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To determine the appropriate landing speed of an airplane, the formula D = .1x 2 − 3x + 22 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 800 feet long? Show all of your work or explain how you came up with your solution

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Konrad509id
[tex]800=0.1x^2-3x+22\\ 0.1x^2-3x-778=0\\ \Delta=(-3)^2-4\cdot0.1\cdot(-778)=9+3112=3121\\ \sqrt{\Delta}=\sqrt{3121}\\ x_1=\dfrac{-(-3)-\sqrt{3121}}{2\cdot0.1}=\dfrac{3-\sqrt{3121}}{0.2}=15-5\sqrt{3121}\approx-264.3\\ x_2=\dfrac{-(-3)+\sqrt{3121}}{2\cdot0.1}=\dfrac{3+\sqrt{3121}}{0.2}=15+5\sqrt{3121}\approx294.3[/tex]

Approx. 294.3 ft/s

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