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    Question on Log Function

    first find dy/dx of y=logx dy/dx = 1/x i'm assuming you mean at the point where x=e^2, so sub this into dy/dx to find the gradient of the tangent to y=logx where x=e^2 .'. gradient of tangent = 1/e^2 now when x=e^2, y = log(e^2) = 2loge = 2 so the point on the curve where x=e^2 is (e^2, 2) now...
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    Locus problems relating to parabola.

    it is meant to be (x^2/a^2) + (1)^2 = 4y/a this is from the line before where he had (p+q)^2 + (p-q)^2 = 4y/a p+q = x/a, so (p+q)^2 = x^2/a^2 and from the condition, p-q = 1, so (p-q)^2 = 1^2 substituting those back in, you get the equation (x^2/a^2) + (1)^2 = 4y/a
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    simple harmonic motion questions

    Q2: acceleration = d(1/2*v^2)/dx = -2 integrating with respect to x, 1/2 * v^2 = -2x + C when t=0, x=8 and v=4 .'. 1/2 * (4^2) = -2*8 + C 16/2 = -16 + C 8 = -16 + C C = 24 .'. 1/2 * v^2 = -2x + 24 v^2 = -4x + 48 v = +- sqrt(-4x + 48) = +- 2sqrt(12-x)
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    Share your 2012 ATAR here

    99.30 ...a bit higher than my aim, lol
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    Titration MC question

    the solution in the conical flask isn't more basic; there's just more moles of base in there, and hence you'll need more acid to neutralise all the base
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    Binomial Probability

    the nCk should not be there; what that's there for normally is to account for the varying ways in which you can have 2 days raining and 5 days not raining out pf 7 days the (2/3)^2*(1/3)^5 by itself (without the 7C2) shows the probability of having 2 days raining and 5 days not raining for only...
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    Parametrics Help

    y = 3sec(theta) - 4 y+4 = 3sec(theta) sec^2(theta) = (y+4)^2/9 ----- 1 x=1+2tan(theta) tan(theta) = (x-1)/2 tan^2(theta) = (x-1)^2/4 ----- 2 1 - 2: sec^2(theta) - tan^2(theta) = (y+4)^2/9 - (x-1)^2/4 1 = (y+4)^2/9 - (x-1)^2/4
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    Multiplier question

    the first one the answer is D because from each year, you can see that consumption and savings have both increased by 100 each, so the MPC and the MPS are both 0.5 i.e. for every extra dollar earned, 50% of it is used for consumption and 50% is saved. since the multiplier = 1/MPS, .'. multiplier...
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    Help with maths

    are you sure it's 2n^2? if it was twice the square of a number, or twice a squared number, i would agree, but twice a number squared sounds more like(2n)^2 to me :/
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    Will this get me a band 5 in English advanced?

    what raw mark would you need to just scrape a band 5?
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    Integration

    tanx/tan2x = (sinx/cosx)/(sin2x/cos2x) = (sinxcos2x)/(sin2xcosx) = (sinx(1-2sin^2(x))/(2sinxcos^2(x)) = (1-2sin^2(x))/(2cos^2(x)) = (1-2sin^2(x))/(2(1-sin^2(x)) = (2(1-sin^2(x))-1)/(2(1-sin^2(x)) = 1 - 1/(2(1-sin^2(x)) = 1 - 1/2cos^2(x) = 1 - 1/2(sec^2(x)) integrating that just gives x...
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    Hidden unemployment and unemployment benefits

    oh, ok, thanks guys! and to bored_of_HSC, i was looking at a question that asked about economic effects of an increase in the participation rate, and the thought sort of came to me...
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    Hidden unemployment and unemployment benefits

    i think that's hard-core unemployment...i'm referring to people who just choose not to actively seek work, and thus aren't counted in unemployment figures
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    Hidden unemployment and unemployment benefits

    Do the hidden unemployed receive unemployment benefits? They aren't actually counted as unemployed, but does that mean they don't receive these benefits?
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    HSC 2012-14 MX2 Integration Marathon (archive)

    Re: MX2 Integration Marathon let u=arcsin(x) I = integral(u^2) dx = integral(u^2) du * dx/du u=arcsin(x) x=sinu dx/du = cosu .'. I = integral (u^2 * cosu) du integrating by parts, m=u^2 m'=2u n'=cosu n=sinu I = u^2*sinu - integral(2u*sinu) du = u^2*sinu - 2*integral(u*sinu)...
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    Probability Question

    i did it differently to the answers, but got the same values for part i, if the computer chooses both your numbers, then the number of combinations where this can happen are 2C2 * 38C11, since 2 of the 13 numbers chosen must be the numbers you chose, and then the computer chooses the other 11...
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    Complex No. : Locus question

    p is the sum of the roots 2 at a time; for product of roots, you're finding the value of q
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    Complex No. : Locus question

    i think nightweaver's one is right
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    Probablity Question Help

    i don't think the answer is purely 4/7, because the question says if at least one gold coin is selected. this doesn't mean that the gold coin was selected first; it could have been selected second, and all we know is that at least one was chosen, so i reckon barbenator's answer is correct
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