Matematika

Pertanyaan

No 3-9 tolong dijawab dong..... tolonggggg yaaa
No 3-9 tolong dijawab dong..... tolonggggg yaaa

1 Jawaban

  • 9) y = mx^2 - 2mx + 10 => a = m, b = -2m
    Absis Titik minimum = x = -b/2a = -(-2m)/(2m) = 1

    8) y = -x^2 - 6x + 10 => a = -1, b = -6
    x = -b/2a = -(-6)/2(-1) = 6/-2 = -3
    y = -(-3)^2 - 6(-3) + 10 = -9 + 18 + 10 = 19
    Karena a < 0 maka titiknya maksimum di (-3, 19)

    7) y = 2x^2 - 4x + 8 => a = 2, b = -4
    x = -b/2a = -(-4)/2(2) = 4/4 = 1
    y = 2(1)^2 - 4(1) + 8 = 2 - 4 + 8 = 6
    Karena a > 0 maka titiknya minimum di (1,6)

    6) x = -1 => x < 0 => f(-1) = 2x + 1 = 2(-1) + 1 = -2 + 1 = -1
    x = 2 => 0 ≤ x < 3 => f(2) = x^2 + 5 = (2)^2 + 5 = 4 + 5 = 9
    x = 5 => x ≥ 3 => f(5) = 20 - x = 20 - 5 = 15
    f(-1) + f(2) + f(5) = -1 + 9 + 15 = 23

    5) f(x) = x^2 + 2x
    f(3) = 3^2 + 2(3) = 9 + 6 = 15

    4) x - y = 5 => x = y + 5
    x^2 - y^2 = 45 => (y + 5)^2 - y^2 = 45
    y^2 + 10y + 25 - y^2 = 45
    10y = 20
    y = 2
    x = y + 5 = 2 + 5 = 7
    HP = {(7, 2)}

    3) 2x + z = 5 => z = 5 - 2x
    x + y = 1 => y = 1 - x
    y - 2z = -3 => (1 - x) - 2(5 - 2x) = -3
    => 1 - x - 10 + 4x = -3
    => 3x = 6
    => x = 2
    z = 5 - 2x = 5 - 2(2) = 1
    y = 1 - x = 1 - 2 = -1
    xo + yo + zo = 2 + (-1) + 1 = 2