SOLUTION: The number of miles M that a certain automobile can travel on one gallon of gasoline at a speed of v mi/hr is given by M=-1/30v^2+5/2v for 0<v<70. a) Find the most economical s

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The number of miles M that a certain automobile can travel on one gallon of gasoline at a speed of v mi/hr is given by M=-1/30v^2+5/2v for 0<v<70. a) Find the most economical s      Log On


   

Question 275004: The number of miles M that a certain automobile can travel on one gallon of gasoline at a speed of v mi/hr is given by M=-1/30v^2+5/2v
for 0 a) Find the most economical speed for a trip.
b) Find the largest value of M.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The number of miles M that a certain automobile can travel on one gallon of gasoline at a speed of v mi/hr is given by M=-1/30v^2+5/2v
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a) Find the most economical speed for a trip.
The max M is at the vertex: v = -b/2a = -(5/2)/(-1/15)
v = 75/2 mph = 37.5 mph
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b) Find the largest value of M.
M(75/2) = -(1/30)*(75/2)^2 + (5/2)*(75/2)
M = 46.875 mpg
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Don't do it in the left lane.