✔ 最佳答案
1.
設f(x) = x³ - 4x² + k - 5
餘數 f(2) = -1
(2)³ - 4(2)² + k - 5 = -1
k - 13 = -1
k = 12
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2.
設f(x) = x³ - 2x² + ax + b
f(x) 除以 x - 1 時,餘數 f(1) = -2
(1)³ - 2(1)² + a(1) + b = -2
a + b = -1 ...... (1)
f(x) 除以 x + 1 時,餘數 f(-1) = -2
(-1)³ - 2(-1)² + a(-1) + b = -2
-a + b = 1 ...... (2)
(1)+(2):
2b = 0
b = 0
(1)-(2):
2a = -2
a = -1
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3.
(a)
遊戲機售價
= $800 * (1 + 60%) * (1 - x%)
= $1280(1 - x%)
(b)
1280(1 - x%) - 800 = 800*12%
1280 - 12.8x - 800 = 96
12.8x = 384
x = 30
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4.
(a)
(y - 1)/(x - 2) = -2
y - 1 = -2x + 4
L: 2x + y - 5 = 0
(b)
把 x = r - 2 及 y = r 代入 L 中:
2(r - 2) + r - 5 = 0
3r = 9
r = 3
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5.
(a)
(x + 1)² + (y - 3)² = (1 + 1)² + (2 - 3)²
x² + 2x + 1 + y² - 6y + 9 = 5
圓的方程: x² + y² + 2x - 6y + 5 = 0
(b)
把 x = -3, y = 4 代入圓的方程中:
左方 =(-3)² + (4)² + 2(-3) - 6(4) + 5 = 0
右方 =0
因為左方 = 右方,所以 (-3, 4) 在圓上。
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6.
(a)
設圓方程為 x² + y² + Dx + Ey + F = 0
A(7, - 8) 在圓上:
(7)² + (-8)² + D(7) + E(-8) + F = 0
7D - 8E + F = -113 ...... (1)
B(7, -2) 在圓上:
(7)² + (-2)² + D(7) + E(-2) + F = 0
7D - 2E + F = -53 ...... (2)
C(6, -9) 在圓上:
(6)² + (-9)² + D(6) + E(-9) + F = 0
6D - 9E + F = -117 ...... (3)
(1)-(2):
-6E = -60
E = 10
(1) - (3):
D + E = 4 ...... (4)
把 E= 10 代入 (4):
D + 10 = 4
D = -6
把 D= -6 及 E = 10 代入 (2):
7(-6) - 2(10) + F = -53
F = 9
圓方程: x² + y² - 6x + 10y + 9 = 0
(b)
圓心 = (6/2, -10/2) = (3, -5)
半徑 = √[(-6/2)²+ (10/2)² - 9] = 5
2011-06-23 01:37:47 補充:
發問時點數已扣除,刪除問題只會損人不利己。