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1. Find the volume of the solid generated by rotating the region bounded by the curves y^2=x and y=x^2 about the line y=x. 2. Use the method of slicing to find the volume of the solid obtained by rotating the region enclosed within the circle (x-1)^2+y^2=1 about the y-axis.

Solve, x; tan^4 x - tan^3 x - 3tan^2 x + 3tan x = 0 for 0 ≤ x ≤ 360<!-- google_ad_section_end --></SPAN>

i)cosA=(b^2+c^2-a^2)/2bc cosA=(49+64-169)/(112) cosA=-1/2 Quadrant 1/ A=60 degrees Since cos is negative in Q II and III, Quadrant 2, A=120 degrees Quadrant 3, A=240 degrees (disregard due to angle orientation) Therefore A=120 degrees ii) A=(1/2)(56)sin120=28 x (rt3/2)=...

(x-h)^2=+-4a(y-k) [General form] Where V(h,k) S(h, k+-a) is still 2u material though. But yeah i agree about it should be considered as a "special case".

1 unit= 2hours/week of lessons. I thought it was the same for all schools?

you just include the coefficient of x in the denominator int (4x+3)^2 dx [(4x+3)^3]/ 4.3 + C (1/12)(4x+3)^3 + C

Hey sorry about the delay in reply. I definitely hope that you're right about that, i thought it would be very stupid aswell. I plan to have a big O-week lol I went to Murray High School, What about you?

Yay, UoM

Exactly! He didn't really specify anything so i thought i would just say what would be almost the best in terms of scaling. To Op, specify more about yourself and we can actually help you out.

-If you drink a moderate quantity of Grapejuice before you go, you get blind drunk off like 1-2 drinks. It's something to do with the Acids within grapejuice causes enzyme breakdown and therefore retaining alcohol...It works. This is a great money saving tool. - Expect to Step before you Walk...

Mathematics Extension 1, Physics, Chemistry, English Advanced, IPT and Business studies. Drop according in yr 12, pick up MX2. Simple.

Just have to use the formula i believe

Sourced in AoPS actually and it's cited now, i'm be more careful with citation of it in the future i guess, it's pretty obvious though

Very easy in comparison to other years, but that does not take anything away from your mark! All i can suggest is try some more papers, make sure you do 2000, 2003 and 2005 which are much more challenging papers imo. Goodluck with the HSC

umm.. i thought it was pretty clear that i asked them on AoPS. Consider the latex is from there, and has AoPS coding throughout the entire thing. Post edited to make it clear. Was merely trying to help the OP, since there were no solutions for sometime

4. Equality occurs when . Otherwise, note that so without loss of generality we can assume that . We cross multiply to get When we have We can prove that by induction on , noting that If , then by the lemma, so the desired inequality follows from induction...

3.Our base case is which is just which is true. ok so suppose that it is true for n=a-1. Now we want to prove that the statement is true for n=a. So we have our a numbers and it is true that by our induction hypothesis. We want to prove that Notice that both sides (especially...

2. For we have , therefore . Assume true up to . For , group and into one, so we can apply the induction hypothesis: . Unfortunately, is not guaranteed. So we need an idea. Well, since , there must be some and some . Redo all of the above with instead of . We reach that last...

http://www.artofproblemsolving.com/Wiki/index.php/Proofs_of_AM-GM

What book did you use then hero?