Maths Query

[Hobbiez]

Hi all,

 

How to prove the area of PQRS (rectangle) is 18x - 2x

[UncleWolve]

NOT AGAIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Megaweb]

> but curious to know why y = 9-x

 

Draw a virtual line from A to the center of B and C, mark it as D and across p and q as w

 

so AD = half of 18 = 9

 

AD = DC = 9

Aw = wq = half of 2x = x

 

therefore x + y = 9, thus y = 9 - x

[Chisiang]

18X - 2X

[Guyver]

  Quote

> but curious to know why y = 9-x

 

Draw a virtual line from A to the center of B and C, mark it as D and across p and q as w

 

so AD = half of 18 = 9

 

AD = DC = 9

Aw = wq = half of 2x = x

 

therefore x + y = 9, thus y = 9 - x

 

How come AD = DC = 9??

[Beei]

Are you a student asking how to do your maths homework?

[UncleWolve]

Hey while we are at it..i have a problem...hope any math major can help.

 

It's called the 3X + 1 problem.

 

Let f(x) be a function defined on the positive integers such that:

 

f(x) = x/2 if x is even

f(x) = (3*x+1)/2 if x is odd

 

Then the conjecture is: iterates of f(x) will eventually reach 1 for any

initial value of x.

 

Can you prove the conjecture?

[Hiphiphoray]

U sure he's a student.

 

He might be the tutor trying despartely to solve this problem for his student. Orelse kena fry cuttlefish!!!!!

[Hiphiphoray]

NOT AGAIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[UncleWolve]

[Karless]

Hobbiez:

 

U must first appreciate this is an isoceles triangle. Reason becos of the right angle triangle ABC with the rectangle pqrs embedded in it.

 

 

Since is it isoceles, drawing a straight vertical line down from A cutting BC (call it D) will give DC= 9.

 

Therefore rC= DC- Dr = 9-x

 

Since ABC is isoceles, angle ACB is 45 degree, therefore triangle qrC is oso isoceles. This will means rC = y = 9-x.

 

Rest u know liao.

 

 

UncleWolve:

I believe ur question is incomplete. There shld be some missing information like restriction to value of X.

Edited January 24, 2008 by Karless

[UncleWolve]

is it?

[Karless]

ya, will throw in some numbers to illustrate.

 

2/2 = 1

3/2= 1.5

4/2= 2

 

So how can iterate values bigger than 1 and expect them to converge to 1?

 

I used to like maths a lot but haven touch for long time. So i just try my best here. Hope to learn something new too.

[Mivec9]

Kudos Are you a lecturer or something

[Karless]

No la, I hate studying to become a lecturer man. Love to give tuition though and seriously given a thot to go teaching.

 

Anyway, purely like maths and cant believe this thread makes me create an acct(been reading the forum like half a yr).

[Mivec9]

that's why i'm curious to see a newbie here. i kw the usual folks will check in

[T_k_w]

my take. 1 look at the triangles without doing any calculations can see liao.

 

Triangle ABC is a right angle triangle, PQRS is a rectangle.

 

so angle Q is a right angle.

 

so if you analyse all the angles lying along AC, you notice, angle CQR is 45 degree.

 

Therefore, triangle CQR is a Right angle triangle so since the 2 sides are equal,

 

y = (18-2x)/2

y = 9-x

[T_k_w]

f(x) = x/2 if x is even,

 

rule 1: even number(>=2) divide by 2,will give you even number; eventually will reach 2/2=1

 

f(x) = (3*x+1)/2 if x is odd,

 

rule 2: odd(3) number * odd(x) number will always give you odd number.

 

rule 3: odd(3*x)number + 1 will always give you an even number, see rule number 1.

 

based on these 3 rules i can settle any positive integer >=2.

 

so we need to settle x=1.

 

f(1)=(3+1)/2=4(even, refer to rule 1.)