# 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...