tolong nomor 53 dan 54 beserta cara pengerjaan nya
Matematika
muhfaturrahman8
Pertanyaan
tolong nomor 53 dan 54 beserta cara pengerjaan nya
1 Jawaban
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1. Jawaban arsetpopeye
53) Tan 165° = Tan (120° + 45°)
= (Tan 120° + Tan 45°)/(1 - Tan 120° Tan 45°)
= (-√3 + 1) / (1 - (-√3)(1))
= (1 - √3)/(1 + √3) . (1 - √3)/(1 - √3)
= (1 - 2√3 + 3) / (1 - 3)
= (-2√3 + 4) / -2
= √3 - 2
54) y = 1/3 x^3 - 1/2 x^2 - x + 1
y' = x^2 - x - 1
m = y' => x^2 - x - 1 = 1
=> x^2 - x - 2 = 0
=> (x - 2)(x + 1) = 0
=> x = 2 atau x = -1
y = 1/3 x^3 - 1/2 x^2 - x + 1
x = 2 => y = 8/3 - 2 - 2 + 1 = 8/3 - 3 = -1/3
x = -1 => y = -1/3 - 1/2 + 1 + 1 = (-2 - 3 + 6 + 6)/6 = 7/6 = 1 1/6
Jadi ordinatnya adalah -1/3 dan 1 1/6