precal question

Question

The gas mileage g (measured in mi/gal) for a particular vehicle, driven at v mi/h, is given by the formula g = 10 + 0.3v − 0.01v²,

 as long as v is between 10 mi/h and 45 mi/h. For what range of speeds (in mi/h) is the vehicle's mileage 12 mi/gal or better? (Enter your answer using interval notation.)

 

Answer 1

The equation g(v) = 10 + 0.3v-0.01v² is the equation of a negative parabola.

The line of symetry of a parabola is the variable being equal to - b/2a using letters for the constants in order: ax² + bx + c. Using this formula the maximum is at v = -0.3 / 2( 10) = -0.3/20 =15.

Solving for velocity equal to 10 g(10) =12

Since a parabola is symmetric around its vertex and the vertex is at 15 the other velocity must be at 20 or 15 + or - 5.

The range is between the two velocities or 10 to 20 written as an interval:[10, 20]. As [ means does include and ( means does not include.