Matematika

Pertanyaan

Tolong dibantu kak nomer 14 dan 15 beserta caranya ya
Tolong dibantu kak nomer 14 dan 15 beserta caranya ya

1 Jawaban

  • Percerminan
    y = 2x
    m = 2 --> tan A = 2 = y/x
    r = √(x²+y²)= √5
    sin A = y/r= 2/√5
    cos A = x/r= 1/√5
    sin 2A = 2 sin A cos A = 2(2/√5)(1/√5)= 4/5
    cos 2A =√( 1 - sin² 2 A) = √(1 - (4/5)² = +_ 3/5
    cos 2A  = - 3/5  ( dikuadran II)

    ( x')= (x) cos 2A  + (y) sin 2A
    x' = 7(-3/5) + (-1) (4/5)
    x' = -21/5 -  4/5 = -25/5 = -5

    (y') = (x)(sin 2A)  + (y) cos 2A
    y' = 7 (3/5)+ (-1)(-4/5)
    y' = 21/5 + 4/5 = 25/5 = 5

    bayangan x',y' = (-5,  5)

    2.
    ⁴log (3-x) + ²log x  > 1/2
    ²log (3-x)¹/² + ²log x > ²log 2¹/2
    ²log x√(3-x) > ²log √2
    x √(3-x) > √2
    x²(3-x) > 2
    3x² - x³ - 2 >0
    x³ - 3x² + 2 > 0 dgn syarat  3-x > 0  atau x > 0
    (x-1)(x² - 2x -2) > 0
    x = 1 , x = 1 - √3, x = 1 + √3 , x  < 3 ,x > 0
    x > 1 + √3
    1 - √3 < x < 1
    x < 3
    x> 0
    HP
    0 < x < 1 atau 1 +√3 < x < 3