Matematika

Pertanyaan

tolong nomer 13 dan 14 beserta cara.. makasih
tolong nomer 13 dan 14 beserta cara.. makasih

1 Jawaban

  • 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