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The gas mileage g (measured in mi/gal) for a particular vehicle, driven at v mi/h, is given by the formula g = 10 + 0.7v − 0.01v2, as long as v is between 10 mi/h and 65 mi/h. For what range of speeds (in mi/h) is the vehicle's mileage 22 mi/gal or better? (Enter your answer using interval notation.)

Answer :

MrRoyal

Answer:

[tex][30,40][/tex]

Step-by-step explanation:

Given

[tex]g = 10 + 0.7v - 0.01v^2[/tex]

Required

Determine v when g = 22

Substitute 22 for g;

We have:

[tex]22 = 10 + 0.7v - 0.01v^2[/tex]

Collect Like Terms

[tex]0.01v^2 -0.7v + 22- 10 = 0[/tex]

[tex]0.01v^2 -0.7v + 12 = 0[/tex]

[tex]0.01v^2 -0.4v-0.3v + 12 = 0[/tex]

[tex]0.01v(v - 40) - 0.3(v - 40) = 0[/tex]

[tex](0.01v - 0.3)(v - 40) = 0[/tex]

Split:

[tex]0.01v - 0.3= 0[/tex] or [tex]v - 40 = 0[/tex]

[tex]0.01v = 0.3[/tex] or [tex]v = 40[/tex]

[tex]v = 0.3/0.01[/tex] or [tex]v = 40[/tex]

[tex]v = 30[/tex] or [tex]v = 40[/tex]

Writing as interval, we have:

[tex][30,40][/tex]

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