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Re: 2012 HSC MX2 Marathon $P is any point on the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1~,~ (a > b); $ A, A' are the ends of the major axis; AP meets the minor axis at Q. Prove that the line through Q parallel to A'P is a tangent to one of the parabolas $ ay^2 \pm 4b^2x = 0.

Re: 2012 HSC MX2 Marathon Diagram: http://i.imgur.com/kEmRg.jpg h: xy = 32 Let~P(ct, \frac{c}{t})~be~a~point~on~h~where~c^2 = 32 $Differentiating both sides w.r.t. x x\frac{dy}{dx} + y = 0 \frac{dy}{dx} = \frac{-y}{x} = -\frac{1}{t^2}~at~P(ct, \frac{c}{t}) \therefore $ Equation of...

Burwood/Hurstville.

With 6, F = qvB and F = \frac{mv^2}{r} \therefore qvB = \frac{mv^2}{r} qB = \frac{mv}{r} r = \frac{mv}{qB} From observing this equation, increasing the magnetic field strength will decrease the radius where as increasing velocity of the charged particle will increase the radius. Therefore...

Since the pH increases by 1, the concentration of hydronium ions decreases by 10 fold meaning volume increases by 10 fold. So if it was initially 90mL, you want it to be 900mL, so you add 810mL of water.

Re: HSC 2012 Marathon :) You wrote xln(2), not x/ln(2). Edit: lol didn't see your 'correction'

Re: HSC 2012 Marathon :) = [(2^x)/ln2] limits 0 to 1 = 2/ln(2) - 1/ln(2) = 1/ln(2)

Make a new thread for your math questions lol. Realised i've solved it before: http://community.boredofstudies.org/showthread.php?t=281674&p=5827740#post5827740

That's why i had the "~". In 2009, 76 raw aligned to 87 exam mark. Doesn't matter anyway lol.. They're both pretty close..

You can do this. Lucky, Derek's an awesome teacher. :)

~80/100

2U students don't do polynomial division!

I suppose so, but it's better to understand them. E.g. For the first question, sin(270 - theta), i know that this would result in it's complementary angle as it's not starting from 180. The result will also be negative as it's in the 3rd quadrant so it would equal to -costheta. You can easily...

For question 8, you showed that two terms are equivalent to another. Notice how the RHS of that expression is very similar to the actual integral? You could divide both sides by two then integrate that expression. So, \frac{1}{2} \int \frac{1}{x - 1} - \frac{1}{x + 1}dx = \frac{1}{2} [ln|x -...

Wow thanks for scanning it! It's so clear too haha. I'll just give you some hints/tips. 7. Notice how the degree of the numerator is the same as the degree of the denominator. This means you can reduce it. E.g. for this, \frac{3x -5}{x + 1} = \frac{3x}{x + 1} - \frac{5}{x + 1} = \frac{3(x +...

Derek, Andrew or DJ

1. sin(270 - theta) = sin(180 + 90 - theta) = -sin(90 - theta) = -costheta 2. cos(90 + theta) = cos(180 - (90 - theta) ) = -cos(90 - theta) = -sintheta 3. tan(theta - 180) = tan(-(180 - theta)) = -tan(180 - theta) = tantheta

Wrong. +c

Ask your school. They're generally mid-term 3.

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