[/tex]If the mileage is 25 mpg.That is, m = 25 mpg,From equation (1),[tex]-0.03x^2+3.7x-43=25[/tex]By the quadratic formula,[tex]x=\frac{-3.7\pm \sqrt{3.7^2-4\times -0.03\times -43}}{2\times -0.03}[/tex][tex]x=\frac{-3.7\pm \sqrt{8.53}}{-0.06}[/tex][tex]\implies x=\frac{-3.7+ \sqrt{8.53}}{-0.06}\text{ or }x=\frac{-3.7- \sqrt{8.53}}{-0.06}[/tex][tex]\implies x\approx 22\text{ or }x\approx 101[/tex]Hence, the speed of the vehicle of the vehicle are approximately 22 mph and 101 mph.