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It's a shame we don't share any subjects except for english haha. I don't think posting it on a forum like this is the best place to look for one though. Just a word of curiosity, what school do you go to? ...If asking that isn't creepy.

Remember a majority of it especially important things like plots, characters, settings and themes, but make the theme in such a way that you can mould it for any situation

It's when you copy your girlfriend's answers in a test

Are you doing your HSC this year or next? "High School Graduation 2012" on your profile, so I'm going to assume...not this year?

Essentially they are the same thing but by theory, they are different. Amphoteric substances relate to having the same properties of acidic and basic oxides whilst amphoprotic relates to the Bronsted-Lowry's definition of an acid and whether they can both donate and accept protons.

^ Holy guacamole, it's mirror image ohexploitable

\text{The quadratic equation }x^2 - x + K = 0\text{ where K is a real number }\\\text{ has two distinct positive real roots, } \alpha \beta \\\\a)\text{ Show that }0<K<\frac{1}{4}\\\\b)\text{ Show that }\alpha^2 + \beta^2 = 1-2K\text{ and deduce that }\alpha^2 + \beta^2 > \frac{1}{2}\\\\c)\text{...

Oops, just beginning to latex, I tend to forget that y%20=%20ae^{bx}\\\frac{dy}{dx}=bae^{bx}\\\frac{d^2y}{d^2x}=b^2ae^{bx}\\\\%20\text{Since%20}%20y%20=%20ae^{bx}\\\frac%20{d^{2}y}{dx^{2}}%20=%20b^{2}y

Yeah god. Product rule on integration duh guys, duh. Hahahahaha

With Respect To

Very good

A DC motor uses a coil in a permanent magnetic field, a split ring commutator is used to reverse direction of current every half revolution, if you supply AC then you reverse direction of current 50 times a second. It won't spin and it won't work

y = ae^{bx}\\\frac{dy}{dx}=bae^{bx}\\\frac{d^2y}{d^2x}=b²ae^{bx}\\\\ \text{Since } y = ae^{bx}\\\frac {d^{2}y}{dx^{2}} = b^{2}y

^ cool story \\\\a)\text{ The polynomial } P(x) = ax^{n+1} + bx^n + 1\text{ is divisible by }(x-1)^2\\ \text{Show that }a = n \text{ and } b = -(1+n) \\\\b)\text{ Show that } P(x) = \frac{x^4}{4!} + \frac{x^3}{3!} + \frac{x^2}{2!} + x + 1\text{ has no double roots}

I typed on word LOL! my bad should be tan(x/2) not inverse

Using t-result substitution and partial fractions I get down to: 2 [int 1/(t²-t+1) dt - int 1/t² +1 dt] 2 [int dt/((t-1/2)² + 3/4)] - 2[int dt/(t²+1)] 2 [2/(√3)*tan-1 (t-1/2)/(√3/2) - tan-1 t] + C which is both unsimplified and illegible because I can't latex

They're the same thing, Imaginary numbers exist in their own plane but it's called the Argand diagram. It's a geometrical interpretation.

Teacher just updated us with the actual notification: Complex Numbers Curve Sketching Polynomials Volumes Integration Harder 3 Unit 2 Hours. Sigh.

Harder 3 Unit, Volumes, Integration, Polynomials and complex

No I completely agree with not dividing both sides, it's just the solutions say there's only 2..