Answer:
The vehicle will get 25 mpg at speeds of approximately 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.
