For certain aircraft there exists a quadratic relationship between an airplane’s maximum speed S (in knots) and its ceiling C, or highest altitude possible (in thousands of feet). The table lists three such airplanes.

(a) If the quadratic relationship between C and S is written as C = aS² + bS + c, use a system of linear equations to determine the constants a, b and c, and give the equation.

(b) A new aircraft of this type has a ceiling of 45,000 ft. Predict its top speed to the nearest knot.

Transcribed Image Text:

Airplane Max Speed (S) Ceiling (C) 33 Hawkeye Corsair 320 600 40 1283 Tomcat 50