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2u Mathematics Marathon v1.0 (1 Viewer)

ice ken

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SoulSearcher said:
Aruguing over the internet over who gets to post a maths question, come on people :eek: I kid :p
go ahead drynxz post rue question
 

drynxz

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lol ok then my turn!!



prove cot(A+B) = (cot A cot B - 1 ) / ( cot A + cot B)
*might have been typed up previously but too lazy to look through 500 posts -_-

EDIT : the text book has the answers wrong, so i edited the question.
 
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Riviet

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drynxz said:
*might have been typed up previously but too lazy to look through 500 posts -_-
From my memory, I don't recall a question like that. So no worries. ;)
 
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pLuvia

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Easy one ;)

int.secxdx

*Hint*
Multiply top and bottom by secx + tanx
 
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Riviet

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pLuvia said:
Easy one ;)

int.secxdx
I think a hint might be good as a 2 unit student wouldn't be able to spot this easily:
Multiply top and bottom by secx + tanx
 
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pLuvia

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Opps, I didn't think it was specifically for a 4u students. Anyway take Riviet's advice
 
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This?

5x+2y-10=0
m<sub>1</sub> = -A/B
m<sub>1</sub> = -5/2
Using m<sub>1</sub>m = -1,
-5/2m = -1
-5m = -2
m = 2/5

Therefor, gradient of line is 2/5
 

Riviet

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Yep, and pLuvia's question needs answering too. :)

P.S int. means "integral of".
 

DistantCube

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Int. sec x =
ln (sec x + tan x) + c

for reference; work the rest our yourselves.
 

SoulSearcher

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I might as well kill 2 birds with one stone. Got nothing else to do at the moment.
drynxz said:
prove cot(A+B) = (cot A cot B - 1 ) / ( cot A + cot B)
cot(A+B) = 1/tan(A+B)
= 1/{(tanA+tanB)/(1-tanAtanB)}
= (1-tanAtanB)/(tanA+tanB)
= {(cotAcotB-1)/(cotAcotB)}/{(cotA+cotB)/cotAcotB)}
= (cotAcotB-1)/(cotA+cotB)
pLuvia said:
int. sec x
int. sec x dx
= int. secx(secx+tanx)/(secx+tanx) dx

d/dx (secx + tanx) = secxtanx + sec2x
= secx(secx+tanx)

Therefore secx(secx+tanx)/(secx+tanx) = f'(x)/f(x), where f(x) = secx+tanx
Therefore int. secx(secx+tanx)/(secx+tanx) dx
= ln (secx+tanx) + C

I'll leave Mountain.Dew's question for someone else to do.
 

Riviet

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Another question:

Solve e4x - 4e2x + 4 = 0
 
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Sober

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Riviet said:
Another question:

Solve e4x - 4ex + 4 = 0
That is equivalent to solving y4 - 4y + 4 = 0 which is beyond the 2 or even 4 unit course. Also, I graphed it using graphing software and it even has no real solutions.
 
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Riviet

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Woops, that wasn't intended. :p I've fixed it up (now it's solvable).
 

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