SOLUTION: The highway mileage min miles per gallon for a compact car is approximated by m(s) = -0.025s^2+2.45s-30 where s is the speed in miles perhour. a.If the car is traveling 65mp

Question 1170722: The highway mileage min miles per gallon for a compact car is approximated by m(s) = -0.025s^2+2.45s-30 where s is the speed in miles perhour.

a.If the car is traveling 65mph, what will the highway mileage be?
b.If the car is traveling 20mph, what will the highway mileage be?
c.What speed will the car be traveling if the mileage is 28 miles per gallon?
d.What speed will the car be traveling if the mileage is 0 miles per gallon?
e.What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? What speed results in this mileage?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The highway mileage min miles per gallon for a compact car is approximated by m(s) = -0.025s^2+2.45s-30 where s is the speed in miles per hour.
a.If the car is traveling 65mph, what will the highway mileage be?
s = 65, therefore
m(s) = -0.025(65^2) + 2.45(65) - 30
m(s) = -.025(4225) + 159.25 - 30
m(s) = -105.625 + 129.25
m(s) = 23.625 mpg
:
b.If the car is traveling 20mph, what will the highway mileage be?
s = 20
m(s) = -0.025(400)+2.45(20)-30
m(s) = -10 + 49 - 30
m(s) = 9 mpg
:
c.What speed will the car be traveling if the mileage is 28 miles per gallon?
-0.025s^2 + 2.45s - 30 = 28
-0.025s^2 + 2.45s - 30 - 28 = 0
-0.025s^2 + 2.45s - 58 = 0
use the quadratic formula a=-.025, b=2.45, c=-58
I got a positive solution of:
s = 40 mph
:
d. What speed will the car be traveling if the mileage is 0 miles per gallon?
-0.025s^2 + 2.45s - 30 = 0
using the quadratic formula; a=-.025, b=2.45, c=-30
Got a rather silly answer of 14.35 mph when mpg = 0
:
e.What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? What speed results in this mileage?
That will occur on the axis of symmetry, x=-b/(2a)
s =
s = 49 mph
Find the mpg
m(s) = -0.025(49^2) + 2.45(49) - 30
m(s) =-.025(2401) + 120.05 - 30
M(s) = -60.025 + 90.05
m(s) = 30.025 ~ 30 mpg
:
Graphically

vertical y is mpg, horizontal x is mph, green line is mpg=30, blueline is 24 mpg
RELATED QUESTIONS
The gas mileage, M, of a compact car is a linear function of the speed,s, at which the... (answered by stanbon)

The gas mileage G(s) (in miles/gallon) of a Ford Tauras when driven at a speed of S mph... (answered by ankor@dixie-net.com)

The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas... (answered by ikleyn)

For a fixed number of miles, the gas mileage of a car (miles per gallon) varies inversely (answered by mananth)

The gas mileage for a certain vehicle can be approximated by m = −0.04x2 + 3.6x... (answered by josmiceli)

solve s^2 + 45s =... (answered by Tatiana_Stebko)

1. Max’s car has a gas mileage of 30 miles per gallon. How many miles can he travel on... (answered by ikleyn)

You know, from actual driving data, that your car gets 17 miles per gallon when your... (answered by stanbon)

can someone please help me with this please - the fuel efficiency F for a particular... (answered by josgarithmetic,MathTherapy)