Gas Mileage The gas mileage g measured in migal for 1 a part

Gas Mileage The gas mileage g (measured in mi/gal) for 1 a particular vehicle, driven at v mi/h, is given by the formula g = 10 + 0.9v - 0.01 v^2, as long as v is between 10 mi/h 1 and 75 mi/h. For what range of speeds is the vehicle\'s mile-1 age 30 mi/gal or better?

Solution

g = 10 + 0.9v - 0.01v^2

range of speeds for which vehicle\'s mileage 30 mi/gal or better

g.> = 30

30 < = 10 +0.9v - 0.01v^2

-0.01v^2 +0.9v -20 >=0

solve the inequality:

it can be re-written as : -1/100v^2 +9/10v -20 >=0

-v^2 +90v -2000>=0

v^2 -90v +2000>=0

(v -40)(v -5)>=0

Now : v <50; (v-50) <0

v>50 ; (v - 50)>0

v<40 (v-40) <0

v >40 (v-40) >0

So, solutuion for the inequality : 40mi/hr <= v < = 50mi/hr