Question

To determine the appropriate landing speed of an airplane, the formula D = 0.10x2 – 3.00x + 22.0 is used, where x is the initial landing speed in feet per second and D is the distance needed in feet. If the landing speed is too fast, the pilot may run out of runway; if the speed is too slow, the plane may stall. What is the appropriate landing speed if the runway is 1019.50 feet long? Round your answer to the nearest whole number XXX

Answer 1

116 ft/s

Step-by-step explanation:

D = 0.10x² – 3.00x + 22.0

1019.50 = 0.10x² – 3.00x + 22.0

0 = 0.10x² – 3.00x – 997.5

0 = x² – 30x – 9975

Solve with quadratic formula:

x = [ -(-30) ± √((-30)² − 4(1)(-9975)) ] / 2(1)

x = [ 30 ± √(900 + 39900) ] / 2

x = (30 ± 20√102) / 2

x = 15 ± 10√102

x ≈ 116