HSC 2013 Maths Marathon (archive) (3 Viewers)

Status
Not open for further replies.

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,730
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

It wouldn't have a limiting sum yeh ? Because |r| is not <1
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

Exaı̸̸̸̸̸̸̸̸lted Member
Joined
Jul 9, 2013
Messages
2,373
Gender
Male
HSC
2013
Re: HSC 2013 2U Marathon

no wonder you can't put the 0 in RHS
 

Badsiii

Member
Joined
Oct 19, 2013
Messages
33
Gender
Male
HSC
2013
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
 
Joined
Oct 29, 2011
Messages
872
Location
Narnia
Gender
Female
HSC
2013
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.
 

Badsiii

Member
Joined
Oct 19, 2013
Messages
33
Gender
Male
HSC
2013
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.
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) ?
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 3)

Top