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HSC 2013 Maths Marathon (archive) (1 Viewer)

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Sy123

Sy123

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Re: HSC 2013 2U Marathon

Badsiii said:
It wouldn't have a limiting sum yeh ? Because |r| is not <1
Click to expand...
Well cosx can be less than 1, for instance if x=pi/4

1 + cos(pi/4) + cos^2(pi/4) + ... has a limiting sum
 
Menomaths

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Re: HSC 2013 2U Marathon

no wonder you can't put the 0 in RHS
 
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Badsiii

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Re: HSC 2013 2U Marathon

The quadratic equation x^2 + Lx + M = 0 has one root twice the other

Prove that
M= 2L^2
.........9
 
girlworld_club

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Re: HSC 2013 2U Marathon

A sector of a circle with radius 5cm and an angle of pi/3 subtended at the centre is cut out of cardboard. It is then curved around to form a cone. Find its exact volume.
 
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Badsiii

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Re: HSC 2013 2U Marathon

girlworld_club said:
A sector of a circle with radius 5cm and an angle of pi/3 subtended at the centre is cut out of cardboard. It is then curved around to form a cone. Find its exact volume.
Click to expand...
Arc length= 5pi/3 = circumference of cone
Hence radius of cone= 5/6
Radius of sector= 5 = slant height of cone
Therefore height of cone, H^2= 5^2 - 25/36
h= root(875/36)
Volume cone= 1/3pi R^2 h
= 1/3 pi 25/36 x root(875/36) ?
 
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