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
Algebra.Com
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
:
*******************************************
speed for maximum fuel efficiency is 43 mph
*******************************************
:
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
:
****************************************************************
The maximum fuel efficiency for the car is 33 miles per gallon
****************************************************************
:
Answer by josmiceli(19441) (Show Source): 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 )
------------------
Here's the plot of the equation:
RELATED QUESTIONS
The fuel efficiency for a cetain midsize car is given by: E(v0 = -0.0235 v^2 + 2.768v -... (answered by solver91311)
The fuel efficiency for a certain midsize car is given by
E(v) = −0.011v2 +... (answered by josmiceli)
The fuel efficiency for a certain midsize car is given by
E(v) = −0.014v2 + 1.176v (answered by ankor@dixie-net.com)
The fuel efficiency for a certain midsize car is given by
E(v) = −0.011v2 +... (answered by richwmiller)
can someone please help me with this please
- the fuel efficiency F for a particular... (answered by josgarithmetic,MathTherapy)
The fuel efficiency F for a particular car is given by F(x) = –0.018 x2 + 1.548 x + 4.2
(answered by Alan3354)
The efficiency e of a gasoline engine as a function of its compression ratio r is given... (answered by Boreal)
Hi there, I could use your help with the following problem:
The fuel efficiency F for... (answered by josmiceli)
The amount of carbon dioxide (in pounds per 15,000 cubic miles) released by a certain SUV (answered by josgarithmetic)