Matematika

Pertanyaan

Tolong dibantu yah para master mm,makasih nomor 16 dan 17
Tolong dibantu yah para master mm,makasih nomor 16 dan 17

1 Jawaban

  • 16) (cos a)/a + (cos b)/b + (cos c)/c
    = [(b^2 + c^2 - a^2)/(2bc)]/a + [(a^2 + c^2 - b^2)/(2ac)]/b + [(a^2 + b^2 - c^2)/(2ab)]/c
    = (b^2 + c^2 - a^2)/(2abc) + (a^2 + c^2 - b^2)/(2abc) + (a^2 + b^2 - c^2)/(2abc)
    = (a^2 + b^2 + c^2)/(2abc)

    17) jarak (P, AB) = 3 jarak (P, CD)
    => AX = 3 DX
    => AX/DX = 3/1
    => AX : DX = 3 : 1
    Anggap panjang AX = 3y dan panjang DX = y
    Misal panjang AB = DC = k cm
    Luas CDXY = a
    => CD . DX = a
    => k . y = a
    => a = ky
    Luas ∆ ABP = b
    => 1/2 . AB . AX = b
    => 1/2 . k . 3y = b
    => b = 3/2 ky

    Jadi a : b = ky : 3/2 ky = 1 : 3/2 = 2 : 3