SOLUTION: The fuel efficiency for a certain midsize car is given by
E(v) = −0.016v2 + 1.376v + 3.8
where
E(v)
is the fuel efficiency in miles per gallon for a car traveling v mil
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-> SOLUTION: The fuel efficiency for a certain midsize car is given by
E(v) = −0.016v2 + 1.376v + 3.8
where
E(v)
is the fuel efficiency in miles per gallon for a car traveling v mil
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Question 1129340: The fuel efficiency for a certain midsize car is given by
E(v) = −0.016v2 + 1.376v + 3.8
where
E(v)
is the fuel efficiency in miles per gallon for a car traveling v miles per hour.
(a) What speed will yield the maximum fuel efficiency? Round to the nearest mile per hour.______mph
(b) What is the maximum fuel efficiency for this car? Round to the nearest mile per gallon.____mpg Found 2 solutions by rothauserc, josmiceli:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! E(v) = -0.016v^2 + 1.376v + 3.8
:
this is the equation of a parabola that curves downward
:
velocity is plotted along the x-axis and fuel efficiency is plotted along the y-axis
:
here is a graph of E(v)
:
:
from the graph, we see that the coordinates of the vertex will give us the answers to the questions a and b
:
a. The speed(v) that will yield the maximum fuel efficiency is found from the formula
:
v = -b/2a, where b and a are from the general form for a quadratic
:
ax^2 +bx +c
:
v = -1.376/(2(-0.016)) = 43
:
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speed for maximum fuel efficiency is 43 mph
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:
b. substitute for v in the equation
:
E(v) = -0.016v^2 + 1.376v + 3.8
:
E(v) = -0.016(43)^2 + 1.376(43) + 3.8 = 33.384 is approximately 33
:
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The maximum fuel efficiency for the car is 33 miles per gallon
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:
You can put this solution on YOUR website! The formula for the v-value of the vertex is: where
(a)
43 mi/hr gives maximum fuel efficiency
(b)
The maximum fuel efficiency for the car is 33 mi/gal
( check my math )
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Here's the plot of the equation:
