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  • 1 decade ago
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    (13) Just simply multiply the function by 2 and we get y = 2x3 - 2

    (14) First translation: y = 2x - 6 (Negate the y for reflection about the x-axis)

    Second translation: y = 4x - 12 (Multiply by 2)

    (15) First translation: Replace x by 2x to get y = x2/4 - x/2 + 1

    Second translation: Replace x by x + 1 to get:

    y = (x + 1)2/4 - (x + 1)/2 + 1

    = x2/4 + x/2 + 1/4 - x/2 - 1/2 + 1

    = x2/4 + 3/4

    (16) First translation: Shft to the right by 2 units

    Second translation: Reflect about the x-axis.

    (17) It should be first reflected about the x-axis to botain -f(x), followed by shifting down by 1 unit to get -1 - f(x)

    Alternatively, we can shft it up by 1 unit to get f(x) + 1, followed by reflecting about the x-axis to get -1 - f(x).

    So ans = D

    (18) First translation: Shifting to the left by 3 units.

    Second translation: Reducing to 1/2 of original along the y-axis.

    (18 Long Q) (a) (i) Original volume of water in cone = π(9)2 x 24/3 = 648π cm3.

    After transfer, depth of water in cone = (h + 5) cm

    By similar triangle, base radius of water portion in the cone = 3(h + 5)/8 and so the volume is:

    [3(h + 5)/8]2 x (h + 5)π/3 = 3(h + 5)3π/64 cm3

    Hence volume of water in cylinder = 36πh cm3

    Thus:

    3(h + 5)3π/64 + 36πh = 648π

    (h + 5)3/64 + 12h = 216

    h3 + 15h2 + 75h + 125 + 768h = 13824

    h3 + 15h2 + 843h - 13699 = 0

    (ii) The line y = 13699 should be added and the solution of h is 11.8 cm (corr. to 0.1 cm)

    (b) Volume of frustum = 648π - 648π(53/243) = 41097π/64 cm3.

    Suppose that the depth of the water is h cm in both cylinder and frustum:

    Volume of water in frustum = 3(h + 5)3π/64 - 648π(53/243) cm3

    Volume of water in cylinder = 36πh cm3

    So,

    3(h + 5)3π/64 - 648π(53/243) + 36πh = 41097π/64

    3(h + 5)3 - 375 + 2304h = 41097

    (h + 5)3 - 125 + 768h = 13699

    h3 + 15h2 + 843h - 13699 = 0

    By (a), we have h = 11.8 cm

    Source(s): My Maths knowledge
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  • Anonymous
    1 decade ago
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