4u Mathematics Marathon V 1.0 (1 Viewer)

[Estel]

but that wasn't much of a hint you gave. i thought hints were supposed to help ppl solve the problem?

It was more of a hint to stay away.

You have an interesting solution that doesn't really use circle properties.
I'm grateful that you posted that.

(IMHO the beautiful thing about these sorts of qs is that there's probably 20 different ways to do it)

 

[Stan..]

Q2
6xlnx + 2ln(x^2 + 1) - 7x - Arctanx
Using Hint.

EDIT: Sorry, Didn't see Estel's post.

 

[who_loves_maths]

Originally Posted by Estel
You have an interesting solution that doesn't really use circle properties.
I'm grateful that you posted that.

I too would be grateful should you post the solution that employs the elegance of the theory of circle geometry

 

[Estel]

AQB ||| AFQ and APC ||| AEP (equiangular)
So AP^2 = AE.AC = AB.AF (product of intercepts of secant from external point) = AQ^2

(Skipping all the various 'angle in a semicircle' steps...)

 

[who_loves_maths]

^ ah ic... pretty much the same as i did, except i spent a whole first page just getting to the equivalent of your use of the secant theorem

 

[icycloud]

he's probably finished the book. In my grade, the top 5 or so had finished 4u a while back.

Haha nar, I've taught myself bits here and there. I'm in the process of looking for a maths tutor so I can start learning things more formally . Oh and my school isn't starting 4U till next year... which is a bit of a disappointment, for me at least.

 

[pLuvia]

Wow self tutor, so good icycloud What topics have you self-tutored?

 

[skepticality]

Haha nar, I've taught myself bits here and there.

Wow self tutor, so good icycloud

its called 'chan coaching'

 

[pLuvia]

its called 'chan coaching'

err fill me in

 

[icycloud]

err fill me in

Haha don't worry about that, just some in-joke about the coaching college I might set up when I get to uni . Umm I've done a bit of everything basically - covered most of integration, complex, graphs... done some polynomials, mechanics and harder 3U - but not much of conics and volumes.

 

[Stan..]

Haha don't worry about that, just some in-joke about the coaching college I might set up when I get to uni . Umm I've done a bit of everything basically - covered most of integration, complex, graphs... done some polynomials, mechanics and harder 3U - but not much of conics and volumes.

Someone has big plans. Self Learning is good.

 

[pLuvia]

damn good work mate, you'll cruise through 4u this year Probably, going to do some self-tutoring in the holidays as well

 

[Riviet]

BUMP!
Let's get this thread up and running again.
Try and keep them to complex numbers since that's what most people are doing now.
Question- Find and describe the locus of:
__
(z³)+z³=0

 

[pLuvia]

Is the locus a straight line
Gradient = 1/root 3
Y-intercept = 0

 

[Riviet]

Don't forget to post up a question as you answer the previous one, go go go pLuvia.

 

[pLuvia]

One root of the equation z⁴ - 6z³ + 13z + k = 0, where k is real, is z = 2+i. Find the other roots and the value of k

Post more complex numbers questions, good practice for my upcoming test

 

[SeDaTeD]

I might have a go, I'm bored.
coefficients are real, therefore 2 -i is also a root. Let the other 2 roots be a and b
therefore (2+i) + (2-i) +a +b = 6 (sum of roots)
a+b = 2 => b = 2-a
(2+i)(2-i)ab = k (product of roots)
5ab = k
ab = k/5
a(2-a) = k/5
-a^2 + 2a = k/5
a^2 - 2a + 1 = -k/5 + 1
(a -1)^2 = -k/5 + 1
a - 1 = +/- sqrt(-k/5 + 1)
a = 1 +/- sqrt(-k/5 + 1)
therefore b is 2-a = 1 -/+ sqrt(-k/5 + 1)

now ab(2-i) + ab(2+i) + 5a + 5b = -13 (sum of prod of roots taken 3 at a time)
5a + 4ab + 5b = -13
5(a+b) + 4(k/5) = -13
10 + 4k/5 = -13
4k/5 = -23
k = -115/4
and sub that in a and b above

I'm pretty sure i made a mistake, perhaps plenty, oh well

Ok a question

integrate 1/(1+e^x) dx

 

[pLuvia]

err, lol k = -10

 

[SeDaTeD]

Hahahaha, knew i made a mistake when the thing turned out looking crazy. Perhaps i shouldve done the sum of products of 3 roots before i did products of roots.

 

[pLuvia]

I'll take a stab at that

integrate 1/(1+e^x) dx

[1/e^x][ln(1+e^x)]

is that right?