• Congratulations to the Class of 2024 on your results!
    Let us know how you went here
    Got a question about your uni preferences? Ask us here

HSC 2013 Maths Marathon (archive) (2 Viewers)

Status
Not open for further replies.
Sy123

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,730
Gender
Male
HSC
2013
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

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
 
B

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
 
girlworld_club

girlworld_club

Member
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.
 
B

Badsiii

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

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top