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  1. A

    Chem HSC help

    the answer is A because citric acid is triprotic --> C3H5O(COOH)3 ---> 3H+ + C3H5O(COO)3 -3 if you were to write out neutralisation reactions for each of those 4 acids, you would see that because citric acid dissociates into 3 hydrogen ions, the mole ratio of NaOH to citric acid would be 3:1...
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    missing solutions for trig equation??

    it's probably best to avoid dividing by an unknown when solving an equation, but if you wanted to, i suppose you could test the solution sinx=0, and if it didn't work, then you could divide the whole equation by sinx
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    Integration with hyp trig

    also, if wolframalpha doesn't give you the answer you're looking for, you can also get it to differentiate your answer, and it should come up with the original function
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    mathematical induction Q help

    = (k/2) [2a+dk-d] + (1/2) [2a+2dk] = [(k+1)/2] [2a+dk-d+2a+2dk] that line was incorrect, you didn't actually factorise that properly (k/2)[2a+dk-d] + (1/2)[2a+2dk] = (1/2)[k(2a+dk-d)] + (1/2)[2a+2dk] = (1/2)[k(2a+dk-d) + 2a + 2dk] = (1/2)[2ak + dk^2 - dk + 2a + 2dk] = (1/2)[2ak + dk^2 +...
  5. A

    Cssa 04

    8. H2SO4 is a diprotic acid, so the concentration of hydrogen ions is twice the concentration of H2SO4 .'. [H+] = 2*[H2SO4] = 2*0.0115 =0.023 mol/L then using pH = -log[H+], pH = 1.638 which is closest to C 15. with this equilibrium, we can see that there are 4 moles of gas on the LHS...
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    Harder 3 unit question!

    (n+1)/2 >/ root(n*1) ((n-1)+2)/2 >/ root((n-1)*2) ---> (n+1)/2 >/ root(2*(n-1)) ((n-2)+3)/2 >/ root((n-2)*3) ---> (n+1)/2 >/ root(3*(n-2)) if we keep doing this, we should eventually get n/2 inequalities similar to those above multiplying them all together: [(n+1)^(n/2)]/2^(n/2) >/...
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    Maximisation Problem

    referring to the image, perimeter is P = 2r + 2h + r*pi for some constant P .'. 2h = P - 2r - r*pi area is 2rh + (pi*r^2)/2 = r(P - 2r - r*pi) + (pi*r^2)/2 = Pr - 2r^2 - (pi*r^2)/2 to find max area, we differentiate this expression: P - 4r - r*pi .'. max area when P - 4r - r*pi = 0 P = 4r...
  8. A

    conics help

    yeah, i felt that that would be the quickest way to answer OP's question. if there were more parts to it, like finding tangents with gradient 2, then i would've done it the same way as carrotsticks
  9. A

    HSC 2012 MX1 Marathon #2 (archive)

    Re: HSC 2012 Marathon :) i got -1/32 as well
  10. A

    conics help

    if tan theta = -4/5, then you know that theta is either pi - arctan(4/5) or 2pi - arctan(4/5) since tan is negative in the second and fourth quadrants from this you can work out the points where they touch the ellipse with the parametric equations x=5cos(theta) and y=4sin(theta), then use the...
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    Just curious...have anyone started doing trial past papers?

    i'll probably start doing trial papers in the holidays...still assignments and other assessment tasks left to do
  12. A

    Integration recurrence formula

    when you were finding the integral of cot^6(x), from the first line to the second, the negative sign should also be carried onto the integral of cot^2(x); two negatives make a positive. you should've had a bracket around -1/3*cot^2(x) - integral cot^2(x), since that whole expression is equal to...
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    H=mc(triangle)T

    isn't there meant to be a negative sign?
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    HSC 2012 MX1 Marathon #2 (archive)

    Re: HSC 2012 Marathon :) x = (u-3)^2 u-3 = rootx u = rootx + 3 dx/du = 2(u-3) dx = 2(u-3) du .'. integral of 1/(3+rootx) dx = integral (2(u-3))/(3+u-3) du = integral (2(u-3))/u du = integral (2 - 6/u) du = 2u - 6ln(u) = 2(rootx + 3) - 6ln(rootx + 3) + C
  15. A

    Please help - Equation of the Normal Q.

    dy/dx = sec^2(x) dy/dx (when x=pi/3) = sec^2(pi/3) = 4 .'. gradient of tangent at (pi/3, root3) is 4 .'. gradient of normal at this point is -1/4 using point gradient formula, y - root3 = -1/4(x-pi/3) 4y - 4root3 = -x + pi/3 x + 4y - (4root3 + pi/3) = 0
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    Similarity Proofs

    in triangles BFC, AFE, angle AFE is common angle FAE = 90 (angles of a rectangle are right angles) similarly, angle ABC = 90 .'. angle FBC = 180 - angle ABC (adjacent supplementary angles) = 90 .'. angle FBC = angle FAE .'. triangle BFC is similar to triangle AFE (equiangular) .'. angle...
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    How do you set out your maths book?

    i use the whole page, but i only write notes or the theory that we get in class, and i do maths questions on scrap pieces of paper which i throw out afterwards
  18. A

    Harder rates of change

    subbing the information into the equation you showed in b), 2 = 10(1-e^(-2*5*k)) 1/5 = 1 - e^(-10k) e^(-10k) = 4/5 -10k = ln(4/5) .'. k = -(ln(4/5))/10 when the difference in water level is 2cm, then 20-x - x = 2, since the level of the water in the compartment which initially had 20cm...
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    Environmental Sustainability Policies

    ah, alright. thanks for the clarification! :)
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    Environmental Sustainability Policies

    Hey everyone, I'm just wondering whether policies such as taxes on goods or services that are environmentally unsustainable or subsidies on more environmentally-friendly goods are microeconomic policies or macroeconomic policies. I'm thinking that they're microeconomic policies, but if so, what...
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