SOLUTION: can someone please help me with this please - the fuel efficiency F for a particular car is given by f(x)=-0.016 x^2 +1.44x +6.4 where x is the speed of the car in miles per

Algebra ->  Average -> SOLUTION: can someone please help me with this please - the fuel efficiency F for a particular car is given by f(x)=-0.016 x^2 +1.44x +6.4 where x is the speed of the car in miles per       Log On


   

Question 1116639: can someone please help me with this please
- the fuel efficiency F for a particular car is given by
f(x)=-0.016 x^2 +1.44x +6.4
where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).
a. What is the fuel efficiency if the car’s speed is 30 mph?
b. What speed will yield the maximum fuel efficiency? Show work.
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
Just substitute and evaluate.

(b)
HINT: Complete the Square and change into f(x)=a(x-h)^2+k form. Read the vertex value directly from that result.
Found should be, the speed is x=1.44%2F%280.032%29=highlight_green%2845%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

can someone please help me with this please
- the fuel efficiency F for a particular car is given by
f(x)=-0.016 x^2 +1.44x +6.4
where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).
a. What is the fuel efficiency if the car’s speed is 30 mph?
b. What speed will yield the maximum fuel efficiency? Show work.
Thank you
a.  matrix%281%2C3%2C+f%28x%29%2C+%22=%22%2C+-+0.016x%5E2+%2B+1.44x+%2B+6.4%29

    matrix%281%2C3%2C+f%2830%29%2C+%22=%22%2C+-+0.016%2830%29%5E2+%2B+1.44%2830%29+%2B+6.4%29 -------- Substituting 30 for x

    matrix%281%2C3%2C+f%2830%29%2C+%22=%22%2C+-+0.016%28900%29+%2B+1.44%2830%29+%2B+6.4%29

    Fuel efficiency if the car’s speed is 30 mph, or highlight_green%28matrix%281%2C4%2C+f%2830%29%2C+%22=%22%2C+35.2%2C+mpg%29%29



b.  The speed that'll yield maximum fuel efficiency occurs where: