linear equation (10PT)

Jessie

2009-12-18 7:57 am

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 airplanes that conform to this relationship.

airplanes(S)(C)
Hawkeye32033
Corsair60040
Tomcat128350

(a) if the quadratic relationship between C and S is written as C = aS^2 + bS + C, use a linear system of equation to determine the constants a, b and c. Give the equation.

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

更新1:

airplanes (S) (C) Hawkeye 320 33 Corsair 600 40 Tomcat 1283 50

回答 (1)

用戶9112

2009-12-18 3:20 pm

✔ 最佳答案

C = aS^2 + bS + c
33 = 320^2a + 320b + c ... (1)
40 = 600^2a + 600b + c ... (2)
50 = 1283^a + 1283b + c ...(3)
(2) - (1) => 7 = 257600a + 280b ... (4)
(3) - (2) => 10 = 1286089a + 683b ... (5)
(4)*683/280 - (5) => 2.900 = -269640a
a = -0.00001076
Sub into (4), 7 = -2.771 + 280b
b = 0.03490
Sub into (1), 33 = -1.102 + 11.167 + c
c = 22.935
When C = 45,
-0.00001076S^2 + 0.03490S + 22.935 = 45
-0.00001076S^2 + 0.03490S - 22.065 = 0
S = [-0.03490 +/- √(0.001218 - 0.0009497)]/(2*-0.00001076)
S = (0.03490 +/- 0.01638)/0.00002152
S = 2383 or S = 860.6

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