Flying too fast or slow wastes fuel For a certain aircraft m

Flying too fast or slow wastes fuel. For a certain aircraft, miles per pound of fuel M was a function of air speed A in miles per hour, modeled by the formula M = -0.000651A^2 + 0.129A - 5.05 a. Use the accompanying graph to estimate the most economical air speed. b. Use the formula to find the value of A that maximizes M. c. How many gallons of fuel were burned per hour if the aircraft was flown at 99 mph and got 1.30 mi/lb of fuel, which weighed 6.12 lb/gal? b. The value of A that maximizes M is mph. (Round to two decimal places as needed.) c. If the aircraft was flown at 99 mph and got 1.30 mi/lb of fuel, which weighed 6.12 lb/gal, the number of gallons of fuel that were burned per hour would have been gal/hr. (Round to two decimal places as needed.)

Solution

solution:

c) we have to found the amount of fuel burnt per hour

in order to do this we have to perform few conversions

we have 99 mph

divide this by 1.3 mi/lb means   99 mph/1.3 mi/lb

which gives 76.15385 lb/hr

now convert lbs to gallons by dividing   76.15385 lb/hr by 6.12 lb/gal

=  76.15385 lb/hr /  6.12 lb/gal

= 12.44344 gal/hr

which is the required solution