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    cssa 2004 polynomials (need help)

    z^5 - 32 = (z-2)(z^4 -2z^3 +4^2 -8z +16) and z^5 - 32 = (z-2){z^2 -(4cos(pi/5)z +4}{z^2 -(4cos(3pi/5)z +4}
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    cssa 2004 polynomials (need help)

    (a)i) Sum and product of roots = 1. Therefore none of the roots can be integral. (Not 100% sure that reason is adequate) ii) Replace x with x+1 in the original polynomial to yield the new polynomial. Now, notice that a+b+c = 1-d (sum of roots). Therefore (a+b+c)(b+c+d)(a+c+d)(a+b+d) =...
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    question on recurring integrals

    int{xsecxtanx dx} = xsecx - int{secx dx} = xsecx - ln|secx + tanx| + C Remember, derivative of secx = secxtanx and derivative of ln|secx + tanx| = secx
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    question on recurring integrals

    int{tan<sup>n</sup>x dx} = int{tan<sup>n-2</sup>x * tan<sup>2</sup>x dx} = int{tan<sup>n-2</sup>x * (sec<sup>2</sup>x - 1) dx} = int{tan<sup>n-2</sup>x * sec<sup>2</sup>x dx} - int{tan<sup>n-2</sup>x dx}...
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    Terry lee question....

    My version of Terry Lee says prove 0, 1, z1 is similar to 0, z2, z1z2. That seems much more reasonable.
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    Guys i seriously need help with conics

    1. This question is similar to the example in the book a few pages earlier. P(2&radic;3,3&radic;3) = P(&radic;3sec(&pi;/3),&radic;3tan(&pi;/3)) &there4; P has parameter &pi;/3. Let Q have parameter &phi;. Now, from part a) of the question, tan(&theta;/2)tan(&phi;/2) = (1-e)/(1+e) or...
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    yet another conics question

    a) Keep trying with the distance formula. Play around with the b<sup>2</sup> = a<sup>2</sup>(e<sup>2</sup> - 1) and tan<sup>2</sup>@ + 1 = sec<sup>2</sup>@ identities and you'll get it eventually. b) No trouble once you've done a).
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    Droppin 4U

    Before you make any decision, I think you should wait to see what result you get and compare it with the people in your class. I remember feeling the same way you did during my first 4u test, but I ended up doing pretty well. Also, try and put things into perspective - it's not the end of...
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    Various qs on complex numbers

    Im(z) = y. Yeah, after looking at the question for a while, it's definitely a parabola.
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    Various qs on complex numbers

    Hmm, isn't |z - i| = [x<sup>2</sup> + (y-1)<sup>2</sup>]<sup>1/2</sup> ? Therefore x<sup>2</sup> + (y-1)<sup>2</sup> = y<sup>2</sup>, giving a parabola with vertex (0,1/2) and directrix x = 0. I may be wrong, can anyone confirm this at all? Thanks.
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    Akhenaton

    Hmm, it's a shame, our teacher is giving us so much information on Akhenaten recently. I know he's getting it all from books, so check your library.
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    [Prelim] Water topic

    For your first question, n(Na2CO3) = m / M = 5.3 / 106 = 0.05 c(Na2CO3) = n / V = 0.05 / 0.2 = 0.25 M
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    Extension courses for year 12? And what are you dropping?

    Hmm, I'm tossing up between dropping SDD or Physics. This time last year I would've thought that Physics would be one of my definite subjects but I'm really annoyed about the new course. I mean, why do we have to learn about electrical safety in the home and seatbelts?! SDD, on the other...
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    how do you remember the activity series?

    K Na Ca Mg Al Zn Fe Sn Pb Cu Ag Au I'll tell you how I remember this activity series, hopefully it helps... I say 'kanakamigal' to myself to remember the first 5 metals. Then 'ZFS' for the next 3. Finally, I know the order of the last 4 off by heart, not that hard to learn. Give...
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    Old School Games

    Skunny Kart, Cyberdogs, Fantasy Zone, Mega Man.
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