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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.)

User Mikej
by
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1 Answer

5 votes

Answer:


[30,40]

Explanation:

Given


g = 10 + 0.7v - 0.01v^2

Required

Determine v when g = 22

Substitute 22 for g;

We have:


22 = 10 + 0.7v - 0.01v^2

Collect Like Terms


0.01v^2 -0.7v + 22- 10 = 0


0.01v^2 -0.7v + 12 = 0


0.01v^2 -0.4v-0.3v + 12 = 0


0.01v(v - 40) - 0.3(v - 40) = 0


(0.01v - 0.3)(v - 40) = 0

Split:


0.01v - 0.3= 0 or
v - 40 = 0


0.01v = 0.3 or
v = 40


v = 0.3/0.01 or
v = 40


v = 30 or
v = 40

Writing as interval, we have:


[30,40]

User Czlowiekwidmo
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7.0k points