HSC 2014 MX2 Marathon (archive) (1 Viewer)

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Trebla

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Sy123

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Re: HSC 2014 4U Marathon

 
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Parvee

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Re: HSC 2014 4U Marathon

 

braintic

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Re: HSC 2014 4U Marathon

Didn't ANYONE read OP's instruction?

"Once a question is posted, it needs to be answered before the next question is raised."
 

Sy123

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Re: HSC 2014 4U Marathon

fixed
 

Resource

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Re: HSC 2014 4U Marathon

Can I just ask what program you use to post maths questions/answers Sy123?
 

Sy123

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Re: HSC 2014 4U Marathon

Can I just ask what program you use to post maths questions/answers Sy123?
Its built into the site, its called LaTeX. To use it you use tags like [.tex] and [./tex] (without the dots). So

[.tex] \frac{5}{3} [./tex]

Becomes



To get a good grasp of the latex language, you can use the buttons here
And then copy paste the generated code into tex tags here.



Are you sure about k > 6?
I don't see anything wrong, and geogebra seems to say its correct.
 

Trebla

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Re: HSC 2014 4U Marathon

I don't see anything wrong, and geogebra seems to say its correct.
I'm assuming you're taking the general equation of the hyperbola as



If k > 6 then we cannot get this equation
 

Sy123

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Re: HSC 2014 4U Marathon

I'm assuming you're taking the general equation of the hyperbola as



If k > 6 then we cannot get this equation
Rather



Which are both hyperbola
 

hit patel

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Re: HSC 2014 4U Marathon

Let x= a^2sin^4 (theta) you get ln (sec theta)-(sin ^2(theta))/2. then use the right angle triangle to find x values and sub them in for theta. Dont know how to use latex sorry.
 

dunjaaa

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Re: HSC 2014 4U Marathon

Product of roots > 0 as c<0
Case #1: all 3 roots are real and positive (trivial case)
Case #2: 2 of the roots are a complex conjugate pair and the other being real and positive (assuming a,b,c are integer coefficients) Note* when you multiply a complex conjugate pair, it will always be positive "process of real-ising", hence the real root must be positive in order for this condition to be satisfied
 
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Sy123

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Re: HSC 2014 4U Marathon

Product of roots > 0 as c<0
Case #1: all 3 roots are real and positive (trivial case)
Case #2: 2 of the roots are a complex conjugate pair and the other being real and positive (assuming a,b,c are integer coefficients) Note* when you multiply a complex conjugate pair, it will always be positive "process of real-ising", hence the real root must be positive in order for this condition to be satisfied
But you can have 2 negative roots and 1 positive root resulting in the product of roots being positive, yet not all roots are positive.
 

dunjaaa

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Re: HSC 2014 4U Marathon

woops forgot about that haha
 

Axio

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Re: HSC 2014 4U Marathon

View attachment Q.pdf
The altitudes AP and BQ in an acute-angled triangle ABC meet at H. AP produced cuts the circle through A, B and C at K.
Prove that HP = PK.
 
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