tolong nomer 13 dan 14 beserta cara.. makasih
Matematika
compushi
Pertanyaan
tolong nomer 13 dan 14 beserta cara.. makasih
1 Jawaban
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1. Jawaban arsetpopeye
13) √3 cos x - sin x = k cos (x - @)
(a, b) = (√3, -1) ==> dikuadran 4
k = √(a^2 + b^2) = √(√3^2 + (-1)^2) = √(3 + 1) = √4 = 2
tan @ = b/a = -1/√3 = -1/3 √3 = tan (-30°)
@ = -30° = -π/6
k cos (x - @) = 2 cos (x - (-π/6)) = 2 cos (x + π/6)
14) x^2 - 4x + k - 1 = 0
1/a^2 + 1/b^2 < 1
(b^2 + a^2)/ a^2 b^2 < 1
((a + b)^2 - 2ab) / (ab)^2 < 1
((4)^2 - 2(k - 1)) / (k - 1)^2 < 1
(16 - 2k + 2)/(k^2 - 2k + 1) - 1 < 0
(18 - 2k - (k^2 - 2k + 1))/(k^2 - 2k + 1) < 0
(17 - k^2)/(k^2 - 2k + 1) < 0
(√17 + k)(√17 - k)/(k - 1)(k - 1) < 0
k = -√17, k = √17, k = 1
Garis bilangan
--- (-√17) +++ (1) +++ (√17) ---
k < -√17 atau k > √17