SOLUTION: The following function describes the miles per gallon a ford Taurus gets when driven at x mls.per hour *NOTE: x is speed in mls.per hr. and f(x) is mls per gallon that the car gets

Question 87939: The following function describes the miles per gallon a ford Taurus gets when driven at x mls.per hour *NOTE: x is speed in mls.per hr. and f(x) is mls per gallon that the car gets when driven at x mls per hr.
f(x)=-0.018x^2+1.93x-25.34
a)how many miles per gallon will the car get at 45miles per hr.?
b)what is the speed of the car that gives you the maximum gas mileage?
c)what is the maximum miles per gallon that the car can get using this function?
Please help me, with this word problem. thanks!!
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
f(x)=-0.018x^2+1.93x-25.34
a)how many miles per gallon will the car get at 45miles per hr.?
f(45)=-0.018(45)^2+1.93(45)-25.34 [substitute (45) for the x-term and solve]
f(45) = 25.06 miles per gallon
.
b)what is the speed of the car that gives you the maximum gas mileage?
The maximum or minimum is the vertex. Use the formula for the vertex:
x-value = -(b)/2a
y-value = plug-in the x-value and solve for the y-value
.
x-value of the vertex: -(b)/2a=-(1.93)/(2*(-0.018)) = 53.611 miles per hour
f(53.611)=-0.018(53.611)^2+1.93(53.611)-25.34
y-value of the vertex: f(53.611) = 26.39 miles per gallon
.
c)what is the maximum miles per gallon that the car can get using this function?
Maximum speed = 26.39 miles per gallon

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