# 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? 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)

1. 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)

posted by bobpursley
2. 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.

a = 43 mph

b = 35 mpg

posted by Bosnian

## Similar Questions

1. ### 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
2. ### 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?
3. ### 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?
4. ### 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
5. ### Calculus

The fuel efficiency, E, in litres per 100 km, for a car driven at speed v, in km/h is E(v)=1600v/(v^2+6400) a)If the speed limit is 50 km/h, determine the legal speed that will maximize the fuel efficiency. Could someone explain
6. ### 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.
7. ### Calculus

The fuel efficiency, E, in litres per 100 km, for a car driven at speed v, in km/h is E(v)=1600v/(v^2+6400) a) determine the legal speed that will maximize the fuel efficiency using speed limit of 50 km/h
8. ### Calculus

The fuel efficiency, E, in litres per 100 km, for a car driven at speed v, in km/h is E(v)=1600v/(v^2+6400). a) Determine the legal speed speed that will maximize the fuel efficiency if the speed limit is 50 km/h. The answer is 50
9. ### 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
10. ### AP Statistics

Suppose a Normal model describes the fuel efficiency of cars currently registered on your state. The mean is 24 mpg, with a standard deviation of 6 mpg. -Describe the fuel efficiency of the worst 20% of all cars. I know that you

More Similar Questions