HSC 2012 MX2 Marathon (archive) (2 Viewers)

SpiralFlex

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Re: 2012 HSC MX2 Marathon

Graphically if you plot some points (or if you already know what the square root function looks like)

Then you can immediately tell the range/domain. Try it. :)
 

Fus Ro Dah

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Re: 2012 HSC MX2 Marathon

Did you mean 'Conjugate' instead of 'Congruent'?

A congruent number is an integer that is the area of the triangle with 3 rational sides.

A cool theorem related to this is "There does NOT exist a square number that is congruent". It is called Fermat's Right Triangle Theorem.
 

barbernator

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Re: 2012 HSC MX2 Marathon

to get the ball rolling again, <a href="http://www.codecogs.com/eqnedit.php?latex=\int \frac{2x^2@plus;13x@plus;16}{(2x@plus;1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int \frac{2x^2+13x+16}{(2x+1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" title="\int \frac{2x^2+13x+16}{(2x+1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" /></a>
 

Fus Ro Dah

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Re: 2012 HSC MX2 Marathon

to get the ball rolling again, <a href="http://www.codecogs.com/eqnedit.php?latex=\int \frac{2x^2@plus;13x@plus;16}{(2x@plus;1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int \frac{2x^2+13x+16}{(2x+1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" title="\int \frac{2x^2+13x+16}{(2x+1)^2(x-2)}~show~all~working.~This~definitely~tests~skill~in~partial~fractions" /></a>


Find the area between the curve and the x axis over the span
 

barbernator

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Re: 2012 HSC MX2 Marathon



Find the area between the curve and the x axis over the span
1 units squared. find the inverse function of <a href="http://www.codecogs.com/eqnedit.php?latex=y=2e^{2x} -14e^x @plus;6" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y=2e^{2x} -14e^x +6" title="y=2e^{2x} -14e^x +6" /></a> and state its new domain and range.
 
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barbernator

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Re: 2012 HSC MX2 Marathon

Would it be possible to see your working? :) I'm having trouble with the question.
integrate: (2x^2+13x+16)/((2x+1)^2(x-2))

put that statement into wolframalpha, and you will get a perfect solution
 
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Re: 2012 HSC MX2 Marathon

I just wolfram alphaed that...WTF LOL
 

seanieg89

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Re: 2012 HSC MX2 Marathon

I just wolfram alphaed that...WTF LOL
If you have trouble spotting any clever substitution to kill such integrals, always remember the brute-force methods. Partial fractions works fine here, as it does for the previous integral.
 

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