Physics: The gas mileage m (in mi/gal) of a car is given as a function of speed v (in mph); m (s) = - 1/28 v^2 + 4y - 80 at what driving speed will this vehicle perform with the best gas mileage? what is the vehicle s gas mileage at that speed?

The gas mileage m (in mi/gal) of a car is given as

poonwagon994

05.01.2022

V = 56 mph.

The mileage of vehicle is 32 mi/gal

Explanation:

Given that

M (s) = - 1/28 v^2 + 4y - 80

But in the above equation on the place of y it should be V(velocity).

$M(s)=-\dfrac{1}{28}V^2+4V-80$ ---------1

We know that if we want to maximize the function then we differentiate that function .

$\dfrac{dM}{dV}=-2\times \dfrac{1}{28}V+4$

$\dfrac{dM}{dV}=- \dfrac{1}{14}V+4$

Foe maximum condition

$\dfrac{dM}{dV}=0$

$-\dfrac{1}{14}V+4=0$

V= 4 x 14

V = 56 mph.

So the speed of vehicle at best mileage is 56 mph.

Now by putting the value of V in the first equation

$M(s)=-\dfrac{1}{28}V^2+4V-80$

$M(s)=-\dfrac{1}{28}\times 56^2+4\times 56-80$

M(s) = 32

So the mileage of vehicle is 32 mi/gal

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