Please solve questions 22, 23 and 24?

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3 Answers

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  • 4 months ago

    Triangle ABC

    angle_A = 60

    angle_B = 30

    angle_C = 90 ← because the sum of the 3 angles of a triangle is always 180

    The area is:

    area = [AC * BC]/2 → but you know that: AC = AB.sin(angle_B)

    aea = [AB.sin(angle_B) * BC]/2 → but you know that: BC = AB.cos(angle_B)

    aea = [AB.sin(angle_B) * AB.cos(angle_B)]/2

    aea = AB².[sin(angle_B) * cos(angle_B)]/2

    aea = AB².[sin(30) * cos(30)]/2 → given that: AB = 8

    aea = 32.[sin(30) * cos(30)]

    aea = 32.[(1/2) * (√3)/2]

    aea = 32.[(√3)/4]

    aea = 8√3 ← D) answer

    Rectangle 1

    ℓ₁: length of the rectangle 1

    ω₁: width of the rectangle 1

    area₁ = ℓ₁ * ω₁

    Rectangle 2

    ℓ₂: length of the rectangle 2

    ω₂: width of the rectangle 2

    area₂ = ℓ₂ * ω₂ → but as the length is tripled, you know that: ℓ₂ = 3 * ℓ₁

    area₂ = 3 * ℓ₁ * ω₂ → but as the width is tripled, you know that: ω ₂ = 3 * ω₁

    area₂ = 3 * ℓ₁ * 3 * ω₁

    area₂ = 9 * ℓ₁ * ω₁ → recall: ℓ₁ * ω₁ = area₁

    area₂ = 9 * area₁

    area₂/area₁ = 9 ← this is the ratio ← C) answer

    Log[3](x) = 2 → recall: Log[a](x) = Ln(x) / Ln(a) ← where a is the base

    Ln(x) / Ln(3) = 2

    Ln(x) = 2.Ln(3) → recall: a.Ln(x) = Ln[x^(a)]

    Ln(x) = Ln(3²)

    x = 3²

    x = 9 ← D) answer

  • ?
    Lv 7
    4 months ago

    See work and solutions below.

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  • 4 months ago

    (22)

    A = ½bh

    C = 180 - A - B = 90°

    AB is oppositie C so it is the hypotenuse of a right triangle.

    30→60→90 triangles go by the pattern 1→2→√3, 2 being the hypotenuse

    Since AB = 8, AC = 4 and BC = 4√3

    A = ½(4)(4√3) = 8√3

    Answer D

    (23)

    A = lw

    A2 = (3l)(3w) = 9lw = 9A

    Answer C

    (24)

    Log3(x) = 2

    3^log3(x) = 3^2

    x = 3^2

    x = 9

    Answer D

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