Algebra
posted by Anonymous .
The fuel efficiency for a certain midsize car is given by
E(v) = −0.017v^ + 1.462v + 3.5 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. answer 43 mph
(b) What is the maximum fuel efficiency for this car? Round to the nearest mile per gallon. ____ mpg (unsure of this answer)

Algebra 
bobpursley
I assume the first term mean to have v squared.
find the zeroes....
0=−0.017v^2 + 1.462v + 3.5
use the quadratic equation to find the two v soutions. Then max will be half way between the two v valuse.
b. put that max v into the fomrula, and copute E(v) 
Algebra 
Bosnian
The vertex of a quadratic equation
y = a x ^ 2 + b x + c
is either a maximum or a minimum of the function.
x =  b / 2 a
gives the x  value (or the value of the function) at its vertex.
y = f (  b / 2 a )
gives the y  value (or the value of the function) at its vertex.
If the value of a is positive, you're going to get the minimum value because as such the parabola opens upwards (the vertex is the lowest the graph can get.
If the value of a is negative, you're going to find the maximum value because as such the parabola opens downward (the vertex is the highest point the graph can get.
In this case a is negative, so a quadratic equation
y = a x ^ 2 + b x + c
have maximum value.
a = − 0.017
b = 1.462
c = 3.5
x =  b / 2 a =  1. 462 / [ ( 2 * (  0.017 ) ] =  1.462 /  0.034 = 43
y = f (  b / 2 a ) =
 0.017 * 43 ^ 2 + 1.462 * 43 + 3.5 =
0.017 * 1849 + 62.866 + 3.5 =
31.433 + 62.866 + 3.5 =
34.933 =
35 mpg
Round to the nearest mile per gallon.
Answers :
a = 43 mph
b = 35 mpg
Respond to this Question
Similar Questions

math
Your Porsche's gas mileage (in miles per gallon) is given as a function M(x) of speed x in miles per hour. It is found that M'(x) = 3,600x−2 − 1 (3,600x−1 + x)2 . Estimate M'(10), M'(60), and M'(110). (Round your … 
Algebra
The amount of carbon dioxide (in pounds per 15,000 cubic miles) released by a certain SUV depends on its fuel efficiency according to the formula W = 33x2 − 2145x + 43,000 (12 ≤ x ≤ 33) where x is the fuel efficiency … 
algera
The fuel efficiency for a certain midsize car is given by E(v) = −0.018v^2 + 1.440v + 3.9 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? 
Algebra
The fuel efficiency for a certain midsize car is given by E(v) = −0.017v^ + 1.462v + 3.5 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? 
algebra
The fuel efficiency for a certain midsize car is given by E(v)= 0.016v^2+1.408v+3.8, where E(v)is the fuel efficiency in miles per gallon for a car traveling v miles per hour. What speed will yield the maximum fuel efficiency? 
math
The fuel efficiency for a certain midsize car is given by E(v)= 0.016v^2+1.408v+3.8, where E(v)is the fuel efficiency in miles per gallon for a car traveling v miles per hour. What speed will yield the maximum fuel efficiency? 
algebra 2
The fuel efficiency rating for a certain car is 28 miles per gallon on the highway and 21 miles per gallon in the city. During one week the car traveled a total of 10.5 gallons of fuel. a) please set up an equation(s) that would model … 
Calculus
The fuel consumption (gallons per hour) of a car traveling at a speed of v miles per hour is c = f(v). 1) What is the meaning of the derivative f ' (v)? 
math
Which car is the cheapest to run?Explain why. Bill's car: average fuel composition 20 miles per gallon Sue's car: average fuel composition 30 miles per gallon Fred's car: average fuel composition 40 miles per gallon I think the answer 
algebra 1
Harold's car has a fuel tank with 12 gallons of fuel in it. The fuel efficiency of Harold's car is 25 miles per gallon. Write an equation to represent the amount of fuel remaining, f, in Harold's car after driving m miles.