HSC Mathematics Marathon (1 Viewer)

[ohexploitable]

Last year I started a Preliminary Maths Marathon which went for almost 40 pages until BoS died I might get a moderator to merge the threads when BoS is restored for a huge epic thread

Anyway, I found it was a great way to revise with other BoSers, rules are simple, answer a question then post a new one.

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[daesol]

Solution to above question:
Let the roots be @/r, @, @r (@ is alpha)
product of roots: @@@ = -d/a......................................(i) (where @@@ = @ cubed)
sum of roots 2 at a time: @@( 1/r + 1 + r) = c/a..............(ii)
sum of roots: @( 1/r + 1 + r) = -b/a...............................(iii)

(ii)/(iii): @@( 1/r + 1 + r)/@( 1/r + 1 + r) = (c/a) / (-b/a)
@ = -c/b

Sub into (i): @@@ = -ccc/bbb = -d/a
Rearranging, accc - bbbd = 0.

New question:
Integrate e^(sqrt x) w.r.t.x using a suitable substitution. [From SK Patel's Excel book]

ps. I need to learn latex xD

 

[jyu]

let u=e^(sqrt x), integrate e^(sqrt x) w.r.t.x =integrate 2lnu du = 2(u lnu - u) +c = 2e^(sqrt x)[sqrt x - 1] + c

hope it is right


Now pass on to you
Is there a cartesian equation for |z + i| + |z - i| = 1?

 

[jyu]

Now pass on to you
Is there a cartesian equation for |z + i| + |z - i| = 1?

 

[ohexploitable]

 

[jyu]

I don't think


Also what shape is it?

 

[deterministic]

Now pass on to you
Is there a cartesian equation for |z + i| + |z - i| = 1?

The answer is no, I'll let you figure out why not.

 

[jyu]

The answer is no, I'll let you figure out why not.

good answer, I'll let others to figure out why not.

 

[jyu]

Isn't that correct?

 

[Bored Of Fail 2]

thats not right

| a +bi| = sqrt ( a^2 +b^2)

 

[deterministic]

Isn't that correct?

 

[ohexploitable]

Silly me... stayed up until 4AM last night...

 

[deterministic]

Oh wait a sec...



There's no solution for z so the Cartesian equation doesn't exist?

z is complex so you cant do that
Think about what really means, and use a diagram to figure out the answer

 

[ohexploitable]

The smallest possible value of |z+i|+|z-1| is 2 (the straight line that joins them).

 

[Bored Of Fail 2]

very nice

 

[ohexploitable]

I really like that question.

 

[UnrealAnchovies]

Can we get some integration or conics questions going? :3

 

[Bored Of Fail 2]

integrate: 1/ [ x^(1/2) + x^(1/3) ] dx between limits [ 64 .. 1 ]

 

[Bored Of Fail 2]

lol^ thats a tough one, and if you really want you can just not bother about it evaluating it with the limits, because thats just boring calculator work.

If that is too hard heres an easier one, and one which is more likely to come up on the hsc paper

integrate : ( 4x^2-15x +29 ) / [ (x-5)(x^2-4x+13) ] dx

 

[deterministic]

Fully describe the locus of: