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I don't think Heron's rule is in the syllabus But nevertheless, it is still a quicker method of solving this question

Complex numbers Graphing Polynomials Integration - Finishing

Finding the recurrence formulae for those gets ridiculous But integrating sin x.cos x ain't a problem

Re: Integration =] This is pretty interesting. Should come in handy when I find some tricky integrals =) Nice find!

Question 2 (without using sum of roots) P(x) = 18x^3 + 3x^2 - 28x + 12 = 0 Since there is a double root, P(x) = P'(x) = 0 P'(x) = 54x^2 + 6x - 28 = 27x^2 + 3x - 14 = 0 (now use quadratic formula to find the zeroes of P'(x)) x = 2/3, -7/9 Therefore either 2/3 or -7/9 can be the double root...

24 cm There may be another easier method but this came up to my mind first

And you're only in Year 11 Oo? Well we just finished the 2U course; now we're doing Inverse Trigonometric Functions and later Further Applications of Calculus in the Physical World

Mm yea I thought so, I've never heard of matrices before. Isn't this in the wrong forum then?

LHS = x^3 + 3x + 2i RHS = (x - A)^2 . (x - B) = x^3 - (2A + B)x^2 + (A^2 + 2AB)x - A^2.B By equating the coefficients of x^2: 2A + B = 0 B = -2A Constant: -BA^2 = 2i -(-2A)A^2 = 2i A^3 = i A^3 = (-i^2)i [note: -i^2 = 1] A^3 = -i^3 A = -i Since B = -2A and A =...

Here's the working out if anyone else needs it: dV = 2 pi xy dx = 2 pi x(4x^2 - x^4) dx = 2 pi (4x^3 - x^5) dx V = 2 pi INT([2, 0] 4x^3 - x^5) = 2 pi [4x^4 / 4 - x^6][2, 0] = 2 pi [32 - 64/3] = 32 pi / 3

I want to help but I don't understand the notation of the conditions for the first question

In Year 11, you can bludge without feeling guilty In Year 12 however, you're gonna hate yourself if you screw up any assessments or go out too much. After all, Year 12 is the real thing and it's a competition across the state So the answer is no, Year 11 is not more stressful than Year 12

Re: blue or black pen? I go for blue because it's the standard, isn't it? Well it looks neater than the black anyway

Shit, I can't take this anymore. Reading this thread is gonna change my concept of maths :|

Yea our Software Design class is boring Reading from the textbook makes me sleepy

I was doing Advance last year but was dropped because the school wanted only the top 40 to do it. I was somewhere on the border line. I could've lodged an appeal to the Head Teacher about it but didn't bother. I half regret not doing Advance, knowing my English has significantly improved, but...

Ohh okay so I was on the right path all along Thanks

The arc of the curve y = cos x from x = 0 to x = pi / 2 is rotated about the y axis. Find the volume of the solid generated. Okay, so when the cos x is rotated about the y axis, it would form a solid similar to a bell. If I take a horizontal slice of it, the radius would be x units. Therefore...

Evaluate the integral of: sin x . cos x --------------- dx sin x + cos x One obvious method is using t-substitution but it doesn't seem to work out that easily. Are there any other working methods that can be used for this?

Mine is the novel We All Fall Down by Robert Cornier