For certain aircraft, there exists a quadratic relationship between an airplane\

Question

For certain aircraft, there exists a quadratic relationship between an airplane's maximum speed S (in knots) and its ceiling Cits highest altitude possible (in thousands of feet). The table below lists three airplanes that conform to this relationship. If the relationship between C and S is written as C = as2 + bS + c, use a linear system of equations to determine the constants a, b, and c. Then predict the top speed of an aircraft with a ceiling of 45,000 feet.

Explanation / Answer

C = as2 + bS + c

30 = a 250^2 + b * 250 + c

38 = a * 400^2 + b*400 + c

48 = a * 817^2 + b * 817 + c

C = 11.4899 + 0.08698 * S - 0.0000517 *S^2

C = 45

45 = 11.4899 + 0.08698 * S - 0.0000517 *S^2

solving we get

S = 597.372

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