HSC 2012 MX1 Marathon #2 (archive) (1 Viewer)

barbernator

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Re: HSC 2012 Marathon :)

cmon guys!!! you havent got the answer yet
 

barbernator

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Re: HSC 2012 Marathon :)

PM me if u want a clue, or the answer to work towards
 

Nooblet94

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Re: HSC 2012 Marathon :)

Was my method correct at least?
 

nightweaver066

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9.8m?

I drew the diagram wrong the first time lol.
 

Nooblet94

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Re: HSC 2012 Marathon :)

Redid it and got 7.1... :s

Oops. typo - 7.3.
 

Timske

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Re: HSC 2012 Marathon :)

Nooblet Can you find y?

Untitled.jpg
 

Timske

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Re: HSC 2012 Marathon :)

Nice well done ,
 

barbernator

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Re: HSC 2012 Marathon :)

Nooblet Can you find y?

View attachment 25260
We can find y. Heres the method for working out. After showing similar triangles and that shit,

use the cos rule for the base triangle with angle 120 degrees. This will give us a relationship between alpha and beta. (the two unknown sides of that base triangle). But we also know that tan of theta and fie (the two angles of the vertical triangles) is 1.8/6.5 and 1.8/9.1 respectively.

We also know that h=(alpha+6.5)tan(theta)=(alpha+6.5)(1.8/6.5) AND h=(beta+9.1)(1.8/9.1) and we can equate these two to find alpha in terms of beta. Now sub this in to the cosine rule equation, and find the positive result for alpha. From this substitute back into the height equation to yield the result. Hey presto, all done.
 

RishBonjour

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Re: HSC 2012 Marathon :)

so the answer is 7.3?

thank god, its not 20 or something. (rounded off all my decimals from the equation to find y)

nice work prolet94
 

Timske

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Re: HSC 2012 Marathon :)

so close...another question barbs?
 

barbernator

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Re: HSC 2012 Marathon :)

Two of the roots of the equation x^3 + ax^2 + b = 0 are reciprocals of each other (a and b are real).
i) show that the third root is equal to -b
ii) show that a= b - 1/b
iii) show that the two roots, which are reciprocals, will be real if -0.5 < = b < = 1/2
 

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