Recent content by mrbunton

1. 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. 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. 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. 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. 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. 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. 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. HSC 2018-2019 MX2 Integration Marathon

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

yup. b)iii) is the most difficult btw
11. difficult probability questions

both items and boxes are distinguishable
12. 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. 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. 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. 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...