4u Mathematics Marathon V 1.0 (1 Viewer)

[vafa]

This is the solution to Yip's question first part:

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[Riviet]

Damn that inducton's alot of work. Care to finish off the rest of the question vafa?

 

[vafa]

If I had to do it for myself, it would take me about 5 minutes but because i was going to make everyone understand what i have done, then I did it in a simple way to make everyone understand the depth of the treatment. I do not know about yu but i never skip a question.

 

[vafa]

Damn that inducton's alot of work. Care to finish off the rest of the question vafa?

Yes, I would like to finish it and I am going to do it tommorrrow. If my mum finds out that I am still doing maths and not english, then I will be dead.

but I guess part b and c would be simpler to understand than the first part.

 

[BIRUNI]

Vafa, Can we please change our brains?

 

[zeek]

i got a different answer.....1/(26!)²

i'm not sure why you used 1/(26!)² im guessing you said that we should sort the lower case letters and then the upper case letters, right?
I said 52! because i considered each letter as an individual in one whole set rather than labelling them upper or lower case and then sorted them out

damn probability!

 

[vafa]

This is the solution to Yip's question part b:

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[onebytwo]

for the probability question, for all the possible arrangments of the lower case letters there are 26! and 26! for the upper case letters (so all together there are (26!)² ways)- for the letters to be in alphabetical order, there is only one way, so its 1/(26!)²

 

[onebytwo]

another question...
i found this challenging question in 3u cambridge in the extension section
find the equations of the four circles that are tangents to the line x+y-2=0 and the coordicate axes.

 

[bboyelement]

This is the solution to Yip's question part b:

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please do the last bit, i have been stuck on it for ages but no one has posted up solution

 

[zeek]

Well here's my diagram to get things started

 

[Yip]

find the equations of the four circles that are tangents to the line x+y-2=0 and the coordicate axes.

Equation of circle, to be tangent to coordinate axis is in the form (x+-a)^2+(y+-a)^2=a^2
Additionally, it must be tangent to the line y=-x+2, i.e upon solving simultaneously with the circle, u must have a discriminant of 0.
(Alternatively u can also use 2 applications of perpendicular distance formula, considering 2 separate cases for each application to get ur 4 points, which is faster in retrospect, reasoning being that the required point must have perpendicular distance a from the line)

the centers end up being -2+-sqrt2 and 2+-sqrt2, and the radius of each respective circle is equal to the square of its x/ycoordiinate

 

[vafa]

This is the proof of irrrationality of e.

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[Forbidden.]

Show that [(√3 + 1) + (√3 - 1)i]³ = 16(1 + i)

 

[beentherdunthat]

lol thats easyyy ^^^

 

[Forbidden.]

lol thats easyyy ^^^

Well I'm soreee, Miss Law student who doesn't have to do MATH1131 at UNSW.
Solve it then.

Spoiler

Apparently it uses the cubic expansion if I'm correct after working it out

 

[beentherdunthat]

lol its [a + b]^3

.... i'm so glad i don't have to do mathhh wehooo
i have nightmares from 4unit i done only like 3 or 4 topics and still managed a 90 god bless scaling

 

[Forbidden.]

lol its [a + b]^3

.... i'm so glad i don't have to do mathhh wehooo
i have nightmares from 4unit i done only like 3 or 4 topics and still managed a 90 god bless scaling

Lol you spoiled it looks like ill solve it myself when noone else solves it.
but hey im gonna face some 4u maths style nightmares myself :'(

 

[beentherdunthat]

awwwwwwww no don't worry it's not all that bad. Like complex is good. I don't know what the hell the last chapters were about but there was a whole of strings and forces :S :S ahhhh!

 

[Mark576]

[(√3 + 1) + (√3 - 1)i]3 = 16(1 + i)
LHS:
[(√3 + 1) + (√3 - 1)i]³
= (√3-i)³(1+i)³ (After taking a common factor)
= -8i(1+i)³
= -8i(-2+2i)
= 16(1+i)
= RHS

EDIT: Couldn't really bother putting the whole working out here, I'm just tired that's all.