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  1. M

    Interesting mathematical statements

    the expression: ( (i0*(1*(1%(((i0 + 1) / (i1 + 1))+1))*(1%(((i0 + 1) / (i2 + 1))+1))*(1%(((i0 + 1) / (i3 + 1))+1))*(1%(((i0 + 1) / (i4 + 1))+1)))) + (i1*(1*(1%(((i1 + 1) / (i0 + 1))+1))*(1%(((i1 + 1) / (i2 + 1))+1))*(1%(((i1 + 1) / (i3 + 1))+1))*(1%(((i1 + 1) / (i4 + 1))+1)))) + (i2*(1*(1%(((i2...
  2. M

    Mechanics (Pendulum) Question

    when a is max; cosa is minimum. a is max when it is right on the edge of the bowl; so height of ball is h; we take R-h to find the adjacent side of the triangle. hence R-h/R is equal to cosa at its minimum value
  3. M

    Mechanics (Pendulum) Question

    b) cot\alpha = \frac{g}{w^2r} (dividing the 2 equations from part a) =\frac{(R^2-r^2)^{0.5}}{r}=\frac{g}{w^2r} (from triangle formed by pendulum) remove r at bottom and divide by R to get answer c) cos a is between a certain region; where it is equal or less than 1 or greater or equal to...
  4. M

    how do you know if you have rank 1 for a subject?

    multiply weighting by mark(out of 100) for each btw; and add together, whoever has the highest score comes first: 96*15+89*25+88*20+91*40=9065 94*15+93*25+90*20+89*40=9095 that person came first im petty sure (if everything is correct); u guys are separated by a weighted average of 0.3%.
  5. M

    Study time?

    about 40% but i regret not studying more. It was worth doing anyway because i feel like it improved my cognitive abilities+ my favourite subject.
  6. M

    Polynomials question

    if two roots lie on unit circle and are reciprocal to each other: (using fan96's and integral95's progress) let x+iy denote one of these imaginary roots. 2x^2-2y^2+a^2+b^2=-3/4 if i didnt make any mistakes, from integral's working. anyway if the root is on unit circle than x^2+y^2=1; x^2=1-y^2 a...
  7. M

    HSC 2018-2019 MX2 Integration Marathon

    Re: HSC 2018 MX2 Integration Marathon correct but the two tan signs are generally said to cancel each other out; although i understand it can vary from +-1. that being said if u look at example at the integral tanx/|tanx| it is a horizontal line being split up into positive and negative in pi/2...
  8. M

    HSC 2018-2019 MX2 Integration Marathon

    Re: HSC 2018 MX2 Integration Marathon only requires u substitution. \int \frac{1}{\sqrt{x^2+x}}
  9. M

    difficult probability questions

    ya;if u do solve it using calculations it will be nearly impossible; unless it is through induction. I still believe its a step up from the probability usually done in highschool.
  10. M

    difficult probability questions

    yup. b)iii) is the most difficult btw
  11. M

    difficult probability questions

    both items and boxes are distinguishable
  12. M

    difficult probability questions

    a) i) there are 5 items to be placed inside 3 boxes. how many ways can this happen. each box can contain any amount of items. ii) if each box must contain at least one item; how many different ways are possible. b) i) There's 100 passengers and 100 seats in the airplane. The first...
  13. M

    Graphs

    making y the subject: y = (-x^3+1)^1/3 factor out x^3 =(x^3)^1/3 * (-1+1/x^3)^1/3 =x (-1+1/x^3)^1/3 as x becomes larger; the part with 1/x^3 becomes smaller and the graph of y=x (-1 + 1/x^3 )^1/3 gets closer and closer to the graph y=x(-1+0)^1/3 or y=-x. of course there will be no solutions but...
  14. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon ya rip me. i misinterpreted what z as a variable point meant. i thought it meant z could be anything and that the line was dependent on what z was; although that doesnt make much sense once you think about it.
  15. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon i) the line created is bx+ay=0.since you said i) is not the locus of z; and z can be truly anything; then we can observe that bx+ay=0 only yields to purely real values; so it becomes the line y=0 on the imaginary number plane ii) (x-p)^2+(y-q)^2= k^2 sub y=0 and...
  16. M

    complex locus

    for i) z-1/z^2 = a+0i, because arg is 0, therefore a number real. equate the imaginary part of the z-1/z^2 to 0 and get it into the form of a circle. for ii) i think it creates a straight line; so simultaneously solve the line and the circle to get the intended values. im too lazy to do it thou...
  17. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon derive equation to get turning points at -1 and 1 find y values of these turning points: (-1,2+k) and (1,k-2) since the poly is odd it will have at least one root. when k>2; both turning points are above the x-axis; so no extra roots are possible. proving that r<-1...
  18. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon rip the circle was meant to have radius 2; i changed it now so the circle touches -5 to -1. edit: i keep writing questions incorrectly; i check next time btw.
  19. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon 2^2*pi/2 = 2pi >6 therefore ii) is possible. remember it has radius 2 not 1 also u got the gradient of the second line for i) incorrect, getting the gradient wrong also affected the y-intercept. noticing k=5 was impressive although.
  20. M

    HSC 2018-2019 MX2 Marathon

    Re: HSC 2018 MX2 Marathon 2u integration+circle geo i made this question myself in paint so dont mind the bad production quality. edit: look for the question which has the circle with one edge on -5 instead of -3. ignore the question where the circle touches -3.
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