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
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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
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