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anonymous
 4 years ago
The highway mileage m in miles per gallon for a compact car is approximated by m(s) = 0.025s2 + 2.45s  30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon?
anonymous
 4 years ago
The highway mileage m in miles per gallon for a compact car is approximated by m(s) = 0.025s2 + 2.45s  30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon?

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Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1This is a parabola that is concave downward since the coefficient of the s^2 term is negative. We could complete the square to find the vertex but it is probably easier to use the fact that the x coordinate of the vertex is x=b/2a and then plug that value in to find the y coordinate of the vertex. So here we go:

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1\[x=\frac{2.45}{2(.025)}= 49\]

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1Now replace s in the original equation with 49 and that will be the y coordinate of the vertex.

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1\[y=.025(49)^{2}+2.45(49)30=30.025\]

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.1So the maximum mileage is 30.0
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