Question 1129340
E(v) = -0.016v^2 + 1.376v + 3.8
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this is the equation of a parabola that curves downward
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velocity is plotted along the x-axis and fuel efficiency is plotted along the y-axis
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here is a graph of E(v)
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{{{ graph( 300, 200, -20, 100, -20, 40, -0.016x^2 +1.376x +3.8) }}}
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from the graph, we see that the coordinates of the vertex will give us the answers to the questions a and b
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a. The speed(v) that will yield the maximum fuel efficiency is found from the formula
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v = -b/2a, where b and a are from the general form for a quadratic
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ax^2 +bx +c
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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
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E(v) = -0.016v^2 + 1.376v + 3.8
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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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